id	sid	tid	token	lemma	pos
ejpam-7015	1	1	european	european	PROPN
ejpam-7015	1	2	journal	journal	PROPN
ejpam-7015	1	3	of	of	ADP
ejpam-7015	1	4	pure	pure	ADJ
ejpam-7015	1	5	and	and	CCONJ
ejpam-7015	1	6	applied	applied	ADJ
ejpam-7015	1	7	mathematics	mathematic	NOUN
ejpam-7015	1	8	2025	2025	NUM
ejpam-7015	1	9	,	,	PUNCT
ejpam-7015	1	10	vol	vol	NOUN
ejpam-7015	1	11	.	.	PROPN
ejpam-7015	1	12	18	18	NUM
ejpam-7015	1	13	,	,	PUNCT
ejpam-7015	1	14	issue	issue	NOUN
ejpam-7015	1	15	4	4	NUM
ejpam-7015	1	16	,	,	PUNCT
ejpam-7015	1	17	article	article	NOUN
ejpam-7015	1	18	number	number	NOUN
ejpam-7015	1	19	7015	7015	NUM
ejpam-7015	1	20	issn	issn	VERB
ejpam-7015	1	21	1307	1307	NUM
ejpam-7015	1	22	-	-	SYM
ejpam-7015	1	23	5543	5543	NUM
ejpam-7015	1	24	–	–	PUNCT
ejpam-7015	1	25	ejpam.com	ejpam.com	X
ejpam-7015	1	26	published	publish	VERB
ejpam-7015	1	27	by	by	ADP
ejpam-7015	1	28	new	new	PROPN
ejpam-7015	1	29	york	york	PROPN
ejpam-7015	1	30	business	business	PROPN
ejpam-7015	1	31	global	global	ADJ
ejpam-7015	1	32	algebraic	algebraic	ADJ
ejpam-7015	1	33	investigations	investigation	NOUN
ejpam-7015	1	34	on	on	ADP
ejpam-7015	1	35	anti	anti	ADJ
ejpam-7015	1	36	-	-	ADJ
ejpam-7015	1	37	fuzzy	fuzzy	ADJ
ejpam-7015	1	38	soft	soft	ADJ
ejpam-7015	1	39	boolean	boolean	ADJ
ejpam-7015	1	40	ring	ring	NOUN
ejpam-7015	1	41	theory	theory	NOUN
ejpam-7015	1	42	d.	d.	PROPN
ejpam-7015	1	43	ramesh1	ramesh1	PROPN
ejpam-7015	1	44	,	,	PUNCT
ejpam-7015	1	45	gadde	gadde	PROPN
ejpam-7015	1	46	sambasiva	sambasiva	PROPN
ejpam-7015	1	47	rao2	rao2	PROPN
ejpam-7015	1	48	,	,	PUNCT
ejpam-7015	1	49	aiyared	aiyare	VERB
ejpam-7015	1	50	iampan3,∗	iampan3,∗	NOUN
ejpam-7015	1	51	,	,	PUNCT
ejpam-7015	1	52	shake	shake	NOUN
ejpam-7015	1	53	baji4	baji4	NOUN
ejpam-7015	1	54	,	,	PUNCT
ejpam-7015	1	55	p.	p.	PROPN
ejpam-7015	1	56	rajani5	rajani5	NOUN
ejpam-7015	1	57	,	,	PUNCT
ejpam-7015	1	58	b.	b.	PROPN
ejpam-7015	1	59	satyanarayana6	satyanarayana6	PROPN
ejpam-7015	1	60	1	1	NUM
ejpam-7015	1	61	department	department	NOUN
ejpam-7015	1	62	of	of	ADP
ejpam-7015	1	63	engineering	engineering	NOUN
ejpam-7015	1	64	mathematics	mathematic	NOUN
ejpam-7015	1	65	,	,	PUNCT
ejpam-7015	1	66	college	college	NOUN
ejpam-7015	1	67	of	of	ADP
ejpam-7015	1	68	engineering	engineering	PROPN
ejpam-7015	1	69	,	,	PUNCT
ejpam-7015	1	70	koneru	koneru	PROPN
ejpam-7015	1	71	lakshmaiah	lakshmaiah	PROPN
ejpam-7015	1	72	educational	educational	ADJ
ejpam-7015	1	73	foundation	foundation	PROPN
ejpam-7015	1	74	,	,	PUNCT
ejpam-7015	1	75	vaddeswaram	vaddeswaram	PROPN
ejpam-7015	1	76	,	,	PUNCT
ejpam-7015	1	77	andhra	andhra	PROPN
ejpam-7015	1	78	pradesh-522302	pradesh-522302	NOUN
ejpam-7015	1	79	,	,	PUNCT
ejpam-7015	1	80	india	india	PROPN
ejpam-7015	1	81	2	2	NUM
ejpam-7015	1	82	department	department	NOUN
ejpam-7015	1	83	of	of	ADP
ejpam-7015	1	84	mathematics	mathematics	PROPN
ejpam-7015	1	85	,	,	PUNCT
ejpam-7015	1	86	sree	sree	PROPN
ejpam-7015	1	87	dattha	dattha	PROPN
ejpam-7015	1	88	group	group	PROPN
ejpam-7015	1	89	of	of	ADP
ejpam-7015	1	90	institutions	institution	NOUN
ejpam-7015	1	91	,	,	PUNCT
ejpam-7015	1	92	sheriguda	sheriguda	NOUN
ejpam-7015	1	93	,	,	PUNCT
ejpam-7015	1	94	ibrahimpatnam	ibrahimpatnam	PROPN
ejpam-7015	1	95	,	,	PUNCT
ejpam-7015	1	96	ranga	ranga	PROPN
ejpam-7015	1	97	reddy	reddy	PROPN
ejpam-7015	1	98	,	,	PUNCT
ejpam-7015	1	99	telangana-501510	telangana-501510	ADJ
ejpam-7015	1	100	,	,	PUNCT
ejpam-7015	1	101	india	india	PROPN
ejpam-7015	1	102	3	3	PROPN
ejpam-7015	1	103	department	department	NOUN
ejpam-7015	1	104	of	of	ADP
ejpam-7015	1	105	mathematics	mathematic	NOUN
ejpam-7015	1	106	,	,	PUNCT
ejpam-7015	1	107	school	school	NOUN
ejpam-7015	1	108	of	of	ADP
ejpam-7015	1	109	science	science	NOUN
ejpam-7015	1	110	,	,	PUNCT
ejpam-7015	1	111	university	university	NOUN
ejpam-7015	1	112	of	of	ADP
ejpam-7015	1	113	phayao	phayao	NOUN
ejpam-7015	1	114	,	,	PUNCT
ejpam-7015	1	115	mae	mae	PROPN
ejpam-7015	1	116	ka	ka	PROPN
ejpam-7015	1	117	,	,	PUNCT
ejpam-7015	1	118	mueang	mueang	PROPN
ejpam-7015	1	119	,	,	PUNCT
ejpam-7015	1	120	phayao	phayao	NOUN
ejpam-7015	1	121	56000	56000	NUM
ejpam-7015	1	122	,	,	PUNCT
ejpam-7015	1	123	thailand	thailand	PROPN
ejpam-7015	1	124	4	4	NUM
ejpam-7015	1	125	department	department	NOUN
ejpam-7015	1	126	of	of	ADP
ejpam-7015	1	127	mathematics	mathematic	NOUN
ejpam-7015	1	128	,	,	PUNCT
ejpam-7015	1	129	sir	sir	PROPN
ejpam-7015	1	130	c.r	c.r	PROPN
ejpam-7015	1	131	.	.	PROPN
ejpam-7015	1	132	reddy	reddy	PROPN
ejpam-7015	1	133	college	college	PROPN
ejpam-7015	1	134	of	of	ADP
ejpam-7015	1	135	engineering	engineering	PROPN
ejpam-7015	1	136	,	,	PUNCT
ejpam-7015	1	137	eluru	eluru	PROPN
ejpam-7015	1	138	,	,	PUNCT
ejpam-7015	1	139	andhra	andhra	PROPN
ejpam-7015	1	140	pradesh-534007	pradesh-534007	PROPN
ejpam-7015	1	141	,	,	PUNCT
ejpam-7015	1	142	india	india	PROPN
ejpam-7015	1	143	5	5	NUM
ejpam-7015	1	144	department	department	NOUN
ejpam-7015	1	145	of	of	ADP
ejpam-7015	1	146	basic	basic	ADJ
ejpam-7015	1	147	sciences	science	NOUN
ejpam-7015	1	148	and	and	CCONJ
ejpam-7015	1	149	humanities	humanity	NOUN
ejpam-7015	1	150	,	,	PUNCT
ejpam-7015	1	151	seshadri	seshadri	NOUN
ejpam-7015	1	152	rao	rao	PROPN
ejpam-7015	1	153	gudlavalleru	gudlavalleru	PROPN
ejpam-7015	1	154	engineering	engineering	PROPN
ejpam-7015	1	155	college	college	PROPN
ejpam-7015	1	156	,	,	PUNCT
ejpam-7015	1	157	seshadri	seshadri	NOUN
ejpam-7015	1	158	rao	rao	PROPN
ejpam-7015	1	159	knowledge	knowledge	NOUN
ejpam-7015	1	160	village	village	NOUN
ejpam-7015	1	161	,	,	PUNCT
ejpam-7015	1	162	gudlavalleru	gudlavalleru	PROPN
ejpam-7015	1	163	,	,	PUNCT
ejpam-7015	1	164	andhra	andhra	PROPN
ejpam-7015	1	165	pradesh-521356	pradesh-521356	NOUN
ejpam-7015	1	166	,	,	PUNCT
ejpam-7015	1	167	india	india	PROPN
ejpam-7015	1	168	6	6	NUM
ejpam-7015	1	169	department	department	NOUN
ejpam-7015	1	170	of	of	ADP
ejpam-7015	1	171	mathematics	mathematic	NOUN
ejpam-7015	1	172	,	,	PUNCT
ejpam-7015	1	173	acharya	acharya	PROPN
ejpam-7015	1	174	nagarjuna	nagarjuna	PROPN
ejpam-7015	1	175	university	university	PROPN
ejpam-7015	1	176	,	,	PUNCT
ejpam-7015	1	177	nagarjuna	nagarjuna	PROPN
ejpam-7015	1	178	nagar	nagar	PROPN
ejpam-7015	1	179	,	,	PUNCT
ejpam-7015	1	180	andhra	andhra	PROPN
ejpam-7015	1	181	pradesh-522510	pradesh-522510	PROPN
ejpam-7015	1	182	,	,	PUNCT
ejpam-7015	1	183	india	india	PROPN
ejpam-7015	1	184	abstract	abstract	NOUN
ejpam-7015	1	185	.	.	PUNCT
ejpam-7015	2	1	in	in	ADP
ejpam-7015	2	2	this	this	DET
ejpam-7015	2	3	paper	paper	NOUN
ejpam-7015	2	4	,	,	PUNCT
ejpam-7015	2	5	we	we	PRON
ejpam-7015	2	6	introduce	introduce	VERB
ejpam-7015	2	7	the	the	DET
ejpam-7015	2	8	concept	concept	NOUN
ejpam-7015	2	9	of	of	ADP
ejpam-7015	2	10	anti	anti	ADJ
ejpam-7015	2	11	-	-	ADJ
ejpam-7015	2	12	fuzzy	fuzzy	ADJ
ejpam-7015	2	13	soft	soft	ADJ
ejpam-7015	2	14	boolean	boolean	ADJ
ejpam-7015	2	15	rings	ring	NOUN
ejpam-7015	2	16	(	(	PUNCT
ejpam-7015	2	17	afsbrs	afsbrs	PROPN
ejpam-7015	2	18	)	)	PUNCT
ejpam-7015	2	19	,	,	PUNCT
ejpam-7015	2	20	which	which	PRON
ejpam-7015	2	21	serve	serve	VERB
ejpam-7015	2	22	as	as	ADP
ejpam-7015	2	23	a	a	DET
ejpam-7015	2	24	complementary	complementary	ADJ
ejpam-7015	2	25	extension	extension	NOUN
ejpam-7015	2	26	to	to	ADP
ejpam-7015	2	27	fuzzy	fuzzy	ADJ
ejpam-7015	2	28	soft	soft	ADJ
ejpam-7015	2	29	boolean	boolean	ADJ
ejpam-7015	2	30	rings	ring	NOUN
ejpam-7015	2	31	.	.	PUNCT
ejpam-7015	3	1	while	while	SCONJ
ejpam-7015	3	2	fuzzy	fuzzy	ADJ
ejpam-7015	3	3	soft	soft	ADJ
ejpam-7015	3	4	structures	structure	NOUN
ejpam-7015	3	5	have	have	AUX
ejpam-7015	3	6	proven	prove	VERB
ejpam-7015	3	7	effective	effective	ADJ
ejpam-7015	3	8	in	in	ADP
ejpam-7015	3	9	modeling	model	VERB
ejpam-7015	3	10	uncertainty	uncertainty	NOUN
ejpam-7015	3	11	through	through	ADP
ejpam-7015	3	12	degrees	degree	NOUN
ejpam-7015	3	13	of	of	ADP
ejpam-7015	3	14	membership	membership	NOUN
ejpam-7015	3	15	,	,	PUNCT
ejpam-7015	3	16	they	they	PRON
ejpam-7015	3	17	often	often	ADV
ejpam-7015	3	18	overlook	overlook	VERB
ejpam-7015	3	19	the	the	DET
ejpam-7015	3	20	critical	critical	ADJ
ejpam-7015	3	21	role	role	NOUN
ejpam-7015	3	22	of	of	ADP
ejpam-7015	3	23	non	non	ADJ
ejpam-7015	3	24	-	-	ADJ
ejpam-7015	3	25	membership	membership	NOUN
ejpam-7015	3	26	or	or	CCONJ
ejpam-7015	3	27	rejection	rejection	NOUN
ejpam-7015	3	28	—	—	PUNCT
ejpam-7015	3	29	an	an	DET
ejpam-7015	3	30	essential	essential	ADJ
ejpam-7015	3	31	aspect	aspect	NOUN
ejpam-7015	3	32	in	in	ADP
ejpam-7015	3	33	contexts	context	NOUN
ejpam-7015	3	34	involving	involve	VERB
ejpam-7015	3	35	contradictions	contradiction	NOUN
ejpam-7015	3	36	,	,	PUNCT
ejpam-7015	3	37	conflict	conflict	NOUN
ejpam-7015	3	38	resolution	resolution	NOUN
ejpam-7015	3	39	,	,	PUNCT
ejpam-7015	3	40	or	or	CCONJ
ejpam-7015	3	41	decision	decision	NOUN
ejpam-7015	3	42	-	-	PUNCT
ejpam-7015	3	43	making	making	NOUN
ejpam-7015	3	44	under	under	ADP
ejpam-7015	3	45	opposition	opposition	NOUN
ejpam-7015	3	46	.	.	PUNCT
ejpam-7015	4	1	motivated	motivate	VERB
ejpam-7015	4	2	by	by	ADP
ejpam-7015	4	3	this	this	DET
ejpam-7015	4	4	gap	gap	NOUN
ejpam-7015	4	5	,	,	PUNCT
ejpam-7015	4	6	the	the	DET
ejpam-7015	4	7	anti	anti	ADJ
ejpam-7015	4	8	-	-	ADJ
ejpam-7015	4	9	fuzzy	fuzzy	ADJ
ejpam-7015	4	10	soft	soft	ADJ
ejpam-7015	4	11	approach	approach	NOUN
ejpam-7015	4	12	emphasizes	emphasize	VERB
ejpam-7015	4	13	the	the	DET
ejpam-7015	4	14	non	non	ADJ
ejpam-7015	4	15	-	-	ADJ
ejpam-7015	4	16	membership	membership	ADJ
ejpam-7015	4	17	aspects	aspect	NOUN
ejpam-7015	4	18	of	of	ADP
ejpam-7015	4	19	elements	element	NOUN
ejpam-7015	4	20	under	under	ADP
ejpam-7015	4	21	uncertainty	uncertainty	NOUN
ejpam-7015	4	22	,	,	PUNCT
ejpam-7015	4	23	offering	offer	VERB
ejpam-7015	4	24	a	a	DET
ejpam-7015	4	25	dual	dual	ADJ
ejpam-7015	4	26	and	and	CCONJ
ejpam-7015	4	27	more	more	ADV
ejpam-7015	4	28	balanced	balanced	ADJ
ejpam-7015	4	29	perspective	perspective	NOUN
ejpam-7015	4	30	.	.	PUNCT
ejpam-7015	5	1	we	we	PRON
ejpam-7015	5	2	formally	formally	ADV
ejpam-7015	5	3	define	define	VERB
ejpam-7015	5	4	the	the	DET
ejpam-7015	5	5	structure	structure	NOUN
ejpam-7015	5	6	of	of	ADP
ejpam-7015	5	7	afsbrs	afsbrs	NOUN
ejpam-7015	5	8	,	,	PUNCT
ejpam-7015	5	9	present	present	ADJ
ejpam-7015	5	10	basic	basic	ADJ
ejpam-7015	5	11	operations	operation	NOUN
ejpam-7015	5	12	,	,	PUNCT
ejpam-7015	5	13	and	and	CCONJ
ejpam-7015	5	14	explore	explore	VERB
ejpam-7015	5	15	their	their	PRON
ejpam-7015	5	16	fundamental	fundamental	ADJ
ejpam-7015	5	17	properties	property	NOUN
ejpam-7015	5	18	through	through	ADP
ejpam-7015	5	19	illustrative	illustrative	ADJ
ejpam-7015	5	20	examples	example	NOUN
ejpam-7015	5	21	and	and	CCONJ
ejpam-7015	5	22	closure	closure	NOUN
ejpam-7015	5	23	theorems	theorem	NOUN
ejpam-7015	5	24	.	.	PUNCT
ejpam-7015	6	1	this	this	DET
ejpam-7015	6	2	study	study	NOUN
ejpam-7015	6	3	not	not	PART
ejpam-7015	6	4	only	only	ADV
ejpam-7015	6	5	deepens	deepen	VERB
ejpam-7015	6	6	the	the	DET
ejpam-7015	6	7	understanding	understanding	NOUN
ejpam-7015	6	8	of	of	ADP
ejpam-7015	6	9	fuzzy	fuzzy	ADJ
ejpam-7015	6	10	algebraic	algebraic	ADJ
ejpam-7015	6	11	systems	system	NOUN
ejpam-7015	6	12	but	but	CCONJ
ejpam-7015	6	13	also	also	ADV
ejpam-7015	6	14	provides	provide	VERB
ejpam-7015	6	15	a	a	DET
ejpam-7015	6	16	robust	robust	ADJ
ejpam-7015	6	17	algebraic	algebraic	ADJ
ejpam-7015	6	18	framework	framework	NOUN
ejpam-7015	6	19	for	for	ADP
ejpam-7015	6	20	modeling	model	VERB
ejpam-7015	6	21	negative	negative	ADJ
ejpam-7015	6	22	information	information	NOUN
ejpam-7015	6	23	in	in	ADP
ejpam-7015	6	24	areas	area	NOUN
ejpam-7015	6	25	such	such	ADJ
ejpam-7015	6	26	as	as	ADP
ejpam-7015	6	27	computational	computational	ADJ
ejpam-7015	6	28	logic	logic	NOUN
ejpam-7015	6	29	,	,	PUNCT
ejpam-7015	6	30	artificial	artificial	ADJ
ejpam-7015	6	31	intelligence	intelligence	NOUN
ejpam-7015	6	32	,	,	PUNCT
ejpam-7015	6	33	and	and	CCONJ
ejpam-7015	6	34	soft	soft	ADJ
ejpam-7015	6	35	computing	computing	NOUN
ejpam-7015	6	36	.	.	PUNCT
ejpam-7015	7	1	2020	2020	NUM
ejpam-7015	7	2	mathematics	mathematic	NOUN
ejpam-7015	7	3	subject	subject	NOUN
ejpam-7015	7	4	classifications	classification	NOUN
ejpam-7015	7	5	:	:	PUNCT
ejpam-7015	7	6	03e72	03e72	NUM
ejpam-7015	7	7	,	,	PUNCT
ejpam-7015	7	8	03g05	03g05	NUM
ejpam-7015	7	9	,	,	PUNCT
ejpam-7015	7	10	28a60	28a60	NUM
ejpam-7015	7	11	,	,	PUNCT
ejpam-7015	7	12	06d72	06d72	VERB
ejpam-7015	7	13	key	key	ADJ
ejpam-7015	7	14	words	word	NOUN
ejpam-7015	7	15	and	and	CCONJ
ejpam-7015	7	16	phrases	phrase	NOUN
ejpam-7015	7	17	:	:	PUNCT
ejpam-7015	7	18	boolean	boolean	ADJ
ejpam-7015	7	19	ring	ring	NOUN
ejpam-7015	7	20	,	,	PUNCT
ejpam-7015	7	21	fuzzy	fuzzy	ADJ
ejpam-7015	7	22	soft	soft	ADJ
ejpam-7015	7	23	set	set	NOUN
ejpam-7015	7	24	,	,	PUNCT
ejpam-7015	7	25	anti	anti	ADJ
ejpam-7015	7	26	-	-	ADJ
ejpam-7015	7	27	fuzzy	fuzzy	ADJ
ejpam-7015	7	28	soft	soft	ADJ
ejpam-7015	7	29	boolean	boolean	ADJ
ejpam-7015	7	30	ring	ring	NOUN
ejpam-7015	7	31	,	,	PUNCT
ejpam-7015	7	32	fuzzy	fuzzy	ADJ
ejpam-7015	7	33	soft	soft	ADJ
ejpam-7015	7	34	sub	sub	NOUN
ejpam-7015	7	35	boolean	boolean	ADJ
ejpam-7015	7	36	ring	ring	NOUN
ejpam-7015	7	37	,	,	PUNCT
ejpam-7015	7	38	fuzzy	fuzzy	ADJ
ejpam-7015	7	39	ideal	ideal	ADJ
ejpam-7015	7	40	,	,	PUNCT
ejpam-7015	7	41	fuzzy	fuzzy	ADJ
ejpam-7015	7	42	soft	soft	ADJ
ejpam-7015	7	43	ideal	ideal	ADJ
ejpam-7015	7	44	∗corresponding	∗corresponde	VERB
ejpam-7015	7	45	author	author	NOUN
ejpam-7015	7	46	.	.	PUNCT
ejpam-7015	8	1	doi	doi	NOUN
ejpam-7015	8	2	:	:	PUNCT
ejpam-7015	8	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7015	https://doi.org/10.29020/nybg.ejpam.v18i4.7015	NUM
ejpam-7015	8	4	email	email	NOUN
ejpam-7015	8	5	addresses	address	NOUN
ejpam-7015	8	6	:	:	PUNCT
ejpam-7015	8	7	ram.fuzzy@gmail.com	ram.fuzzy@gmail.com	PROPN
ejpam-7015	8	8	(	(	PUNCT
ejpam-7015	8	9	d.	d.	PROPN
ejpam-7015	8	10	ramesh	ramesh	PROPN
ejpam-7015	8	11	)	)	PUNCT
ejpam-7015	8	12	,	,	PUNCT
ejpam-7015	8	13	gaddesambasivarao1@gmail.com	gaddesambasivarao1@gmail.com	X
ejpam-7015	8	14	(	(	PUNCT
ejpam-7015	8	15	g.	g.	PROPN
ejpam-7015	8	16	s.	s.	PROPN
ejpam-7015	8	17	rao	rao	PROPN
ejpam-7015	8	18	)	)	PUNCT
ejpam-7015	8	19	,	,	PUNCT
ejpam-7015	8	20	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-7015	8	21	(	(	PUNCT
ejpam-7015	8	22	a.	a.	NOUN
ejpam-7015	8	23	iampan	iampan	PROPN
ejpam-7015	8	24	)	)	PUNCT
ejpam-7015	8	25	,	,	PUNCT
ejpam-7015	8	26	shakebaji6@gmail.com	shakebaji6@gmail.com	X
ejpam-7015	8	27	(	(	PUNCT
ejpam-7015	8	28	s.	s.	PROPN
ejpam-7015	8	29	baji	baji	PROPN
ejpam-7015	8	30	)	)	PUNCT
ejpam-7015	8	31	,	,	PUNCT
ejpam-7015	8	32	rajanipapers@gmail.com	rajanipapers@gmail.com	PROPN
ejpam-7015	8	33	(	(	PUNCT
ejpam-7015	8	34	p.	p.	PROPN
ejpam-7015	8	35	rajani	rajani	PROPN
ejpam-7015	8	36	)	)	PUNCT
ejpam-7015	8	37	,	,	PUNCT
ejpam-7015	8	38	drbsn63@yahoo.co.in	drbsn63@yahoo.co.in	NOUN
ejpam-7015	8	39	(	(	PUNCT
ejpam-7015	8	40	b.	b.	PROPN
ejpam-7015	8	41	satyanarayana	satyanarayana	PROPN
ejpam-7015	8	42	)	)	PUNCT
ejpam-7015	8	43	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7015	8	44	1	1	NUM
ejpam-7015	8	45	copyright	copyright	NOUN
ejpam-7015	8	46	:	:	PUNCT
ejpam-7015	9	1	©	©	PROPN
ejpam-7015	9	2	2025	2025	NUM
ejpam-7015	9	3	the	the	DET
ejpam-7015	9	4	author(s	author(s	NOUN
ejpam-7015	9	5	)	)	PUNCT
ejpam-7015	9	6	.	.	PUNCT
ejpam-7015	10	1	(	(	PUNCT
ejpam-7015	10	2	cc	cc	NOUN
ejpam-7015	10	3	by	by	ADP
ejpam-7015	10	4	-	-	PUNCT
ejpam-7015	10	5	nc	nc	PROPN
ejpam-7015	10	6	4.0	4.0	NUM
ejpam-7015	10	7	)	)	PUNCT
ejpam-7015	10	8	d.	d.	PROPN
ejpam-7015	10	9	ramesh	ramesh	PROPN
ejpam-7015	10	10	et	et	PROPN
ejpam-7015	10	11	al	al	PROPN
ejpam-7015	10	12	.	.	PUNCT
ejpam-7015	10	13	/	/	SYM
ejpam-7015	10	14	eur	eur	PROPN
ejpam-7015	10	15	.	.	PUNCT
ejpam-7015	11	1	j.	j.	PROPN
ejpam-7015	11	2	pure	pure	PROPN
ejpam-7015	11	3	appl	appl	PROPN
ejpam-7015	11	4	.	.	PROPN
ejpam-7015	11	5	math	math	PROPN
ejpam-7015	11	6	,	,	PUNCT
ejpam-7015	11	7	18	18	NUM
ejpam-7015	11	8	(	(	PUNCT
ejpam-7015	11	9	4	4	NUM
ejpam-7015	11	10	)	)	PUNCT
ejpam-7015	11	11	(	(	PUNCT
ejpam-7015	11	12	2025	2025	NUM
ejpam-7015	11	13	)	)	PUNCT
ejpam-7015	11	14	,	,	PUNCT
ejpam-7015	11	15	7015	7015	NUM
ejpam-7015	11	16	2	2	NUM
ejpam-7015	11	17	of	of	ADP
ejpam-7015	11	18	11	11	NUM
ejpam-7015	11	19	1	1	NUM
ejpam-7015	11	20	.	.	PUNCT
ejpam-7015	12	1	introduction	introduction	NOUN
ejpam-7015	12	2	zadeh	zadeh	NOUN
ejpam-7015	12	3	[	[	X
ejpam-7015	12	4	1	1	NUM
ejpam-7015	12	5	]	]	PUNCT
ejpam-7015	12	6	created	create	VERB
ejpam-7015	12	7	fuzzy	fuzzy	ADJ
ejpam-7015	12	8	set	set	NOUN
ejpam-7015	12	9	theory	theory	NOUN
ejpam-7015	12	10	in	in	ADP
ejpam-7015	12	11	1965	1965	NUM
ejpam-7015	12	12	as	as	ADP
ejpam-7015	12	13	a	a	DET
ejpam-7015	12	14	mathematical	mathematical	ADJ
ejpam-7015	12	15	approach	approach	NOUN
ejpam-7015	12	16	for	for	ADP
ejpam-7015	12	17	simulating	simulate	VERB
ejpam-7015	12	18	uncertainty	uncertainty	NOUN
ejpam-7015	12	19	and	and	CCONJ
ejpam-7015	12	20	ambiguity	ambiguity	NOUN
ejpam-7015	12	21	.	.	PUNCT
ejpam-7015	13	1	molodtsov	molodtsov	NOUN
ejpam-7015	14	1	[	[	X
ejpam-7015	14	2	2	2	NUM
ejpam-7015	14	3	]	]	PUNCT
ejpam-7015	14	4	later	later	ADV
ejpam-7015	14	5	introduced	introduce	VERB
ejpam-7015	14	6	the	the	DET
ejpam-7015	14	7	concept	concept	NOUN
ejpam-7015	14	8	of	of	ADP
ejpam-7015	14	9	soft	soft	ADJ
ejpam-7015	14	10	sets	set	NOUN
ejpam-7015	14	11	as	as	ADP
ejpam-7015	14	12	a	a	DET
ejpam-7015	14	13	general	general	ADJ
ejpam-7015	14	14	framework	framework	NOUN
ejpam-7015	14	15	for	for	ADP
ejpam-7015	14	16	handling	handle	VERB
ejpam-7015	14	17	parameterised	parameterise	VERB
ejpam-7015	14	18	uncertainties	uncertainty	NOUN
ejpam-7015	14	19	that	that	PRON
ejpam-7015	14	20	are	be	AUX
ejpam-7015	14	21	difficult	difficult	ADJ
ejpam-7015	14	22	to	to	PART
ejpam-7015	14	23	handle	handle	VERB
ejpam-7015	14	24	with	with	ADP
ejpam-7015	14	25	conventional	conventional	ADJ
ejpam-7015	14	26	techniques	technique	NOUN
ejpam-7015	14	27	.	.	PUNCT
ejpam-7015	15	1	these	these	DET
ejpam-7015	15	2	two	two	NUM
ejpam-7015	15	3	ideas	idea	NOUN
ejpam-7015	15	4	were	be	AUX
ejpam-7015	15	5	combined	combine	VERB
ejpam-7015	15	6	to	to	PART
ejpam-7015	15	7	generate	generate	VERB
ejpam-7015	15	8	fsss	fsss	NOUN
ejpam-7015	15	9	,	,	PUNCT
ejpam-7015	15	10	which	which	PRON
ejpam-7015	15	11	have	have	AUX
ejpam-7015	15	12	been	be	AUX
ejpam-7015	15	13	the	the	DET
ejpam-7015	15	14	focus	focus	NOUN
ejpam-7015	15	15	of	of	ADP
ejpam-7015	15	16	a	a	DET
ejpam-7015	15	17	lot	lot	NOUN
ejpam-7015	15	18	of	of	ADP
ejpam-7015	15	19	research	research	NOUN
ejpam-7015	15	20	due	due	ADP
ejpam-7015	15	21	to	to	ADP
ejpam-7015	15	22	their	their	PRON
ejpam-7015	15	23	many	many	ADJ
ejpam-7015	15	24	applications	application	NOUN
ejpam-7015	15	25	in	in	ADP
ejpam-7015	15	26	information	information	NOUN
ejpam-7015	15	27	systems	system	NOUN
ejpam-7015	15	28	,	,	PUNCT
ejpam-7015	15	29	decision	decision	NOUN
ejpam-7015	15	30	-	-	PUNCT
ejpam-7015	15	31	making	making	NOUN
ejpam-7015	15	32	,	,	PUNCT
ejpam-7015	15	33	and	and	CCONJ
ejpam-7015	15	34	algebraic	algebraic	ADJ
ejpam-7015	15	35	structures	structure	NOUN
ejpam-7015	15	36	.	.	PUNCT
ejpam-7015	16	1	soft	soft	ADJ
ejpam-7015	16	2	set	set	NOUN
ejpam-7015	16	3	theory	theory	NOUN
ejpam-7015	16	4	,	,	PUNCT
ejpam-7015	16	5	introduced	introduce	VERB
ejpam-7015	16	6	by	by	ADP
ejpam-7015	16	7	maji	maji	PROPN
ejpam-7015	16	8	et	et	PROPN
ejpam-7015	16	9	al	al	PROPN
ejpam-7015	16	10	.	.	PUNCT
ejpam-7015	17	1	[	[	X
ejpam-7015	17	2	3	3	NUM
ejpam-7015	17	3	,	,	PUNCT
ejpam-7015	17	4	4	4	NUM
ejpam-7015	17	5	]	]	PUNCT
ejpam-7015	17	6	,	,	PUNCT
ejpam-7015	17	7	established	establish	VERB
ejpam-7015	17	8	a	a	DET
ejpam-7015	17	9	flexible	flexible	ADJ
ejpam-7015	17	10	parameterized	parameterized	ADJ
ejpam-7015	17	11	framework	framework	NOUN
ejpam-7015	17	12	for	for	ADP
ejpam-7015	17	13	modeling	model	VERB
ejpam-7015	17	14	uncertainty	uncertainty	NOUN
ejpam-7015	17	15	,	,	PUNCT
ejpam-7015	17	16	later	later	ADV
ejpam-7015	17	17	expanded	expand	VERB
ejpam-7015	17	18	through	through	ADP
ejpam-7015	17	19	fuzzy	fuzzy	ADJ
ejpam-7015	17	20	soft	soft	ADJ
ejpam-7015	17	21	sets	set	NOUN
ejpam-7015	17	22	that	that	PRON
ejpam-7015	17	23	integrate	integrate	VERB
ejpam-7015	17	24	the	the	DET
ejpam-7015	17	25	vagueness	vagueness	NOUN
ejpam-7015	17	26	of	of	ADP
ejpam-7015	17	27	fuzzy	fuzzy	ADJ
ejpam-7015	17	28	sets	set	NOUN
ejpam-7015	17	29	with	with	ADP
ejpam-7015	17	30	the	the	DET
ejpam-7015	17	31	structural	structural	ADJ
ejpam-7015	17	32	adaptability	adaptability	NOUN
ejpam-7015	17	33	of	of	ADP
ejpam-7015	17	34	soft	soft	ADJ
ejpam-7015	17	35	sets	set	NOUN
ejpam-7015	17	36	.	.	PUNCT
ejpam-7015	18	1	earlier	early	ADJ
ejpam-7015	18	2	algebraic	algebraic	ADJ
ejpam-7015	18	3	generalizations	generalization	NOUN
ejpam-7015	18	4	,	,	PUNCT
ejpam-7015	18	5	such	such	ADJ
ejpam-7015	18	6	as	as	ADP
ejpam-7015	18	7	fuzzy	fuzzy	ADJ
ejpam-7015	18	8	rings	ring	NOUN
ejpam-7015	18	9	,	,	PUNCT
ejpam-7015	18	10	provided	provide	VERB
ejpam-7015	18	11	a	a	DET
ejpam-7015	18	12	foundation	foundation	NOUN
ejpam-7015	18	13	for	for	ADP
ejpam-7015	18	14	embedding	embed	VERB
ejpam-7015	18	15	fuzziness	fuzziness	NOUN
ejpam-7015	18	16	into	into	ADP
ejpam-7015	18	17	ring	ring	NOUN
ejpam-7015	18	18	theory	theory	NOUN
ejpam-7015	18	19	[	[	X
ejpam-7015	18	20	5	5	NUM
ejpam-7015	18	21	]	]	PUNCT
ejpam-7015	18	22	.	.	PUNCT
ejpam-7015	19	1	subsequent	subsequent	ADJ
ejpam-7015	19	2	works	work	NOUN
ejpam-7015	19	3	deepened	deepen	VERB
ejpam-7015	19	4	these	these	DET
ejpam-7015	19	5	connections	connection	NOUN
ejpam-7015	19	6	,	,	PUNCT
ejpam-7015	19	7	with	with	ADP
ejpam-7015	19	8	ahmat	ahmat	NOUN
ejpam-7015	19	9	and	and	CCONJ
ejpam-7015	19	10	kharal	kharal	ADJ
ejpam-7015	19	11	[	[	X
ejpam-7015	19	12	6	6	NUM
ejpam-7015	19	13	]	]	PUNCT
ejpam-7015	19	14	formalizing	formalizing	ADJ
ejpam-7015	19	15	fuzzy	fuzzy	ADJ
ejpam-7015	19	16	soft	soft	ADJ
ejpam-7015	19	17	sets	set	NOUN
ejpam-7015	19	18	and	and	CCONJ
ejpam-7015	19	19	acar	acar	VERB
ejpam-7015	19	20	et	et	PROPN
ejpam-7015	19	21	al	al	PROPN
ejpam-7015	19	22	.	.	PUNCT
ejpam-7015	20	1	[	[	X
ejpam-7015	20	2	7	7	X
ejpam-7015	20	3	]	]	PUNCT
ejpam-7015	20	4	introducing	introduce	VERB
ejpam-7015	20	5	soft	soft	ADJ
ejpam-7015	20	6	rings	ring	NOUN
ejpam-7015	20	7	as	as	ADP
ejpam-7015	20	8	a	a	DET
ejpam-7015	20	9	bridge	bridge	NOUN
ejpam-7015	20	10	to	to	ADP
ejpam-7015	20	11	algebraic	algebraic	ADJ
ejpam-7015	20	12	applications	application	NOUN
ejpam-7015	20	13	.	.	PUNCT
ejpam-7015	21	1	despite	despite	SCONJ
ejpam-7015	21	2	these	these	DET
ejpam-7015	21	3	advances	advance	NOUN
ejpam-7015	21	4	,	,	PUNCT
ejpam-7015	21	5	most	most	ADJ
ejpam-7015	21	6	studies	study	NOUN
ejpam-7015	21	7	focus	focus	VERB
ejpam-7015	21	8	on	on	ADP
ejpam-7015	21	9	membership	membership	NOUN
ejpam-7015	21	10	-	-	PUNCT
ejpam-7015	21	11	oriented	orient	VERB
ejpam-7015	21	12	information	information	NOUN
ejpam-7015	21	13	,	,	PUNCT
ejpam-7015	21	14	leaving	leave	VERB
ejpam-7015	21	15	limited	limited	ADJ
ejpam-7015	21	16	attention	attention	NOUN
ejpam-7015	21	17	to	to	ADP
ejpam-7015	21	18	the	the	DET
ejpam-7015	21	19	complementary	complementary	ADJ
ejpam-7015	21	20	notion	notion	NOUN
ejpam-7015	21	21	of	of	ADP
ejpam-7015	21	22	non	non	ADJ
ejpam-7015	21	23	-	-	ADJ
ejpam-7015	21	24	membership	membership	NOUN
ejpam-7015	21	25	or	or	CCONJ
ejpam-7015	21	26	opposition	opposition	NOUN
ejpam-7015	21	27	—	—	PUNCT
ejpam-7015	21	28	an	an	DET
ejpam-7015	21	29	essential	essential	ADJ
ejpam-7015	21	30	perspective	perspective	NOUN
ejpam-7015	21	31	for	for	ADP
ejpam-7015	21	32	modeling	model	VERB
ejpam-7015	21	33	contradictions	contradiction	NOUN
ejpam-7015	21	34	.	.	PUNCT
ejpam-7015	22	1	this	this	DET
ejpam-7015	22	2	gap	gap	NOUN
ejpam-7015	22	3	motivates	motivate	VERB
ejpam-7015	22	4	the	the	DET
ejpam-7015	22	5	study	study	NOUN
ejpam-7015	22	6	of	of	ADP
ejpam-7015	22	7	anti	anti	ADJ
ejpam-7015	22	8	-	-	ADJ
ejpam-7015	22	9	fuzzy	fuzzy	ADJ
ejpam-7015	22	10	soft	soft	ADJ
ejpam-7015	22	11	boolean	boolean	ADJ
ejpam-7015	22	12	rings	ring	NOUN
ejpam-7015	22	13	as	as	ADP
ejpam-7015	22	14	a	a	DET
ejpam-7015	22	15	natural	natural	ADJ
ejpam-7015	22	16	extension	extension	NOUN
ejpam-7015	22	17	of	of	ADP
ejpam-7015	22	18	fuzzy	fuzzy	ADJ
ejpam-7015	22	19	soft	soft	ADJ
ejpam-7015	22	20	algebraic	algebraic	ADJ
ejpam-7015	22	21	systems	system	NOUN
ejpam-7015	22	22	.	.	PUNCT
ejpam-7015	23	1	additional	additional	ADJ
ejpam-7015	23	2	developments	development	NOUN
ejpam-7015	23	3	include	include	VERB
ejpam-7015	23	4	the	the	DET
ejpam-7015	23	5	study	study	NOUN
ejpam-7015	23	6	of	of	ADP
ejpam-7015	23	7	anti	anti	ADJ
ejpam-7015	23	8	-	-	ADJ
ejpam-7015	23	9	fuzzy	fuzzy	ADJ
ejpam-7015	23	10	h	h	NOUN
ejpam-7015	23	11	-	-	PUNCT
ejpam-7015	23	12	ideals	ideal	NOUN
ejpam-7015	23	13	in	in	ADP
ejpam-7015	23	14	hemirings	hemiring	NOUN
ejpam-7015	23	15	by	by	ADP
ejpam-7015	23	16	akram	akram	PROPN
ejpam-7015	23	17	and	and	CCONJ
ejpam-7015	23	18	dar	dar	NOUN
ejpam-7015	24	1	[	[	X
ejpam-7015	24	2	8	8	NUM
ejpam-7015	24	3	]	]	PUNCT
ejpam-7015	24	4	,	,	PUNCT
ejpam-7015	24	5	the	the	DET
ejpam-7015	24	6	study	study	NOUN
ejpam-7015	24	7	of	of	ADP
ejpam-7015	24	8	anti	anti	ADJ
ejpam-7015	24	9	-	-	ADJ
ejpam-7015	24	10	fuzzy	fuzzy	ADJ
ejpam-7015	24	11	ideals	ideal	NOUN
ejpam-7015	24	12	of	of	ADP
ejpam-7015	24	13	bck	bck	NOUN
ejpam-7015	24	14	-	-	PUNCT
ejpam-7015	24	15	algebras	algebras	PROPN
ejpam-7015	24	16	by	by	ADP
ejpam-7015	24	17	hong	hong	PROPN
ejpam-7015	24	18	and	and	CCONJ
ejpam-7015	24	19	jun	jun	PROPN
ejpam-7015	25	1	[	[	X
ejpam-7015	25	2	9	9	NUM
ejpam-7015	25	3	]	]	PUNCT
ejpam-7015	25	4	,	,	PUNCT
ejpam-7015	25	5	and	and	CCONJ
ejpam-7015	25	6	other	other	ADJ
ejpam-7015	25	7	extensions	extension	NOUN
ejpam-7015	25	8	of	of	ADP
ejpam-7015	25	9	fuzzy	fuzzy	ADJ
ejpam-7015	25	10	ideals	ideal	NOUN
ejpam-7015	25	11	and	and	CCONJ
ejpam-7015	25	12	anti	anti	ADJ
ejpam-7015	25	13	-	-	ADJ
ejpam-7015	25	14	fuzzy	fuzzy	ADJ
ejpam-7015	25	15	ideals	ideal	NOUN
ejpam-7015	25	16	in	in	ADP
ejpam-7015	25	17	ordered	order	VERB
ejpam-7015	25	18	semigroups	semigroup	NOUN
ejpam-7015	25	19	,	,	PUNCT
ejpam-7015	25	20	γsemirings	γsemiring	NOUN
ejpam-7015	25	21	,	,	PUNCT
ejpam-7015	25	22	and	and	CCONJ
ejpam-7015	25	23	related	relate	VERB
ejpam-7015	25	24	algebraic	algebraic	ADJ
ejpam-7015	25	25	structures	structure	NOUN
ejpam-7015	25	26	.	.	PUNCT
ejpam-7015	26	1	these	these	DET
ejpam-7015	26	2	works	work	NOUN
ejpam-7015	26	3	illustrate	illustrate	VERB
ejpam-7015	26	4	the	the	DET
ejpam-7015	26	5	growing	grow	VERB
ejpam-7015	26	6	importance	importance	NOUN
ejpam-7015	26	7	of	of	ADP
ejpam-7015	26	8	anti	anti	ADJ
ejpam-7015	26	9	-	-	ADJ
ejpam-7015	26	10	fuzzy	fuzzy	ADJ
ejpam-7015	26	11	ideas	idea	NOUN
ejpam-7015	26	12	,	,	PUNCT
ejpam-7015	26	13	which	which	PRON
ejpam-7015	26	14	provide	provide	VERB
ejpam-7015	26	15	an	an	DET
ejpam-7015	26	16	opposite	opposite	ADJ
ejpam-7015	26	17	perspective	perspective	NOUN
ejpam-7015	26	18	by	by	ADP
ejpam-7015	26	19	representing	represent	VERB
ejpam-7015	26	20	non	non	ADJ
ejpam-7015	26	21	-	-	ADJ
ejpam-7015	26	22	membership	membership	NOUN
ejpam-7015	26	23	or	or	CCONJ
ejpam-7015	26	24	opposing	oppose	VERB
ejpam-7015	26	25	information	information	NOUN
ejpam-7015	26	26	.	.	PUNCT
ejpam-7015	27	1	soft	soft	ADJ
ejpam-7015	27	2	set	set	NOUN
ejpam-7015	27	3	theory	theory	NOUN
ejpam-7015	27	4	has	have	AUX
ejpam-7015	27	5	also	also	ADV
ejpam-7015	27	6	been	be	AUX
ejpam-7015	27	7	successfully	successfully	ADV
ejpam-7015	27	8	applied	apply	VERB
ejpam-7015	27	9	to	to	ADP
ejpam-7015	27	10	a	a	DET
ejpam-7015	27	11	variety	variety	NOUN
ejpam-7015	27	12	of	of	ADP
ejpam-7015	27	13	uncertainty	uncertainty	NOUN
ejpam-7015	27	14	models	model	NOUN
ejpam-7015	27	15	,	,	PUNCT
ejpam-7015	27	16	such	such	ADJ
ejpam-7015	27	17	as	as	ADP
ejpam-7015	27	18	intuitionistic	intuitionistic	ADJ
ejpam-7015	27	19	fuzzy	fuzzy	ADJ
ejpam-7015	27	20	sets	set	NOUN
ejpam-7015	27	21	,	,	PUNCT
ejpam-7015	27	22	neutrosophic	neutrosophic	ADJ
ejpam-7015	27	23	sets	set	NOUN
ejpam-7015	27	24	,	,	PUNCT
ejpam-7015	27	25	and	and	CCONJ
ejpam-7015	27	26	bipolar	bipolar	ADJ
ejpam-7015	27	27	fuzzy	fuzzy	ADJ
ejpam-7015	27	28	sets	set	NOUN
ejpam-7015	27	29	,	,	PUNCT
ejpam-7015	27	30	leading	lead	VERB
ejpam-7015	27	31	to	to	ADP
ejpam-7015	27	32	the	the	DET
ejpam-7015	27	33	development	development	NOUN
ejpam-7015	27	34	of	of	ADP
ejpam-7015	27	35	intuitionistic	intuitionistic	ADJ
ejpam-7015	27	36	fuzzy	fuzzy	ADJ
ejpam-7015	27	37	soft	soft	ADJ
ejpam-7015	27	38	sets	set	NOUN
ejpam-7015	27	39	,	,	PUNCT
ejpam-7015	27	40	neutrosophic	neutrosophic	ADJ
ejpam-7015	27	41	soft	soft	ADJ
ejpam-7015	27	42	sets	set	NOUN
ejpam-7015	27	43	,	,	PUNCT
ejpam-7015	27	44	and	and	CCONJ
ejpam-7015	27	45	bipolar	bipolar	ADJ
ejpam-7015	27	46	fuzzy	fuzzy	ADJ
ejpam-7015	27	47	soft	soft	ADJ
ejpam-7015	27	48	sets	set	NOUN
ejpam-7015	27	49	,	,	PUNCT
ejpam-7015	27	50	respectively	respectively	ADV
ejpam-7015	27	51	.	.	PUNCT
ejpam-7015	28	1	these	these	DET
ejpam-7015	28	2	hybrid	hybrid	NOUN
ejpam-7015	28	3	models	model	NOUN
ejpam-7015	28	4	have	have	AUX
ejpam-7015	28	5	improved	improve	VERB
ejpam-7015	28	6	the	the	DET
ejpam-7015	28	7	theoretical	theoretical	ADJ
ejpam-7015	28	8	and	and	CCONJ
ejpam-7015	28	9	practical	practical	ADJ
ejpam-7015	28	10	aspects	aspect	NOUN
ejpam-7015	28	11	of	of	ADP
ejpam-7015	28	12	uncertainty	uncertainty	NOUN
ejpam-7015	28	13	modeling	modeling	NOUN
ejpam-7015	28	14	.	.	PUNCT
ejpam-7015	29	1	however	however	ADV
ejpam-7015	29	2	,	,	PUNCT
ejpam-7015	29	3	the	the	DET
ejpam-7015	29	4	related	related	ADJ
ejpam-7015	29	5	notion	notion	NOUN
ejpam-7015	29	6	of	of	ADP
ejpam-7015	29	7	fuzziness	fuzziness	NOUN
ejpam-7015	29	8	in	in	ADP
ejpam-7015	29	9	the	the	DET
ejpam-7015	29	10	soft	soft	ADJ
ejpam-7015	29	11	set	set	VERB
ejpam-7015	29	12	framework	framework	NOUN
ejpam-7015	29	13	,	,	PUNCT
ejpam-7015	29	14	anti	anti	ADJ
ejpam-7015	29	15	-	-	ADJ
ejpam-7015	29	16	fuzzy	fuzzy	ADJ
ejpam-7015	29	17	soft	soft	ADJ
ejpam-7015	29	18	sets	set	NOUN
ejpam-7015	29	19	,	,	PUNCT
ejpam-7015	29	20	has	have	AUX
ejpam-7015	29	21	not	not	PART
ejpam-7015	29	22	received	receive	VERB
ejpam-7015	29	23	much	much	ADJ
ejpam-7015	29	24	attention	attention	NOUN
ejpam-7015	29	25	.	.	PUNCT
ejpam-7015	30	1	rao	rao	NOUN
ejpam-7015	30	2	et	et	PROPN
ejpam-7015	30	3	al	al	PROPN
ejpam-7015	30	4	.	.	PROPN
ejpam-7015	30	5	have	have	AUX
ejpam-7015	30	6	made	make	VERB
ejpam-7015	30	7	more	more	ADJ
ejpam-7015	30	8	contributions	contribution	NOUN
ejpam-7015	30	9	in	in	ADP
ejpam-7015	30	10	this	this	DET
ejpam-7015	30	11	field	field	NOUN
ejpam-7015	30	12	by	by	ADP
ejpam-7015	30	13	analysing	analyse	VERB
ejpam-7015	30	14	soft	soft	ADJ
ejpam-7015	30	15	boolean	boolean	ADJ
ejpam-7015	30	16	nearrings	nearring	NOUN
ejpam-7015	30	17	[	[	X
ejpam-7015	30	18	10	10	NUM
ejpam-7015	30	19	]	]	PUNCT
ejpam-7015	30	20	,	,	PUNCT
ejpam-7015	30	21	introducing	introduce	VERB
ejpam-7015	30	22	fuzzy	fuzzy	ADJ
ejpam-7015	30	23	soft	soft	ADJ
ejpam-7015	30	24	boolean	boolean	ADJ
ejpam-7015	30	25	rings	ring	NOUN
ejpam-7015	30	26	[	[	X
ejpam-7015	30	27	11	11	NUM
ejpam-7015	30	28	]	]	PUNCT
ejpam-7015	30	29	,	,	PUNCT
ejpam-7015	30	30	and	and	CCONJ
ejpam-7015	30	31	investigating	investigate	VERB
ejpam-7015	30	32	the	the	DET
ejpam-7015	30	33	structure	structure	NOUN
ejpam-7015	30	34	of	of	ADP
ejpam-7015	30	35	soft	soft	ADJ
ejpam-7015	30	36	intersection	intersection	NOUN
ejpam-7015	30	37	boolean	boolean	ADJ
ejpam-7015	30	38	near	near	ADJ
ejpam-7015	30	39	-	-	PUNCT
ejpam-7015	30	40	rings	ring	NOUN
ejpam-7015	30	41	[	[	X
ejpam-7015	30	42	12	12	NUM
ejpam-7015	30	43	]	]	PUNCT
ejpam-7015	30	44	.	.	PUNCT
ejpam-7015	31	1	as	as	ADP
ejpam-7015	31	2	an	an	DET
ejpam-7015	31	3	extension	extension	NOUN
ejpam-7015	31	4	of	of	ADP
ejpam-7015	31	5	fuzzy	fuzzy	ADJ
ejpam-7015	31	6	soft	soft	ADJ
ejpam-7015	31	7	algebraic	algebraic	ADJ
ejpam-7015	31	8	structures	structure	NOUN
ejpam-7015	31	9	,	,	PUNCT
ejpam-7015	31	10	they	they	PRON
ejpam-7015	31	11	introduced	introduce	VERB
ejpam-7015	31	12	(	(	PUNCT
ejpam-7015	31	13	∈,∈	∈,∈	X
ejpam-7015	31	14	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-7015	31	15	soft	soft	ADJ
ejpam-7015	31	16	boolean	boolean	ADJ
ejpam-7015	31	17	near	near	ADJ
ejpam-7015	31	18	-	-	PUNCT
ejpam-7015	31	19	rings	ring	NOUN
ejpam-7015	31	20	[	[	X
ejpam-7015	31	21	13	13	NUM
ejpam-7015	31	22	]	]	PUNCT
ejpam-7015	31	23	and	and	CCONJ
ejpam-7015	31	24	developed	develop	VERB
ejpam-7015	31	25	fuzzy	fuzzy	ADJ
ejpam-7015	31	26	soft	soft	ADJ
ejpam-7015	31	27	boolean	boolean	ADJ
ejpam-7015	31	28	near	near	ADJ
ejpam-7015	31	29	-	-	PUNCT
ejpam-7015	31	30	rings	ring	NOUN
ejpam-7015	31	31	[	[	X
ejpam-7015	31	32	14	14	NUM
ejpam-7015	31	33	]	]	PUNCT
ejpam-7015	31	34	with	with	ADP
ejpam-7015	31	35	their	their	PRON
ejpam-7015	31	36	idealistic	idealistic	ADJ
ejpam-7015	31	37	versions	version	NOUN
ejpam-7015	31	38	to	to	PART
ejpam-7015	31	39	improve	improve	VERB
ejpam-7015	31	40	the	the	DET
ejpam-7015	31	41	algebraic	algebraic	ADJ
ejpam-7015	31	42	basis	basis	NOUN
ejpam-7015	31	43	for	for	ADP
ejpam-7015	31	44	soft	soft	ADJ
ejpam-7015	31	45	computing	computing	NOUN
ejpam-7015	31	46	.	.	PUNCT
ejpam-7015	32	1	additionally	additionally	ADV
ejpam-7015	32	2	,	,	PUNCT
ejpam-7015	32	3	rao	rao	PROPN
ejpam-7015	32	4	et	et	PROPN
ejpam-7015	32	5	al	al	PROPN
ejpam-7015	32	6	.	.	PUNCT
ejpam-7015	33	1	[	[	X
ejpam-7015	33	2	15	15	NUM
ejpam-7015	33	3	]	]	PUNCT
ejpam-7015	33	4	presented	present	VERB
ejpam-7015	33	5	(	(	PUNCT
ejpam-7015	33	6	∈,∈	∈,∈	X
ejpam-7015	33	7	∨qk)-intuitionistic	∨qk)-intuitionistic	ADJ
ejpam-7015	33	8	fuzzy	fuzzy	ADJ
ejpam-7015	33	9	soft	soft	ADJ
ejpam-7015	33	10	boolean	boolean	ADJ
ejpam-7015	33	11	near	near	ADJ
ejpam-7015	33	12	-	-	PUNCT
ejpam-7015	33	13	rings	ring	NOUN
ejpam-7015	33	14	,	,	PUNCT
ejpam-7015	33	15	which	which	PRON
ejpam-7015	33	16	combine	combine	VERB
ejpam-7015	33	17	generalised	generalised	ADJ
ejpam-7015	33	18	membership	membership	NOUN
ejpam-7015	33	19	ideas	idea	NOUN
ejpam-7015	33	20	with	with	ADP
ejpam-7015	33	21	intuitionistic	intuitionistic	ADJ
ejpam-7015	33	22	fuzzy	fuzzy	ADJ
ejpam-7015	33	23	logic	logic	NOUN
ejpam-7015	33	24	.	.	PUNCT
ejpam-7015	34	1	further	further	ADJ
ejpam-7015	34	2	developments	development	NOUN
ejpam-7015	34	3	extended	extend	VERB
ejpam-7015	34	4	these	these	DET
ejpam-7015	34	5	ideas	idea	NOUN
ejpam-7015	34	6	to	to	ADP
ejpam-7015	34	7	intuitionistic	intuitionistic	ADJ
ejpam-7015	34	8	fuzzy	fuzzy	ADJ
ejpam-7015	34	9	soft	soft	ADJ
ejpam-7015	34	10	boolean	boolean	ADJ
ejpam-7015	34	11	rings	ring	NOUN
ejpam-7015	34	12	[	[	X
ejpam-7015	34	13	16	16	NUM
ejpam-7015	34	14	]	]	X
ejpam-7015	34	15	,	,	PUNCT
ejpam-7015	34	16	which	which	PRON
ejpam-7015	34	17	incorporate	incorporate	VERB
ejpam-7015	34	18	intuitionistic	intuitionistic	ADJ
ejpam-7015	34	19	fuzzy	fuzzy	ADJ
ejpam-7015	34	20	sets	set	NOUN
ejpam-7015	34	21	into	into	ADP
ejpam-7015	34	22	the	the	DET
ejpam-7015	34	23	soft	soft	ADJ
ejpam-7015	34	24	boolean	boolean	ADJ
ejpam-7015	34	25	framework	framework	NOUN
ejpam-7015	34	26	,	,	PUNCT
ejpam-7015	34	27	thereby	thereby	ADV
ejpam-7015	34	28	enriching	enrich	VERB
ejpam-7015	34	29	the	the	DET
ejpam-7015	34	30	treatment	treatment	NOUN
ejpam-7015	34	31	of	of	ADP
ejpam-7015	34	32	dual	dual	ADJ
ejpam-7015	34	33	membership	membership	NOUN
ejpam-7015	34	34	and	and	CCONJ
ejpam-7015	34	35	non	non	ADJ
ejpam-7015	34	36	-	-	ADJ
ejpam-7015	34	37	membership	membership	ADJ
ejpam-7015	34	38	information	information	NOUN
ejpam-7015	34	39	.	.	PUNCT
ejpam-7015	35	1	more	more	ADV
ejpam-7015	35	2	recently	recently	ADV
ejpam-7015	35	3	,	,	PUNCT
ejpam-7015	35	4	algebraic	algebraic	ADJ
ejpam-7015	35	5	aspects	aspect	NOUN
ejpam-7015	35	6	of	of	ADP
ejpam-7015	35	7	bipolar	bipolar	ADJ
ejpam-7015	35	8	fuzzy	fuzzy	ADJ
ejpam-7015	35	9	soft	soft	ADJ
ejpam-7015	35	10	boolean	boolean	ADJ
ejpam-7015	35	11	rings	ring	NOUN
ejpam-7015	35	12	[	[	X
ejpam-7015	35	13	17	17	NUM
ejpam-7015	35	14	]	]	PUNCT
ejpam-7015	35	15	have	have	AUX
ejpam-7015	35	16	been	be	AUX
ejpam-7015	35	17	studied	study	VERB
ejpam-7015	35	18	,	,	PUNCT
ejpam-7015	35	19	capturing	capture	VERB
ejpam-7015	35	20	both	both	CCONJ
ejpam-7015	35	21	positive	positive	ADJ
ejpam-7015	35	22	and	and	CCONJ
ejpam-7015	35	23	negative	negative	ADJ
ejpam-7015	35	24	degrees	degree	NOUN
ejpam-7015	35	25	of	of	ADP
ejpam-7015	35	26	membership	membership	NOUN
ejpam-7015	35	27	simultaneously	simultaneously	ADV
ejpam-7015	35	28	and	and	CCONJ
ejpam-7015	35	29	offering	offer	VERB
ejpam-7015	35	30	a	a	DET
ejpam-7015	35	31	richer	rich	ADJ
ejpam-7015	35	32	perspective	perspective	NOUN
ejpam-7015	35	33	for	for	ADP
ejpam-7015	35	34	uncertainty	uncertainty	NOUN
ejpam-7015	35	35	representation	representation	NOUN
ejpam-7015	35	36	.	.	PUNCT
ejpam-7015	36	1	further	further	ADJ
ejpam-7015	36	2	developments	development	NOUN
ejpam-7015	36	3	on	on	ADP
ejpam-7015	36	4	classical	classical	ADJ
ejpam-7015	36	5	boolean	boolean	ADJ
ejpam-7015	36	6	d.	d.	PROPN
ejpam-7015	36	7	ramesh	ramesh	PROPN
ejpam-7015	36	8	et	et	PROPN
ejpam-7015	36	9	al	al	PROPN
ejpam-7015	36	10	.	.	PUNCT
ejpam-7015	36	11	/	/	SYM
ejpam-7015	36	12	eur	eur	PROPN
ejpam-7015	36	13	.	.	PUNCT
ejpam-7015	37	1	j.	j.	PROPN
ejpam-7015	37	2	pure	pure	PROPN
ejpam-7015	37	3	appl	appl	PROPN
ejpam-7015	37	4	.	.	PROPN
ejpam-7015	37	5	math	math	PROPN
ejpam-7015	37	6	,	,	PUNCT
ejpam-7015	37	7	18	18	NUM
ejpam-7015	37	8	(	(	PUNCT
ejpam-7015	37	9	4	4	NUM
ejpam-7015	37	10	)	)	PUNCT
ejpam-7015	37	11	(	(	PUNCT
ejpam-7015	37	12	2025	2025	NUM
ejpam-7015	37	13	)	)	PUNCT
ejpam-7015	37	14	,	,	PUNCT
ejpam-7015	37	15	7015	7015	NUM
ejpam-7015	37	16	3	3	NUM
ejpam-7015	37	17	of	of	ADP
ejpam-7015	37	18	11	11	NUM
ejpam-7015	37	19	rings	ring	NOUN
ejpam-7015	37	20	have	have	AUX
ejpam-7015	37	21	also	also	ADV
ejpam-7015	37	22	contributed	contribute	VERB
ejpam-7015	37	23	to	to	ADP
ejpam-7015	37	24	the	the	DET
ejpam-7015	37	25	field	field	NOUN
ejpam-7015	37	26	:	:	PUNCT
ejpam-7015	37	27	hamsa	hamsa	NOUN
ejpam-7015	37	28	et	et	PROPN
ejpam-7015	37	29	al	al	PROPN
ejpam-7015	37	30	.	.	PUNCT
ejpam-7015	38	1	[	[	X
ejpam-7015	38	2	18	18	NUM
ejpam-7015	38	3	]	]	PUNCT
ejpam-7015	38	4	investigated	investigate	VERB
ejpam-7015	38	5	central	central	ADJ
ejpam-7015	38	6	boolean	boolean	ADJ
ejpam-7015	38	7	rings	ring	NOUN
ejpam-7015	38	8	and	and	CCONJ
ejpam-7015	38	9	introduced	introduce	VERB
ejpam-7015	38	10	boolean	boolean	ADJ
ejpam-7015	38	11	-	-	PUNCT
ejpam-7015	38	12	type	type	NOUN
ejpam-7015	38	13	fuzzy	fuzzy	ADJ
ejpam-7015	38	14	ideals	ideal	NOUN
ejpam-7015	38	15	,	,	PUNCT
ejpam-7015	38	16	enhancing	enhance	VERB
ejpam-7015	38	17	the	the	DET
ejpam-7015	38	18	interplay	interplay	NOUN
ejpam-7015	38	19	between	between	ADP
ejpam-7015	38	20	fuzzy	fuzzy	ADJ
ejpam-7015	38	21	algebra	algebra	NOUN
ejpam-7015	38	22	and	and	CCONJ
ejpam-7015	38	23	classical	classical	ADJ
ejpam-7015	38	24	boolean	boolean	ADJ
ejpam-7015	38	25	logic	logic	NOUN
ejpam-7015	38	26	.	.	PUNCT
ejpam-7015	39	1	chalapathi	chalapathi	VERB
ejpam-7015	39	2	and	and	CCONJ
ejpam-7015	39	3	madhavi	madhavi	PROPN
ejpam-7015	39	4	[	[	X
ejpam-7015	39	5	19	19	NUM
ejpam-7015	39	6	]	]	PUNCT
ejpam-7015	39	7	proposed	propose	VERB
ejpam-7015	39	8	neutrosophic	neutrosophic	ADJ
ejpam-7015	39	9	boolean	boolean	ADJ
ejpam-7015	39	10	rings	ring	NOUN
ejpam-7015	39	11	,	,	PUNCT
ejpam-7015	39	12	integrating	integrate	VERB
ejpam-7015	39	13	indeterminacy	indeterminacy	NOUN
ejpam-7015	39	14	as	as	ADP
ejpam-7015	39	15	a	a	DET
ejpam-7015	39	16	formal	formal	ADJ
ejpam-7015	39	17	element	element	NOUN
ejpam-7015	39	18	into	into	ADP
ejpam-7015	39	19	the	the	DET
ejpam-7015	39	20	boolean	boolean	ADJ
ejpam-7015	39	21	structure	structure	NOUN
ejpam-7015	39	22	.	.	PUNCT
ejpam-7015	40	1	similarly	similarly	ADV
ejpam-7015	40	2	,	,	PUNCT
ejpam-7015	40	3	ameri	ameri	PROPN
ejpam-7015	40	4	et	et	PROPN
ejpam-7015	40	5	al	al	PROPN
ejpam-7015	40	6	.	.	PUNCT
ejpam-7015	41	1	[	[	X
ejpam-7015	41	2	20	20	NUM
ejpam-7015	41	3	]	]	SYM
ejpam-7015	41	4	formulated	formulate	VERB
ejpam-7015	41	5	boolean	boolean	ADJ
ejpam-7015	41	6	rings	ring	NOUN
ejpam-7015	41	7	based	base	VERB
ejpam-7015	41	8	on	on	ADP
ejpam-7015	41	9	multirings	multiring	NOUN
ejpam-7015	41	10	,	,	PUNCT
ejpam-7015	41	11	extending	extend	VERB
ejpam-7015	41	12	the	the	DET
ejpam-7015	41	13	classical	classical	ADJ
ejpam-7015	41	14	ring	ring	NOUN
ejpam-7015	41	15	framework	framework	NOUN
ejpam-7015	41	16	to	to	PART
ejpam-7015	41	17	encompass	encompass	VERB
ejpam-7015	41	18	multivalued	multivalued	ADJ
ejpam-7015	41	19	logic	logic	NOUN
ejpam-7015	41	20	and	and	CCONJ
ejpam-7015	41	21	offering	offer	VERB
ejpam-7015	41	22	new	new	ADJ
ejpam-7015	41	23	interpretations	interpretation	NOUN
ejpam-7015	41	24	for	for	ADP
ejpam-7015	41	25	algebraic	algebraic	ADJ
ejpam-7015	41	26	reasoning	reasoning	NOUN
ejpam-7015	41	27	.	.	PUNCT
ejpam-7015	42	1	collectively	collectively	ADV
ejpam-7015	42	2	,	,	PUNCT
ejpam-7015	42	3	these	these	DET
ejpam-7015	42	4	contributions	contribution	NOUN
ejpam-7015	42	5	demonstrate	demonstrate	VERB
ejpam-7015	42	6	a	a	DET
ejpam-7015	42	7	progressive	progressive	ADJ
ejpam-7015	42	8	effort	effort	NOUN
ejpam-7015	42	9	to	to	PART
ejpam-7015	42	10	expand	expand	VERB
ejpam-7015	42	11	the	the	DET
ejpam-7015	42	12	algebraic	algebraic	ADJ
ejpam-7015	42	13	foundations	foundation	NOUN
ejpam-7015	42	14	of	of	ADP
ejpam-7015	42	15	fuzzy	fuzzy	ADJ
ejpam-7015	42	16	soft	soft	ADJ
ejpam-7015	42	17	systems	system	NOUN
ejpam-7015	42	18	and	and	CCONJ
ejpam-7015	42	19	to	to	PART
ejpam-7015	42	20	address	address	VERB
ejpam-7015	42	21	increasingly	increasingly	ADV
ejpam-7015	42	22	complex	complex	ADJ
ejpam-7015	42	23	forms	form	NOUN
ejpam-7015	42	24	of	of	ADP
ejpam-7015	42	25	uncertainty	uncertainty	NOUN
ejpam-7015	42	26	in	in	ADP
ejpam-7015	42	27	mathematical	mathematical	ADJ
ejpam-7015	42	28	structures	structure	NOUN
ejpam-7015	42	29	.	.	PUNCT
ejpam-7015	43	1	in	in	ADP
ejpam-7015	43	2	this	this	DET
ejpam-7015	43	3	study	study	NOUN
ejpam-7015	43	4	,	,	PUNCT
ejpam-7015	43	5	we	we	PRON
ejpam-7015	43	6	introduce	introduce	VERB
ejpam-7015	43	7	the	the	DET
ejpam-7015	43	8	concepts	concept	NOUN
ejpam-7015	43	9	of	of	ADP
ejpam-7015	43	10	afsbrs	afsbrs	NOUN
ejpam-7015	43	11	and	and	CCONJ
ejpam-7015	43	12	afsis	afsis	NOUN
ejpam-7015	43	13	within	within	ADP
ejpam-7015	43	14	the	the	DET
ejpam-7015	43	15	framework	framework	NOUN
ejpam-7015	43	16	of	of	ADP
ejpam-7015	43	17	boolean	boolean	ADJ
ejpam-7015	43	18	rings	ring	NOUN
ejpam-7015	43	19	(	(	PUNCT
ejpam-7015	43	20	brs	brs	NOUN
ejpam-7015	43	21	)	)	PUNCT
ejpam-7015	43	22	,	,	PUNCT
ejpam-7015	43	23	and	and	CCONJ
ejpam-7015	43	24	establish	establish	VERB
ejpam-7015	43	25	their	their	PRON
ejpam-7015	43	26	fundamental	fundamental	ADJ
ejpam-7015	43	27	algebraic	algebraic	ADJ
ejpam-7015	43	28	properties	property	NOUN
ejpam-7015	43	29	.	.	PUNCT
ejpam-7015	44	1	by	by	ADP
ejpam-7015	44	2	extending	extend	VERB
ejpam-7015	44	3	the	the	DET
ejpam-7015	44	4	scope	scope	NOUN
ejpam-7015	44	5	of	of	ADP
ejpam-7015	44	6	fuzzy	fuzzy	ADJ
ejpam-7015	44	7	soft	soft	ADJ
ejpam-7015	44	8	structures	structure	NOUN
ejpam-7015	44	9	to	to	PART
ejpam-7015	44	10	incorporate	incorporate	VERB
ejpam-7015	44	11	non	non	ADJ
ejpam-7015	44	12	-	-	ADJ
ejpam-7015	44	13	membership	membership	ADJ
ejpam-7015	44	14	information	information	NOUN
ejpam-7015	44	15	,	,	PUNCT
ejpam-7015	44	16	this	this	DET
ejpam-7015	44	17	work	work	NOUN
ejpam-7015	44	18	contributes	contribute	VERB
ejpam-7015	44	19	to	to	ADP
ejpam-7015	44	20	strengthening	strengthen	VERB
ejpam-7015	44	21	the	the	DET
ejpam-7015	44	22	theoretical	theoretical	ADJ
ejpam-7015	44	23	foundations	foundation	NOUN
ejpam-7015	44	24	of	of	ADP
ejpam-7015	44	25	soft	soft	ADJ
ejpam-7015	44	26	algebraic	algebraic	ADJ
ejpam-7015	44	27	systems	system	NOUN
ejpam-7015	44	28	.	.	PUNCT
ejpam-7015	45	1	moreover	moreover	ADV
ejpam-7015	45	2	,	,	PUNCT
ejpam-7015	45	3	the	the	DET
ejpam-7015	45	4	results	result	NOUN
ejpam-7015	45	5	are	be	AUX
ejpam-7015	45	6	intended	intend	VERB
ejpam-7015	45	7	to	to	PART
ejpam-7015	45	8	provide	provide	VERB
ejpam-7015	45	9	a	a	DET
ejpam-7015	45	10	clear	clear	ADJ
ejpam-7015	45	11	and	and	CCONJ
ejpam-7015	45	12	accessible	accessible	ADJ
ejpam-7015	45	13	framework	framework	NOUN
ejpam-7015	45	14	that	that	PRON
ejpam-7015	45	15	can	can	AUX
ejpam-7015	45	16	support	support	VERB
ejpam-7015	45	17	further	further	ADJ
ejpam-7015	45	18	exploration	exploration	NOUN
ejpam-7015	45	19	by	by	ADP
ejpam-7015	45	20	students	student	NOUN
ejpam-7015	45	21	and	and	CCONJ
ejpam-7015	45	22	young	young	ADJ
ejpam-7015	45	23	researchers	researcher	NOUN
ejpam-7015	45	24	in	in	ADP
ejpam-7015	45	25	the	the	DET
ejpam-7015	45	26	field	field	NOUN
ejpam-7015	45	27	of	of	ADP
ejpam-7015	45	28	algebraic	algebraic	ADJ
ejpam-7015	45	29	approaches	approach	NOUN
ejpam-7015	45	30	to	to	ADP
ejpam-7015	45	31	uncertainty	uncertainty	NOUN
ejpam-7015	45	32	.	.	PUNCT
ejpam-7015	46	1	2	2	X
ejpam-7015	46	2	.	.	X
ejpam-7015	46	3	preliminaries	preliminary	NOUN
ejpam-7015	46	4	to	to	PART
ejpam-7015	46	5	begin	begin	VERB
ejpam-7015	46	6	,	,	PUNCT
ejpam-7015	46	7	we	we	PRON
ejpam-7015	46	8	will	will	AUX
ejpam-7015	46	9	present	present	VERB
ejpam-7015	46	10	basic	basic	ADJ
ejpam-7015	46	11	definitions	definition	NOUN
ejpam-7015	46	12	.	.	PUNCT
ejpam-7015	47	1	definition	definition	NOUN
ejpam-7015	47	2	1	1	NUM
ejpam-7015	47	3	.	.	PUNCT
ejpam-7015	47	4	for	for	ADP
ejpam-7015	47	5	a	a	DET
ejpam-7015	47	6	set	set	NOUN
ejpam-7015	47	7	ℵ	ℵ	NOUN
ejpam-7015	47	8	,	,	PUNCT
ejpam-7015	47	9	when	when	SCONJ
ejpam-7015	47	10	two	two	NUM
ejpam-7015	47	11	binary	binary	ADJ
ejpam-7015	47	12	operations	operation	NOUN
ejpam-7015	47	13	are	be	AUX
ejpam-7015	47	14	available	available	ADJ
ejpam-7015	47	15	,	,	PUNCT
ejpam-7015	47	16	namely	namely	ADV
ejpam-7015	47	17	addition	addition	NOUN
ejpam-7015	47	18	+	+	CCONJ
ejpam-7015	47	19	and	and	CCONJ
ejpam-7015	47	20	multiplication	multiplication	NOUN
ejpam-7015	47	21	·	·	PUNCT
ejpam-7015	47	22	,	,	PUNCT
ejpam-7015	47	23	if	if	SCONJ
ejpam-7015	47	24	any	any	PRON
ejpam-7015	47	25	of	of	ADP
ejpam-7015	47	26	the	the	DET
ejpam-7015	47	27	following	follow	VERB
ejpam-7015	47	28	characteristics	characteristic	NOUN
ejpam-7015	47	29	apply	apply	VERB
ejpam-7015	47	30	,	,	PUNCT
ejpam-7015	47	31	it	it	PRON
ejpam-7015	47	32	is	be	AUX
ejpam-7015	47	33	considered	consider	VERB
ejpam-7015	47	34	to	to	PART
ejpam-7015	47	35	be	be	AUX
ejpam-7015	47	36	a	a	DET
ejpam-7015	47	37	ring	ring	NOUN
ejpam-7015	47	38	:	:	PUNCT
ejpam-7015	47	39	(	(	PUNCT
ejpam-7015	47	40	i	i	NOUN
ejpam-7015	47	41	)	)	PUNCT
ejpam-7015	47	42	ℵ	ℵ	NOUN
ejpam-7015	47	43	is	be	AUX
ejpam-7015	47	44	a	a	DET
ejpam-7015	47	45	group	group	NOUN
ejpam-7015	47	46	under	under	ADP
ejpam-7015	47	47	+	+	PROPN
ejpam-7015	47	48	,	,	PUNCT
ejpam-7015	47	49	(	(	PUNCT
ejpam-7015	47	50	ii	ii	NOUN
ejpam-7015	47	51	)	)	PUNCT
ejpam-7015	47	52	ℵ	ℵ	NOUN
ejpam-7015	47	53	is	be	AUX
ejpam-7015	47	54	a	a	DET
ejpam-7015	47	55	semigroup	semigroup	NOUN
ejpam-7015	47	56	under	under	ADP
ejpam-7015	47	57	·	·	PUNCT
ejpam-7015	47	58	,	,	PUNCT
ejpam-7015	47	59	(	(	PUNCT
ejpam-7015	47	60	iii	iii	NOUN
ejpam-7015	47	61	)	)	PUNCT
ejpam-7015	47	62	(	(	PUNCT
ejpam-7015	47	63	g+	g+	NOUN
ejpam-7015	47	64	s)r	s)r	VERB
ejpam-7015	48	1	=	=	PUNCT
ejpam-7015	48	2	gr+	gr+	PROPN
ejpam-7015	48	3	sr	sr	PROPN
ejpam-7015	48	4	and	and	CCONJ
ejpam-7015	48	5	g(s+	g(s+	NUM
ejpam-7015	48	6	r	r	NOUN
ejpam-7015	48	7	)	)	PUNCT
ejpam-7015	48	8	=	=	VERB
ejpam-7015	48	9	gs+	gs+	VERB
ejpam-7015	48	10	gr	gr	ADP
ejpam-7015	48	11	,	,	PUNCT
ejpam-7015	48	12	∀g	∀g	NOUN
ejpam-7015	48	13	,	,	PUNCT
ejpam-7015	48	14	s	s	PART
ejpam-7015	48	15	,	,	PUNCT
ejpam-7015	48	16	r	r	NOUN
ejpam-7015	48	17	∈	∈	PROPN
ejpam-7015	48	18	ℵ.	ℵ.	NOUN
ejpam-7015	48	19	definition	definition	NOUN
ejpam-7015	48	20	2	2	NUM
ejpam-7015	48	21	.	.	PUNCT
ejpam-7015	49	1	if	if	SCONJ
ejpam-7015	49	2	x2	x2	PROPN
ejpam-7015	50	1	=	=	PUNCT
ejpam-7015	50	2	x,∀x	x,∀x	PUNCT
ejpam-7015	50	3	∈	∈	PROPN
ejpam-7015	50	4	ℵ	ℵ	NOUN
ejpam-7015	50	5	,	,	PUNCT
ejpam-7015	50	6	then	then	ADV
ejpam-7015	50	7	a	a	DET
ejpam-7015	50	8	ring	ring	NOUN
ejpam-7015	50	9	ℵ	ℵ	NOUN
ejpam-7015	50	10	is	be	AUX
ejpam-7015	50	11	a	a	DET
ejpam-7015	50	12	boolean	boolean	ADJ
ejpam-7015	50	13	ring	ring	NOUN
ejpam-7015	50	14	(	(	PUNCT
ejpam-7015	50	15	br	br	NOUN
ejpam-7015	50	16	)	)	PUNCT
ejpam-7015	50	17	.	.	PUNCT
ejpam-7015	51	1	definition	definition	NOUN
ejpam-7015	51	2	3	3	X
ejpam-7015	51	3	.	.	PUNCT
ejpam-7015	52	1	let	let	VERB
ejpam-7015	52	2	a	a	DET
ejpam-7015	52	3	symbolise	symbolise	NOUN
ejpam-7015	52	4	a	a	DET
ejpam-7015	52	5	starting	start	VERB
ejpam-7015	52	6	universe	universe	NOUN
ejpam-7015	52	7	,	,	PUNCT
ejpam-7015	52	8	e	e	X
ejpam-7015	52	9	symbolise	symbolise	VERB
ejpam-7015	52	10	a	a	DET
ejpam-7015	52	11	set	set	NOUN
ejpam-7015	52	12	of	of	ADP
ejpam-7015	52	13	parameters	parameter	NOUN
ejpam-7015	52	14	,	,	PUNCT
ejpam-7015	52	15	and	and	CCONJ
ejpam-7015	52	16	i	i	PRON
ejpam-7015	52	17	symbolise	symbolise	VERB
ejpam-7015	52	18	the	the	DET
ejpam-7015	52	19	closed	closed	ADJ
ejpam-7015	52	20	unit	unit	NOUN
ejpam-7015	52	21	interval	interval	NOUN
ejpam-7015	52	22	,	,	PUNCT
ejpam-7015	52	23	or	or	CCONJ
ejpam-7015	52	24	i	i	PRON
ejpam-7015	52	25	=	=	PUNCT
ejpam-7015	53	1	[	[	X
ejpam-7015	53	2	0	0	NUM
ejpam-7015	53	3	,	,	PUNCT
ejpam-7015	53	4	1	1	NUM
ejpam-7015	53	5	]	]	PUNCT
ejpam-7015	53	6	.	.	PUNCT
ejpam-7015	54	1	p	p	X
ejpam-7015	54	2	(	(	PUNCT
ejpam-7015	54	3	a	a	NOUN
ejpam-7015	54	4	)	)	PUNCT
ejpam-7015	54	5	denotes	denote	VERB
ejpam-7015	54	6	the	the	DET
ejpam-7015	54	7	power	power	NOUN
ejpam-7015	54	8	set	set	NOUN
ejpam-7015	54	9	of	of	ADP
ejpam-7015	54	10	a.	a.	NOUN
ejpam-7015	54	11	a	a	DET
ejpam-7015	54	12	function	function	NOUN
ejpam-7015	54	13	with	with	ADP
ejpam-7015	54	14	a	a	DET
ejpam-7015	54	15	set	set	VERB
ejpam-7015	54	16	value	value	NOUN
ejpam-7015	54	17	is	be	AUX
ejpam-7015	54	18	ג	ג	X
ejpam-7015	54	19	:	:	PUNCT
ejpam-7015	54	20	e	e	PROPN
ejpam-7015	54	21	→	→	SYM
ejpam-7015	54	22	ia	ia	PROPN
ejpam-7015	54	23	,	,	PUNCT
ejpam-7015	54	24	where	where	SCONJ
ejpam-7015	54	25	ia	ia	PROPN
ejpam-7015	54	26	indicates	indicate	VERB
ejpam-7015	54	27	the	the	DET
ejpam-7015	54	28	total	total	ADJ
ejpam-7015	54	29	number	number	NOUN
ejpam-7015	54	30	of	of	ADP
ejpam-7015	54	31	all	all	DET
ejpam-7015	54	32	the	the	DET
ejpam-7015	54	33	fuzzy	fuzzy	ADJ
ejpam-7015	54	34	sets	set	NOUN
ejpam-7015	54	35	on	on	ADP
ejpam-7015	54	36	a.	a.	NOUN
ejpam-7015	54	37	definition	definition	NOUN
ejpam-7015	54	38	4	4	NUM
ejpam-7015	54	39	.	.	PUNCT
ejpam-7015	55	1	a	a	DET
ejpam-7015	55	2	pair	pair	NOUN
ejpam-7015	55	3	of	of	ADP
ejpam-7015	55	4	fsss	fsss	NOUN
ejpam-7015	55	5	,	,	PUNCT
ejpam-7015	55	6	(	(	PUNCT
ejpam-7015	55	7	u	u	NOUN
ejpam-7015	55	8	,	,	PUNCT
ejpam-7015	55	9	ג	ג	PROPN
ejpam-7015	55	10	)	)	PUNCT
ejpam-7015	55	11	and	and	CCONJ
ejpam-7015	55	12	(	(	PUNCT
ejpam-7015	55	13	ξ	ξ	PROPN
ejpam-7015	55	14	,	,	PUNCT
ejpam-7015	55	15	h	h	NOUN
ejpam-7015	55	16	)	)	PUNCT
ejpam-7015	55	17	,	,	PUNCT
ejpam-7015	55	18	with	with	ADP
ejpam-7015	55	19	u	u	NOUN
ejpam-7015	55	20	∩	∩	ADJ
ejpam-7015	55	21	h	h	NOUN
ejpam-7015	55	22	6=	6=	NOUN
ejpam-7015	55	23	∅	∅	NOUN
ejpam-7015	55	24	,	,	PUNCT
ejpam-7015	55	25	are	be	AUX
ejpam-7015	55	26	considered	consider	VERB
ejpam-7015	55	27	.	.	PUNCT
ejpam-7015	56	1	if	if	SCONJ
ejpam-7015	56	2	s	s	PRON
ejpam-7015	56	3	=	=	SYM
ejpam-7015	56	4	u	u	NOUN
ejpam-7015	56	5	∩	∩	ADJ
ejpam-7015	56	6	h	h	NOUN
ejpam-7015	56	7	and	and	CCONJ
ejpam-7015	56	8	ωx	ωx	PROPN
ejpam-7015	56	9	=	=	SYM
ejpam-7015	56	10	xג	xג	PROPN
ejpam-7015	56	11	∧	∧	PROPN
ejpam-7015	56	12	ξx	ξx	PROPN
ejpam-7015	56	13	,	,	PUNCT
ejpam-7015	56	14	∀x	∀x	X
ejpam-7015	56	15	∈	∈	PROPN
ejpam-7015	56	16	u	u	NOUN
ejpam-7015	56	17	,	,	PUNCT
ejpam-7015	56	18	the	the	DET
ejpam-7015	56	19	fss	fss	PROPN
ejpam-7015	56	20	(	(	PUNCT
ejpam-7015	56	21	ω	ω	PROPN
ejpam-7015	56	22	,	,	PUNCT
ejpam-7015	56	23	s	s	PART
ejpam-7015	56	24	)	)	PUNCT
ejpam-7015	56	25	is	be	AUX
ejpam-7015	56	26	generated	generate	VERB
ejpam-7015	56	27	by	by	ADP
ejpam-7015	56	28	the	the	DET
ejpam-7015	56	29	intersection	intersection	NOUN
ejpam-7015	56	30	of	of	ADP
ejpam-7015	56	31	(	(	PUNCT
ejpam-7015	56	32	u	u	NOUN
ejpam-7015	56	33	,	,	PUNCT
ejpam-7015	56	34	ג	ג	PROPN
ejpam-7015	56	35	)	)	PUNCT
ejpam-7015	56	36	and	and	CCONJ
ejpam-7015	56	37	(	(	PUNCT
ejpam-7015	56	38	ξ	ξ	PROPN
ejpam-7015	56	39	,	,	PUNCT
ejpam-7015	56	40	h	h	NOUN
ejpam-7015	56	41	)	)	PUNCT
ejpam-7015	56	42	.	.	PUNCT
ejpam-7015	57	1	the	the	DET
ejpam-7015	57	2	formula	formula	NOUN
ejpam-7015	57	3	(	(	PUNCT
ejpam-7015	57	4	u	u	NOUN
ejpam-7015	57	5	,	,	PUNCT
ejpam-7015	57	6	ג	ג	NOUN
ejpam-7015	57	7	)	)	PUNCT
ejpam-7015	57	8	∩	∩	NOUN
ejpam-7015	57	9	(	(	PUNCT
ejpam-7015	57	10	ξ	ξ	PROPN
ejpam-7015	57	11	,	,	PUNCT
ejpam-7015	57	12	h	h	NOUN
ejpam-7015	57	13	)	)	PUNCT
ejpam-7015	57	14	=	=	SYM
ejpam-7015	57	15	(	(	PUNCT
ejpam-7015	57	16	ω	ω	PROPN
ejpam-7015	57	17	,	,	PUNCT
ejpam-7015	57	18	s	s	PART
ejpam-7015	57	19	)	)	PUNCT
ejpam-7015	57	20	can	can	AUX
ejpam-7015	57	21	be	be	AUX
ejpam-7015	57	22	represented	represent	VERB
ejpam-7015	57	23	.	.	PUNCT
ejpam-7015	58	1	definition	definition	NOUN
ejpam-7015	58	2	5	5	NUM
ejpam-7015	58	3	.	.	PUNCT
ejpam-7015	59	1	a	a	DET
ejpam-7015	59	2	pair	pair	NOUN
ejpam-7015	59	3	of	of	ADP
ejpam-7015	59	4	fsss	fsss	NOUN
ejpam-7015	59	5	,	,	PUNCT
ejpam-7015	59	6	(	(	PUNCT
ejpam-7015	59	7	u	u	NOUN
ejpam-7015	59	8	,	,	PUNCT
ejpam-7015	59	9	ג	ג	PROPN
ejpam-7015	59	10	)	)	PUNCT
ejpam-7015	59	11	and	and	CCONJ
ejpam-7015	59	12	(	(	PUNCT
ejpam-7015	59	13	ξ	ξ	PROPN
ejpam-7015	59	14	,	,	PUNCT
ejpam-7015	59	15	h	h	NOUN
ejpam-7015	59	16	)	)	PUNCT
ejpam-7015	59	17	.	.	PUNCT
ejpam-7015	60	1	the	the	DET
ejpam-7015	60	2	union	union	PROPN
ejpam-7015	60	3	of	of	ADP
ejpam-7015	60	4	(	(	PUNCT
ejpam-7015	60	5	u	u	NOUN
ejpam-7015	60	6	,	,	PUNCT
ejpam-7015	60	7	ג	ג	PROPN
ejpam-7015	60	8	)	)	PUNCT
ejpam-7015	60	9	and	and	CCONJ
ejpam-7015	60	10	(	(	PUNCT
ejpam-7015	60	11	ξ	ξ	PROPN
ejpam-7015	60	12	,	,	PUNCT
ejpam-7015	60	13	h	h	NOUN
ejpam-7015	60	14	)	)	PUNCT
ejpam-7015	60	15	forms	form	VERB
ejpam-7015	60	16	the	the	DET
ejpam-7015	60	17	fss	fss	NOUN
ejpam-7015	60	18	(	(	PUNCT
ejpam-7015	60	19	ω	ω	PROPN
ejpam-7015	60	20	,	,	PUNCT
ejpam-7015	60	21	s	s	PART
ejpam-7015	60	22	)	)	PUNCT
ejpam-7015	60	23	,	,	PUNCT
ejpam-7015	60	24	where	where	SCONJ
ejpam-7015	60	25	s	s	VERB
ejpam-7015	60	26	=	=	SYM
ejpam-7015	60	27	u	u	NOUN
ejpam-7015	60	28	∪	∪	NOUN
ejpam-7015	60	29	h	h	NOUN
ejpam-7015	60	30	and	and	CCONJ
ejpam-7015	60	31	ωx	ωx	PRON
ejpam-7015	60	32	=	=	PUNCT
ejpam-7015	61	1			PUNCT
ejpam-7015	61	2	xג	xג	INTJ
ejpam-7015	61	3	if	if	SCONJ
ejpam-7015	61	4	x	x	SYM
ejpam-7015	61	5	∈	∈	PROPN
ejpam-7015	61	6	u−	u−	PROPN
ejpam-7015	61	7	h	h	NOUN
ejpam-7015	61	8	ξx	ξx	NOUN
ejpam-7015	61	9	if	if	SCONJ
ejpam-7015	61	10	x	x	SYM
ejpam-7015	61	11	∈	∈	PROPN
ejpam-7015	61	12	h−	h−	PROPN
ejpam-7015	61	13	u	u	NOUN
ejpam-7015	61	14	xג	xג	PROPN
ejpam-7015	61	15	∨	∨	NUM
ejpam-7015	61	16	ξx	ξx	PROPN
ejpam-7015	61	17	if	if	SCONJ
ejpam-7015	61	18	x	x	PROPN
ejpam-7015	61	19	∈	∈	PROPN
ejpam-7015	61	20	u	u	NOUN
ejpam-7015	61	21	∩	∩	ADJ
ejpam-7015	61	22	h	h	NOUN
ejpam-7015	61	23	,	,	PUNCT
ejpam-7015	61	24	∀x	∀x	X
ejpam-7015	61	25	∈	∈	PROPN
ejpam-7015	61	26	s.	s.	PROPN
ejpam-7015	61	27	next	next	ADV
ejpam-7015	61	28	,	,	PUNCT
ejpam-7015	61	29	we	we	PRON
ejpam-7015	61	30	will	will	AUX
ejpam-7015	61	31	write	write	VERB
ejpam-7015	61	32	(	(	PUNCT
ejpam-7015	61	33	u	u	NOUN
ejpam-7015	61	34	,	,	PUNCT
ejpam-7015	61	35	ג	ג	NOUN
ejpam-7015	61	36	)	)	PUNCT
ejpam-7015	61	37	∪	∪	NOUN
ejpam-7015	61	38	(	(	PUNCT
ejpam-7015	61	39	ξ	ξ	PROPN
ejpam-7015	61	40	,	,	PUNCT
ejpam-7015	61	41	h	h	NOUN
ejpam-7015	61	42	)	)	PUNCT
ejpam-7015	61	43	=	=	SYM
ejpam-7015	61	44	(	(	PUNCT
ejpam-7015	61	45	ω	ω	PROPN
ejpam-7015	61	46	,	,	PUNCT
ejpam-7015	61	47	s	s	PART
ejpam-7015	61	48	)	)	PUNCT
ejpam-7015	61	49	.	.	PUNCT
ejpam-7015	62	1	d.	d.	PROPN
ejpam-7015	62	2	ramesh	ramesh	PROPN
ejpam-7015	62	3	et	et	PROPN
ejpam-7015	62	4	al	al	PROPN
ejpam-7015	62	5	.	.	PUNCT
ejpam-7015	62	6	/	/	SYM
ejpam-7015	62	7	eur	eur	PROPN
ejpam-7015	62	8	.	.	PUNCT
ejpam-7015	63	1	j.	j.	PROPN
ejpam-7015	63	2	pure	pure	PROPN
ejpam-7015	63	3	appl	appl	PROPN
ejpam-7015	63	4	.	.	PROPN
ejpam-7015	63	5	math	math	PROPN
ejpam-7015	63	6	,	,	PUNCT
ejpam-7015	63	7	18	18	NUM
ejpam-7015	63	8	(	(	PUNCT
ejpam-7015	63	9	4	4	NUM
ejpam-7015	63	10	)	)	PUNCT
ejpam-7015	63	11	(	(	PUNCT
ejpam-7015	63	12	2025	2025	NUM
ejpam-7015	63	13	)	)	PUNCT
ejpam-7015	63	14	,	,	PUNCT
ejpam-7015	63	15	7015	7015	NUM
ejpam-7015	63	16	4	4	NUM
ejpam-7015	63	17	of	of	ADP
ejpam-7015	63	18	11	11	NUM
ejpam-7015	63	19	definition	definition	NOUN
ejpam-7015	63	20	6	6	NUM
ejpam-7015	63	21	.	.	PUNCT
ejpam-7015	64	1	consider	consider	VERB
ejpam-7015	64	2	(	(	PUNCT
ejpam-7015	64	3	u	u	NOUN
ejpam-7015	64	4	,	,	PUNCT
ejpam-7015	64	5	ג	ג	PROPN
ejpam-7015	64	6	)	)	PUNCT
ejpam-7015	64	7	and	and	CCONJ
ejpam-7015	64	8	(	(	PUNCT
ejpam-7015	64	9	ξ	ξ	PROPN
ejpam-7015	64	10	,	,	PUNCT
ejpam-7015	64	11	h	h	NOUN
ejpam-7015	64	12	)	)	PUNCT
ejpam-7015	64	13	to	to	PART
ejpam-7015	64	14	be	be	AUX
ejpam-7015	64	15	two	two	NUM
ejpam-7015	64	16	fsss	fsss	NOUN
ejpam-7015	64	17	.	.	PUNCT
ejpam-7015	65	1	then	then	ADV
ejpam-7015	65	2	,	,	PUNCT
ejpam-7015	65	3	(	(	PUNCT
ejpam-7015	65	4	u	u	NOUN
ejpam-7015	65	5	,	,	PUNCT
ejpam-7015	65	6	ג	ג	PROPN
ejpam-7015	65	7	)	)	PUNCT
ejpam-7015	65	8	and	and	CCONJ
ejpam-7015	65	9	(	(	PUNCT
ejpam-7015	65	10	ξ	ξ	PROPN
ejpam-7015	65	11	,	,	PUNCT
ejpam-7015	65	12	h	h	NOUN
ejpam-7015	65	13	)	)	PUNCT
ejpam-7015	65	14	are	be	AUX
ejpam-7015	65	15	symbolised	symbolise	VERB
ejpam-7015	65	16	by	by	ADP
ejpam-7015	65	17	(	(	PUNCT
ejpam-7015	65	18	u	u	NOUN
ejpam-7015	65	19	,	,	PUNCT
ejpam-7015	65	20	ג	ג	NOUN
ejpam-7015	65	21	)	)	PUNCT
ejpam-7015	65	22	∧	∧	PROPN
ejpam-7015	65	23	(	(	PUNCT
ejpam-7015	65	24	ξ	ξ	PROPN
ejpam-7015	65	25	,	,	PUNCT
ejpam-7015	65	26	h	h	NOUN
ejpam-7015	65	27	)	)	PUNCT
ejpam-7015	65	28	,	,	PUNCT
ejpam-7015	65	29	and	and	CCONJ
ejpam-7015	65	30	it	it	PRON
ejpam-7015	65	31	is	be	AUX
ejpam-7015	65	32	suggested	suggest	VERB
ejpam-7015	65	33	by	by	ADP
ejpam-7015	65	34	(	(	PUNCT
ejpam-7015	65	35	ω	ω	PROPN
ejpam-7015	65	36	,	,	PUNCT
ejpam-7015	65	37	u	u	PROPN
ejpam-7015	65	38	×	×	PROPN
ejpam-7015	65	39	h	h	NOUN
ejpam-7015	65	40	)	)	PUNCT
ejpam-7015	65	41	,	,	PUNCT
ejpam-7015	65	42	where	where	SCONJ
ejpam-7015	65	43	ω(x	ω(x	X
ejpam-7015	65	44	,	,	PUNCT
ejpam-7015	65	45	y	y	NOUN
ejpam-7015	65	46	)	)	PUNCT
ejpam-7015	65	47	=	=	SYM
ejpam-7015	66	1	xג	xג	PROPN
ejpam-7015	66	2	∧	∧	PROPN
ejpam-7015	66	3	ξx	ξx	PROPN
ejpam-7015	66	4	for	for	ADP
ejpam-7015	66	5	each	each	DET
ejpam-7015	66	6	(	(	PUNCT
ejpam-7015	66	7	x	x	NOUN
ejpam-7015	66	8	,	,	PUNCT
ejpam-7015	66	9	y	y	NOUN
ejpam-7015	66	10	)	)	PUNCT
ejpam-7015	66	11	∈	∈	PROPN
ejpam-7015	67	1	u×	u×	PROPN
ejpam-7015	67	2	h.	h.	NOUN
ejpam-7015	67	3	definition	definition	NOUN
ejpam-7015	67	4	7	7	NUM
ejpam-7015	67	5	.	.	PUNCT
ejpam-7015	68	1	consider	consider	VERB
ejpam-7015	68	2	(	(	PUNCT
ejpam-7015	68	3	u	u	NOUN
ejpam-7015	68	4	,	,	PUNCT
ejpam-7015	68	5	ג	ג	PROPN
ejpam-7015	68	6	)	)	PUNCT
ejpam-7015	68	7	and	and	CCONJ
ejpam-7015	68	8	(	(	PUNCT
ejpam-7015	68	9	ξ	ξ	PROPN
ejpam-7015	68	10	,	,	PUNCT
ejpam-7015	68	11	h	h	NOUN
ejpam-7015	68	12	)	)	PUNCT
ejpam-7015	68	13	to	to	PART
ejpam-7015	68	14	be	be	AUX
ejpam-7015	68	15	two	two	NUM
ejpam-7015	68	16	fsss	fsss	NOUN
ejpam-7015	68	17	.	.	PUNCT
ejpam-7015	69	1	then	then	ADV
ejpam-7015	69	2	,	,	PUNCT
ejpam-7015	69	3	(	(	PUNCT
ejpam-7015	69	4	u	u	NOUN
ejpam-7015	69	5	,	,	PUNCT
ejpam-7015	69	6	ג	ג	PROPN
ejpam-7015	69	7	)	)	PUNCT
ejpam-7015	69	8	or	or	CCONJ
ejpam-7015	69	9	(	(	PUNCT
ejpam-7015	69	10	ξ	ξ	PROPN
ejpam-7015	69	11	,	,	PUNCT
ejpam-7015	69	12	h	h	NOUN
ejpam-7015	69	13	)	)	PUNCT
ejpam-7015	69	14	are	be	AUX
ejpam-7015	69	15	symbolised	symbolise	VERB
ejpam-7015	69	16	by	by	ADP
ejpam-7015	69	17	(	(	PUNCT
ejpam-7015	69	18	u	u	NOUN
ejpam-7015	69	19	,	,	PUNCT
ejpam-7015	69	20	ג	ג	NOUN
ejpam-7015	69	21	)	)	PUNCT
ejpam-7015	69	22	∨	∨	NOUN
ejpam-7015	69	23	(	(	PUNCT
ejpam-7015	69	24	ξ	ξ	PROPN
ejpam-7015	69	25	,	,	PUNCT
ejpam-7015	69	26	h	h	NOUN
ejpam-7015	69	27	)	)	PUNCT
ejpam-7015	69	28	,	,	PUNCT
ejpam-7015	69	29	and	and	CCONJ
ejpam-7015	69	30	it	it	PRON
ejpam-7015	69	31	is	be	AUX
ejpam-7015	69	32	suggested	suggest	VERB
ejpam-7015	69	33	by	by	ADP
ejpam-7015	69	34	(	(	PUNCT
ejpam-7015	69	35	ω	ω	PROPN
ejpam-7015	69	36	,	,	PUNCT
ejpam-7015	69	37	u×h	u×h	NUM
ejpam-7015	69	38	)	)	PUNCT
ejpam-7015	69	39	,	,	PUNCT
ejpam-7015	69	40	where	where	SCONJ
ejpam-7015	69	41	ω(x	ω(x	X
ejpam-7015	69	42	,	,	PUNCT
ejpam-7015	69	43	y	y	NOUN
ejpam-7015	69	44	)	)	PUNCT
ejpam-7015	69	45	=	=	SYM
ejpam-7015	70	1	xג	xג	PROPN
ejpam-7015	70	2	∨	∨	NUM
ejpam-7015	70	3	ξx	ξx	PROPN
ejpam-7015	70	4	for	for	ADP
ejpam-7015	70	5	each	each	DET
ejpam-7015	70	6	(	(	PUNCT
ejpam-7015	70	7	x	x	NOUN
ejpam-7015	70	8	,	,	PUNCT
ejpam-7015	70	9	y	y	NOUN
ejpam-7015	70	10	)	)	PUNCT
ejpam-7015	70	11	∈	∈	PROPN
ejpam-7015	70	12	u×	u×	PROPN
ejpam-7015	70	13	h.	h.	NOUN
ejpam-7015	70	14	definition	definition	NOUN
ejpam-7015	70	15	8	8	NUM
ejpam-7015	70	16	.	.	PUNCT
ejpam-7015	71	1	let	let	VERB
ejpam-7015	71	2	(	(	PUNCT
ejpam-7015	71	3	u	u	NOUN
ejpam-7015	71	4	,	,	PUNCT
ejpam-7015	71	5	ג	ג	PROPN
ejpam-7015	71	6	)	)	PUNCT
ejpam-7015	71	7	be	be	AUX
ejpam-7015	71	8	an	an	DET
ejpam-7015	71	9	fss	fss	NOUN
ejpam-7015	71	10	.	.	PUNCT
ejpam-7015	72	1	a	a	DET
ejpam-7015	72	2	known	know	VERB
ejpam-7015	72	3	support	support	NOUN
ejpam-7015	72	4	of	of	ADP
ejpam-7015	72	5	the	the	DET
ejpam-7015	72	6	fss	fss	PROPN
ejpam-7015	72	7	(	(	PUNCT
ejpam-7015	72	8	u	u	NOUN
ejpam-7015	72	9	,	,	PUNCT
ejpam-7015	72	10	ג	ג	NOUN
ejpam-7015	72	11	)	)	PUNCT
ejpam-7015	72	12	is	be	AUX
ejpam-7015	72	13	the	the	DET
ejpam-7015	72	14	set	set	PROPN
ejpam-7015	72	15	supp(ג	supp(ג	PROPN
ejpam-7015	72	16	,	,	PUNCT
ejpam-7015	72	17	u	u	NOUN
ejpam-7015	72	18	)	)	PUNCT
ejpam-7015	72	19	=	=	SYM
ejpam-7015	73	1	{	{	PUNCT
ejpam-7015	73	2	x	x	PUNCT
ejpam-7015	73	3	∈	∈	PROPN
ejpam-7015	73	4	u	u	NOUN
ejpam-7015	73	5	:	:	PUNCT
ejpam-7015	73	6	(	(	PUNCT
ejpam-7015	73	7	x)ג	x)ג	PUNCT
ejpam-7015	73	8	=	=	SYM
ejpam-7015	73	9	xג	xג	PROPN
ejpam-7015	73	10	6=	6=	ADP
ejpam-7015	73	11	∅	∅	NOUN
ejpam-7015	73	12	}	}	PUNCT
ejpam-7015	73	13	.	.	PUNCT
ejpam-7015	74	1	an	an	DET
ejpam-7015	74	2	fss	fss	ADJ
ejpam-7015	74	3	(	(	PUNCT
ejpam-7015	74	4	u	u	NOUN
ejpam-7015	74	5	,	,	PUNCT
ejpam-7015	74	6	ג	ג	NOUN
ejpam-7015	74	7	)	)	PUNCT
ejpam-7015	74	8	is	be	AUX
ejpam-7015	74	9	said	say	VERB
ejpam-7015	74	10	to	to	PART
ejpam-7015	74	11	be	be	AUX
ejpam-7015	74	12	non	non	ADJ
ejpam-7015	74	13	-	-	ADJ
ejpam-7015	74	14	null	null	ADJ
ejpam-7015	74	15	if	if	SCONJ
ejpam-7015	74	16	its	its	PRON
ejpam-7015	74	17	support	support	NOUN
ejpam-7015	74	18	is	be	AUX
ejpam-7015	74	19	non	non	ADJ
ejpam-7015	74	20	-	-	ADJ
ejpam-7015	74	21	empty	empty	ADJ
ejpam-7015	74	22	,	,	PUNCT
ejpam-7015	74	23	i.e.	i.e.	X
ejpam-7015	74	24	,	,	PUNCT
ejpam-7015	74	25	supp(ג	supp(ג	PROPN
ejpam-7015	74	26	,	,	PUNCT
ejpam-7015	74	27	u	u	NOUN
ejpam-7015	74	28	)	)	PUNCT
ejpam-7015	74	29	6=	6=	ADP
ejpam-7015	74	30	∅.	∅.	PRON
ejpam-7015	74	31	definition	definition	NOUN
ejpam-7015	74	32	9	9	NUM
ejpam-7015	74	33	.	.	PUNCT
ejpam-7015	75	1	let	let	VERB
ejpam-7015	75	2	(	(	PUNCT
ejpam-7015	75	3	u	u	NOUN
ejpam-7015	75	4	,	,	PUNCT
ejpam-7015	75	5	ג	ג	PROPN
ejpam-7015	75	6	)	)	PUNCT
ejpam-7015	75	7	be	be	AUX
ejpam-7015	75	8	an	an	DET
ejpam-7015	75	9	fss	fss	NOUN
ejpam-7015	75	10	that	that	PRON
ejpam-7015	75	11	is	be	AUX
ejpam-7015	75	12	non	non	ADJ
ejpam-7015	75	13	-	-	ADJ
ejpam-7015	75	14	null	null	ADJ
ejpam-7015	75	15	.	.	PUNCT
ejpam-7015	76	1	if	if	SCONJ
ejpam-7015	76	2	(	(	PUNCT
ejpam-7015	76	3	a)ג	a)ג	NOUN
ejpam-7015	76	4	=	=	PRON
ejpam-7015	76	5	aג	aג	PROPN
ejpam-7015	76	6	is	be	AUX
ejpam-7015	76	7	an	an	DET
ejpam-7015	76	8	f	f	NOUN
ejpam-7015	76	9	-	-	PUNCT
ejpam-7015	76	10	sub	sub	NOUN
ejpam-7015	76	11	-	-	NOUN
ejpam-7015	76	12	br	br	NOUN
ejpam-7015	76	13	of	of	ADP
ejpam-7015	76	14	ℵ	ℵ	NOUN
ejpam-7015	76	15	for	for	ADP
ejpam-7015	76	16	each	each	DET
ejpam-7015	76	17	a	a	DET
ejpam-7015	76	18	∈	∈	PROPN
ejpam-7015	76	19	u	u	NOUN
ejpam-7015	76	20	,	,	PUNCT
ejpam-7015	76	21	then	then	ADV
ejpam-7015	76	22	(	(	PUNCT
ejpam-7015	76	23	u	u	NOUN
ejpam-7015	76	24	,	,	PUNCT
ejpam-7015	76	25	ג	ג	NOUN
ejpam-7015	76	26	)	)	PUNCT
ejpam-7015	76	27	is	be	AUX
ejpam-7015	76	28	an	an	DET
ejpam-7015	76	29	fsbr	fsbr	NOUN
ejpam-7015	76	30	of	of	ADP
ejpam-7015	76	31	ℵ	ℵ	NOUN
ejpam-7015	76	32	,	,	PUNCT
ejpam-7015	76	33	i.e.	i.e.	X
ejpam-7015	76	34	,	,	PUNCT
ejpam-7015	76	35	(	(	PUNCT
ejpam-7015	76	36	i	i	NOUN
ejpam-7015	76	37	)	)	PUNCT
ejpam-7015	76	38	−a(xג	−a(xג	PROPN
ejpam-7015	76	39	y	y	PROPN
ejpam-7015	76	40	)	)	PUNCT
ejpam-7015	76	41	≥	≥	NOUN
ejpam-7015	76	42	a(x)ג	a(x)ג	PROPN
ejpam-7015	76	43	∧	∧	PROPN
ejpam-7015	76	44	,	,	PUNCT
ejpam-7015	76	45	a(y)ג	a(y)ג	PROPN
ejpam-7015	76	46	(	(	PUNCT
ejpam-7015	76	47	ii	ii	PROPN
ejpam-7015	76	48	)	)	PUNCT
ejpam-7015	76	49	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	76	50	≥	≥	NOUN
ejpam-7015	76	51	a(x)ג	a(x)ג	PROPN
ejpam-7015	76	52	∧	∧	PROPN
ejpam-7015	76	53	,	,	PUNCT
ejpam-7015	76	54	a(y)ג	a(y)ג	PROPN
ejpam-7015	76	55	∀x	∀x	NUM
ejpam-7015	76	56	,	,	PUNCT
ejpam-7015	76	57	y	y	PROPN
ejpam-7015	76	58	∈	∈	PROPN
ejpam-7015	76	59	ℵ.	ℵ.	PROPN
ejpam-7015	76	60	definition	definition	NOUN
ejpam-7015	76	61	10	10	NUM
ejpam-7015	76	62	.	.	PUNCT
ejpam-7015	77	1	an	an	DET
ejpam-7015	77	2	fsbr	fsbr	NOUN
ejpam-7015	77	3	of	of	ADP
ejpam-7015	77	4	ℵ	ℵ	PROPN
ejpam-7015	77	5	is	be	AUX
ejpam-7015	77	6	assumed	assume	VERB
ejpam-7015	77	7	to	to	PART
ejpam-7015	77	8	be	be	AUX
ejpam-7015	77	9	.(u	.(u	PROPN
ejpam-7015	77	10	,	,	PUNCT
ejpam-7015	77	11	ג	ג	X
ejpam-7015	77	12	)	)	PUNCT
ejpam-7015	77	13	if	if	SCONJ
ejpam-7015	77	14	the	the	DET
ejpam-7015	77	15	following	follow	VERB
ejpam-7015	77	16	criteria	criterion	NOUN
ejpam-7015	77	17	are	be	AUX
ejpam-7015	77	18	met	meet	VERB
ejpam-7015	77	19	,	,	PUNCT
ejpam-7015	77	20	an	an	DET
ejpam-7015	77	21	fss	fss	ADJ
ejpam-7015	77	22	(	(	PUNCT
ejpam-7015	77	23	ξ	ξ	PROPN
ejpam-7015	77	24	,	,	PUNCT
ejpam-7015	77	25	h	h	NOUN
ejpam-7015	77	26	)	)	PUNCT
ejpam-7015	77	27	will	will	AUX
ejpam-7015	77	28	be	be	AUX
ejpam-7015	77	29	referred	refer	VERB
ejpam-7015	77	30	to	to	ADP
ejpam-7015	77	31	as	as	ADP
ejpam-7015	77	32	a	a	DET
ejpam-7015	77	33	fuzzy	fuzzy	ADJ
ejpam-7015	77	34	soft	soft	ADJ
ejpam-7015	77	35	ideal	ideal	NOUN
ejpam-7015	77	36	(	(	PUNCT
ejpam-7015	77	37	fsi	fsi	PROPN
ejpam-7015	77	38	)	)	PUNCT
ejpam-7015	77	39	of	of	ADP
ejpam-7015	77	40	,	,	PUNCT
ejpam-7015	77	41	(	(	PUNCT
ejpam-7015	77	42	u	u	NOUN
ejpam-7015	77	43	,	,	PUNCT
ejpam-7015	77	44	ג	ג	PROPN
ejpam-7015	77	45	)	)	PUNCT
ejpam-7015	77	46	symbolised	symbolise	VERB
ejpam-7015	77	47	by	by	ADP
ejpam-7015	77	48	(	(	PUNCT
ejpam-7015	77	49	ξ	ξ	PROPN
ejpam-7015	77	50	,	,	PUNCT
ejpam-7015	77	51	h)c	h)c	PUNCT
ejpam-7015	77	52	,	,	PUNCT
ejpam-7015	77	53	(	(	PUNCT
ejpam-7015	77	54	u	u	NOUN
ejpam-7015	77	55	,	,	PUNCT
ejpam-7015	77	56	ג	ג	NOUN
ejpam-7015	77	57	)	)	PUNCT
ejpam-7015	77	58	i.e.	i.e.	X
ejpam-7015	77	59	,	,	PUNCT
ejpam-7015	77	60	(	(	PUNCT
ejpam-7015	77	61	i	i	NOUN
ejpam-7015	77	62	)	)	PUNCT
ejpam-7015	77	63	h	h	PROPN
ejpam-7015	77	64	⊆	⊆	NUM
ejpam-7015	77	65	u	u	NOUN
ejpam-7015	77	66	,	,	PUNCT
ejpam-7015	77	67	(	(	PUNCT
ejpam-7015	77	68	ii	ii	NOUN
ejpam-7015	77	69	)	)	PUNCT
ejpam-7015	77	70	for	for	ADP
ejpam-7015	77	71	each	each	DET
ejpam-7015	77	72	a	a	DET
ejpam-7015	77	73	∈	∈	PROPN
ejpam-7015	77	74	supp(ξ	supp(ξ	PROPN
ejpam-7015	77	75	,	,	PUNCT
ejpam-7015	77	76	h	h	NOUN
ejpam-7015	77	77	)	)	PUNCT
ejpam-7015	77	78	,	,	PUNCT
ejpam-7015	77	79	the	the	DET
ejpam-7015	77	80	fuzzy	fuzzy	ADJ
ejpam-7015	77	81	set	set	VERB
ejpam-7015	77	82	ξa	ξa	PROPN
ejpam-7015	77	83	is	be	AUX
ejpam-7015	77	84	a	a	DET
ejpam-7015	77	85	fuzzy	fuzzy	ADJ
ejpam-7015	77	86	ideal	ideal	NOUN
ejpam-7015	77	87	(	(	PUNCT
ejpam-7015	77	88	fi	fi	NOUN
ejpam-7015	77	89	)	)	PUNCT
ejpam-7015	77	90	of	of	ADP
ejpam-7015	77	91	the	the	DET
ejpam-7015	77	92	fuzzy	fuzzy	ADJ
ejpam-7015	77	93	boolean	boolean	ADJ
ejpam-7015	77	94	ring	ring	NOUN
ejpam-7015	77	95	,	,	PUNCT
ejpam-7015	77	96	aג	aג	PROPN
ejpam-7015	77	97	i.e.	i.e.	X
ejpam-7015	77	98	,	,	PUNCT
ejpam-7015	77	99	(	(	PUNCT
ejpam-7015	77	100	i	i	NOUN
ejpam-7015	77	101	)	)	PUNCT
ejpam-7015	77	102	ξa(x−	ξa(x−	PROPN
ejpam-7015	77	103	y	y	PROPN
ejpam-7015	77	104	)	)	PUNCT
ejpam-7015	77	105	≥	≥	NOUN
ejpam-7015	77	106	ξa(x	ξa(x	NOUN
ejpam-7015	77	107	)	)	PUNCT
ejpam-7015	77	108	∧	∧	PROPN
ejpam-7015	77	109	ξa(y	ξa(y	NOUN
ejpam-7015	77	110	)	)	PUNCT
ejpam-7015	77	111	,	,	PUNCT
ejpam-7015	77	112	(	(	PUNCT
ejpam-7015	77	113	ii	ii	NOUN
ejpam-7015	77	114	)	)	PUNCT
ejpam-7015	77	115	ξa(xy	ξa(xy	PROPN
ejpam-7015	77	116	)	)	PUNCT
ejpam-7015	77	117	≥	≥	NOUN
ejpam-7015	77	118	ξa(x	ξa(x	NOUN
ejpam-7015	77	119	)	)	PUNCT
ejpam-7015	77	120	∧	∧	PROPN
ejpam-7015	77	121	ξa(y	ξa(y	NOUN
ejpam-7015	77	122	)	)	PUNCT
ejpam-7015	77	123	,	,	PUNCT
ejpam-7015	77	124	(	(	PUNCT
ejpam-7015	77	125	iii	iii	NOUN
ejpam-7015	77	126	)	)	PUNCT
ejpam-7015	78	1	ξa(x	ξa(x	ADP
ejpam-7015	78	2	)	)	PUNCT
ejpam-7015	78	3	≤	≤	NOUN
ejpam-7015	78	4	,	,	PUNCT
ejpam-7015	78	5	a(x)ג	a(x)ג	PROPN
ejpam-7015	78	6	∀x	∀x	NUM
ejpam-7015	78	7	,	,	PUNCT
ejpam-7015	78	8	y	y	PROPN
ejpam-7015	78	9	∈	∈	PROPN
ejpam-7015	78	10	ℵ.	ℵ.	PROPN
ejpam-7015	79	1	3	3	X
ejpam-7015	79	2	.	.	X
ejpam-7015	79	3	anti	anti	ADJ
ejpam-7015	79	4	-	-	ADJ
ejpam-7015	79	5	fuzzy	fuzzy	ADJ
ejpam-7015	79	6	soft	soft	ADJ
ejpam-7015	79	7	boolean	boolean	ADJ
ejpam-7015	79	8	rings	ring	NOUN
ejpam-7015	79	9	the	the	DET
ejpam-7015	79	10	concept	concept	NOUN
ejpam-7015	79	11	of	of	ADP
ejpam-7015	79	12	fsbrs	fsbrs	PROPN
ejpam-7015	79	13	was	be	AUX
ejpam-7015	79	14	proposed	propose	VERB
ejpam-7015	79	15	by	by	ADP
ejpam-7015	79	16	rao	rao	PROPN
ejpam-7015	79	17	et	et	PROPN
ejpam-7015	79	18	al	al	PROPN
ejpam-7015	79	19	.	.	PUNCT
ejpam-7015	80	1	[	[	X
ejpam-7015	80	2	11	11	NUM
ejpam-7015	80	3	]	]	PUNCT
ejpam-7015	80	4	.	.	PUNCT
ejpam-7015	81	1	in	in	ADP
ejpam-7015	81	2	this	this	DET
ejpam-7015	81	3	section	section	NOUN
ejpam-7015	81	4	,	,	PUNCT
ejpam-7015	81	5	we	we	PRON
ejpam-7015	81	6	define	define	VERB
ejpam-7015	81	7	afsbrs	afsbrs	ADJ
ejpam-7015	81	8	and	and	CCONJ
ejpam-7015	81	9	discuss	discuss	VERB
ejpam-7015	81	10	some	some	PRON
ejpam-7015	81	11	of	of	ADP
ejpam-7015	81	12	their	their	PRON
ejpam-7015	81	13	fundamental	fundamental	ADJ
ejpam-7015	81	14	properties	property	NOUN
ejpam-7015	81	15	.	.	PUNCT
ejpam-7015	82	1	ℵ	ℵ	DET
ejpam-7015	82	2	denotes	denote	NOUN
ejpam-7015	82	3	a	a	DET
ejpam-7015	82	4	br	br	NOUN
ejpam-7015	82	5	from	from	ADP
ejpam-7015	82	6	now	now	ADV
ejpam-7015	82	7	on	on	ADV
ejpam-7015	82	8	,	,	PUNCT
ejpam-7015	82	9	and	and	CCONJ
ejpam-7015	82	10	all	all	DET
ejpam-7015	82	11	fsss	fsss	NOUN
ejpam-7015	82	12	are	be	AUX
ejpam-7015	82	13	preferred	prefer	VERB
ejpam-7015	82	14	over	over	ADP
ejpam-7015	82	15	ℵ.	ℵ.	PROPN
ejpam-7015	82	16	definition	definition	NOUN
ejpam-7015	82	17	11	11	NUM
ejpam-7015	82	18	.	.	PUNCT
ejpam-7015	83	1	an	an	DET
ejpam-7015	83	2	fss	fss	ADJ
ejpam-7015	83	3	(	(	PUNCT
ejpam-7015	83	4	u	u	NOUN
ejpam-7015	83	5	,	,	PUNCT
ejpam-7015	83	6	ג	ג	NOUN
ejpam-7015	83	7	)	)	PUNCT
ejpam-7015	83	8	over	over	ADP
ejpam-7015	83	9	ℵ	ℵ	NOUN
ejpam-7015	83	10	is	be	AUX
ejpam-7015	83	11	called	call	VERB
ejpam-7015	83	12	an	an	DET
ejpam-7015	83	13	anti	anti	ADJ
ejpam-7015	83	14	-	-	ADJ
ejpam-7015	83	15	fuzzy	fuzzy	ADJ
ejpam-7015	83	16	soft	soft	ADJ
ejpam-7015	83	17	boolean	boolean	ADJ
ejpam-7015	83	18	ring	ring	NOUN
ejpam-7015	83	19	(	(	PUNCT
ejpam-7015	83	20	afsbr	afsbr	NOUN
ejpam-7015	83	21	)	)	PUNCT
ejpam-7015	83	22	of	of	ADP
ejpam-7015	83	23	ℵ	ℵ	NOUN
ejpam-7015	84	1	if	if	SCONJ
ejpam-7015	84	2	(	(	PUNCT
ejpam-7015	84	3	i	i	NOUN
ejpam-7015	84	4	)	)	PUNCT
ejpam-7015	85	1	+	+	ADP
ejpam-7015	85	2	a(xג	a(xג	PROPN
ejpam-7015	85	3	y	y	NOUN
ejpam-7015	85	4	)	)	PUNCT
ejpam-7015	85	5	≤	≤	PART
ejpam-7015	85	6	a(x)ג	a(x)ג	PROPN
ejpam-7015	85	7	∨	∨	NUM
ejpam-7015	85	8	,	,	PUNCT
ejpam-7015	85	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	85	10	(	(	PUNCT
ejpam-7015	85	11	ii	ii	PROPN
ejpam-7015	85	12	)	)	PUNCT
ejpam-7015	85	13	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	85	14	≤	≤	PROPN
ejpam-7015	85	15	a(x)ג	a(x)ג	PROPN
ejpam-7015	85	16	∨	∨	NUM
ejpam-7015	85	17	,	,	PUNCT
ejpam-7015	85	18	a(y)ג	a(y)ג	PROPN
ejpam-7015	85	19	∀x	∀x	NUM
ejpam-7015	85	20	,	,	PUNCT
ejpam-7015	85	21	y	y	PROPN
ejpam-7015	85	22	∈	∈	PROPN
ejpam-7015	85	23	ℵ.	ℵ.	PROPN
ejpam-7015	85	24	example	example	NOUN
ejpam-7015	86	1	1	1	X
ejpam-7015	86	2	.	.	PUNCT
ejpam-7015	87	1	let	let	VERB
ejpam-7015	87	2	ℵ	ℵ	NOUN
ejpam-7015	87	3	=	=	SYM
ejpam-7015	87	4	{	{	PUNCT
ejpam-7015	87	5	0	0	NUM
ejpam-7015	87	6	,	,	PUNCT
ejpam-7015	87	7	a∗	a∗	ADJ
ejpam-7015	87	8	,	,	PUNCT
ejpam-7015	87	9	c∗	c∗	PROPN
ejpam-7015	87	10	,	,	PUNCT
ejpam-7015	87	11	n∗	n∗	PROPN
ejpam-7015	87	12	}	}	PUNCT
ejpam-7015	87	13	be	be	VERB
ejpam-7015	87	14	a	a	DET
ejpam-7015	87	15	non	non	ADJ
ejpam-7015	87	16	-	-	ADJ
ejpam-7015	87	17	empty	empty	ADJ
ejpam-7015	87	18	set	set	NOUN
ejpam-7015	87	19	with	with	ADP
ejpam-7015	87	20	two	two	NUM
ejpam-7015	87	21	binary	binary	ADJ
ejpam-7015	87	22	operations	operation	NOUN
ejpam-7015	87	23	+	+	CCONJ
ejpam-7015	87	24	and	and	CCONJ
ejpam-7015	87	25	·	·	PUNCT
ejpam-7015	87	26	defined	define	VERB
ejpam-7015	87	27	as	as	SCONJ
ejpam-7015	87	28	follows	follow	VERB
ejpam-7015	87	29	:	:	PUNCT
ejpam-7015	88	1	d.	d.	PROPN
ejpam-7015	88	2	ramesh	ramesh	PROPN
ejpam-7015	88	3	et	et	PROPN
ejpam-7015	88	4	al	al	PROPN
ejpam-7015	88	5	.	.	PUNCT
ejpam-7015	88	6	/	/	SYM
ejpam-7015	88	7	eur	eur	PROPN
ejpam-7015	88	8	.	.	PUNCT
ejpam-7015	89	1	j.	j.	PROPN
ejpam-7015	89	2	pure	pure	PROPN
ejpam-7015	89	3	appl	appl	PROPN
ejpam-7015	89	4	.	.	PROPN
ejpam-7015	89	5	math	math	PROPN
ejpam-7015	89	6	,	,	PUNCT
ejpam-7015	89	7	18	18	NUM
ejpam-7015	89	8	(	(	PUNCT
ejpam-7015	89	9	4	4	NUM
ejpam-7015	89	10	)	)	PUNCT
ejpam-7015	89	11	(	(	PUNCT
ejpam-7015	89	12	2025	2025	NUM
ejpam-7015	89	13	)	)	PUNCT
ejpam-7015	89	14	,	,	PUNCT
ejpam-7015	89	15	7015	7015	NUM
ejpam-7015	89	16	5	5	NUM
ejpam-7015	89	17	of	of	ADP
ejpam-7015	89	18	11	11	NUM
ejpam-7015	89	19	+	+	SYM
ejpam-7015	89	20	0	0	NUM
ejpam-7015	89	21	a∗	a∗	PROPN
ejpam-7015	89	22	c∗	c∗	PROPN
ejpam-7015	89	23	n∗	n∗	PROPN
ejpam-7015	89	24	0	0	NUM
ejpam-7015	89	25	0	0	NUM
ejpam-7015	89	26	a∗	a∗	PROPN
ejpam-7015	89	27	c∗	c∗	PROPN
ejpam-7015	89	28	n∗	n∗	VERB
ejpam-7015	89	29	a∗	a∗	PROPN
ejpam-7015	89	30	a∗	a∗	PROPN
ejpam-7015	89	31	0	0	NUM
ejpam-7015	89	32	n∗	n∗	PROPN
ejpam-7015	89	33	c∗	c∗	PROPN
ejpam-7015	89	34	c∗	c∗	PROPN
ejpam-7015	89	35	c∗	c∗	PROPN
ejpam-7015	89	36	n∗	n∗	PROPN
ejpam-7015	89	37	0	0	NUM
ejpam-7015	89	38	a∗	a∗	PROPN
ejpam-7015	89	39	n∗	n∗	PROPN
ejpam-7015	89	40	n∗	n∗	VERB
ejpam-7015	89	41	c∗	c∗	PROPN
ejpam-7015	89	42	a∗	a∗	PROPN
ejpam-7015	89	43	0	0	NUM
ejpam-7015	89	44	·	·	SYM
ejpam-7015	89	45	0	0	NUM
ejpam-7015	89	46	a∗	a∗	PROPN
ejpam-7015	89	47	c∗	c∗	PROPN
ejpam-7015	89	48	n∗	n∗	PROPN
ejpam-7015	89	49	0	0	NUM
ejpam-7015	89	50	0	0	NUM
ejpam-7015	89	51	0	0	NUM
ejpam-7015	89	52	0	0	NUM
ejpam-7015	89	53	0	0	NUM
ejpam-7015	89	54	a∗	a∗	PROPN
ejpam-7015	89	55	0	0	NUM
ejpam-7015	89	56	a∗	a∗	PROPN
ejpam-7015	89	57	n∗	n∗	PROPN
ejpam-7015	89	58	c∗	c∗	PROPN
ejpam-7015	89	59	c∗	c∗	PROPN
ejpam-7015	89	60	0	0	NUM
ejpam-7015	90	1	n∗	n∗	PROPN
ejpam-7015	90	2	c∗	c∗	PROPN
ejpam-7015	90	3	a∗	a∗	PROPN
ejpam-7015	90	4	n∗	n∗	PROPN
ejpam-7015	90	5	0	0	NUM
ejpam-7015	90	6	c∗	c∗	PROPN
ejpam-7015	90	7	a∗	a∗	PROPN
ejpam-7015	90	8	n∗	n∗	PROPN
ejpam-7015	90	9	let	let	VERB
ejpam-7015	90	10	u	u	PRON
ejpam-7015	90	11	=	=	X
ejpam-7015	90	12	{	{	PUNCT
ejpam-7015	90	13	ι11	ι11	NOUN
ejpam-7015	90	14	,	,	PUNCT
ejpam-7015	90	15	ι12	ι12	NOUN
ejpam-7015	90	16	,	,	PUNCT
ejpam-7015	90	17	ι13	ι13	NOUN
ejpam-7015	90	18	}	}	PUNCT
ejpam-7015	90	19	be	be	VERB
ejpam-7015	90	20	the	the	DET
ejpam-7015	90	21	set	set	NOUN
ejpam-7015	90	22	of	of	ADP
ejpam-7015	90	23	parameters	parameter	NOUN
ejpam-7015	90	24	and	and	CCONJ
ejpam-7015	90	25	now	now	ADV
ejpam-7015	90	26	define	define	VERB
ejpam-7015	90	27	a	a	DET
ejpam-7015	90	28	fss	fss	ADJ
ejpam-7015	90	29	(	(	PUNCT
ejpam-7015	90	30	u	u	NOUN
ejpam-7015	90	31	,	,	PUNCT
ejpam-7015	90	32	ג	ג	NOUN
ejpam-7015	90	33	)	)	PUNCT
ejpam-7015	90	34	over	over	ADP
ejpam-7015	90	35	ℵ	ℵ	NOUN
ejpam-7015	90	36	as	as	SCONJ
ejpam-7015	90	37	follows	follow	VERB
ejpam-7015	90	38	:	:	PUNCT
ejpam-7015	90	39	(	(	PUNCT
ejpam-7015	90	40	ι11)ג	ι11)ג	PUNCT
ejpam-7015	90	41	=	=	X
ejpam-7015	90	42	{	{	PUNCT
ejpam-7015	90	43	(	(	PUNCT
ejpam-7015	90	44	0	0	NUM
ejpam-7015	90	45	,	,	PUNCT
ejpam-7015	90	46	0.9	0.9	NUM
ejpam-7015	90	47	)	)	PUNCT
ejpam-7015	90	48	,	,	PUNCT
ejpam-7015	90	49	(	(	PUNCT
ejpam-7015	90	50	a∗	a∗	ADJ
ejpam-7015	90	51	,	,	PUNCT
ejpam-7015	90	52	0.6	0.6	NUM
ejpam-7015	90	53	)	)	PUNCT
ejpam-7015	90	54	,	,	PUNCT
ejpam-7015	90	55	(	(	PUNCT
ejpam-7015	90	56	c∗	c∗	PROPN
ejpam-7015	90	57	,	,	PUNCT
ejpam-7015	90	58	0.4	0.4	NUM
ejpam-7015	90	59	)	)	PUNCT
ejpam-7015	90	60	,	,	PUNCT
ejpam-7015	90	61	(	(	PUNCT
ejpam-7015	90	62	n∗	n∗	PROPN
ejpam-7015	90	63	,	,	PUNCT
ejpam-7015	90	64	0.6	0.6	NUM
ejpam-7015	90	65	)	)	PUNCT
ejpam-7015	90	66	}	}	PUNCT
ejpam-7015	90	67	(	(	PUNCT
ejpam-7015	90	68	ι12)ג	ι12)ג	PUNCT
ejpam-7015	90	69	=	=	SYM
ejpam-7015	90	70	{	{	PUNCT
ejpam-7015	90	71	(	(	PUNCT
ejpam-7015	90	72	0	0	NUM
ejpam-7015	90	73	,	,	PUNCT
ejpam-7015	90	74	0.8	0.8	NUM
ejpam-7015	90	75	)	)	PUNCT
ejpam-7015	90	76	,	,	PUNCT
ejpam-7015	90	77	(	(	PUNCT
ejpam-7015	90	78	a∗	a∗	PROPN
ejpam-7015	90	79	,	,	PUNCT
ejpam-7015	90	80	0.5	0.5	NUM
ejpam-7015	90	81	)	)	PUNCT
ejpam-7015	90	82	,	,	PUNCT
ejpam-7015	90	83	(	(	PUNCT
ejpam-7015	90	84	c∗	c∗	PROPN
ejpam-7015	90	85	,	,	PUNCT
ejpam-7015	90	86	0.5	0.5	NUM
ejpam-7015	90	87	)	)	PUNCT
ejpam-7015	90	88	,	,	PUNCT
ejpam-7015	90	89	(	(	PUNCT
ejpam-7015	90	90	n∗	n∗	PROPN
ejpam-7015	90	91	,	,	PUNCT
ejpam-7015	90	92	0.5	0.5	NUM
ejpam-7015	90	93	)	)	PUNCT
ejpam-7015	90	94	}	}	PUNCT
ejpam-7015	90	95	(	(	PUNCT
ejpam-7015	90	96	ι13)ג	ι13)ג	PUNCT
ejpam-7015	90	97	=	=	X
ejpam-7015	90	98	{	{	PUNCT
ejpam-7015	90	99	(	(	PUNCT
ejpam-7015	90	100	0	0	NUM
ejpam-7015	90	101	,	,	PUNCT
ejpam-7015	90	102	0.7	0.7	NUM
ejpam-7015	90	103	)	)	PUNCT
ejpam-7015	90	104	,	,	PUNCT
ejpam-7015	90	105	(	(	PUNCT
ejpam-7015	90	106	a∗	a∗	PROPN
ejpam-7015	90	107	,	,	PUNCT
ejpam-7015	90	108	0.3	0.3	NUM
ejpam-7015	90	109	)	)	PUNCT
ejpam-7015	90	110	,	,	PUNCT
ejpam-7015	90	111	(	(	PUNCT
ejpam-7015	90	112	c∗	c∗	PROPN
ejpam-7015	90	113	,	,	PUNCT
ejpam-7015	90	114	0.3	0.3	NUM
ejpam-7015	90	115	)	)	PUNCT
ejpam-7015	90	116	,	,	PUNCT
ejpam-7015	90	117	(	(	PUNCT
ejpam-7015	90	118	n∗	n∗	PROPN
ejpam-7015	90	119	,	,	PUNCT
ejpam-7015	90	120	0.1	0.1	NUM
ejpam-7015	90	121	)	)	PUNCT
ejpam-7015	90	122	}	}	PUNCT
ejpam-7015	90	123	hence	hence	ADV
ejpam-7015	90	124	,	,	PUNCT
ejpam-7015	90	125	(	(	PUNCT
ejpam-7015	90	126	u	u	NOUN
ejpam-7015	90	127	,	,	PUNCT
ejpam-7015	90	128	ג	ג	PROPN
ejpam-7015	90	129	)	)	PUNCT
ejpam-7015	90	130	an	an	DET
ejpam-7015	90	131	afsbr	afsbr	NOUN
ejpam-7015	90	132	of	of	ADP
ejpam-7015	90	133	ℵ.	ℵ.	PROPN
ejpam-7015	90	134	theorem	theorem	ADJ
ejpam-7015	90	135	1	1	X
ejpam-7015	90	136	.	.	PUNCT
ejpam-7015	91	1	let	let	VERB
ejpam-7015	91	2	(	(	PUNCT
ejpam-7015	91	3	u	u	NOUN
ejpam-7015	91	4	,	,	PUNCT
ejpam-7015	91	5	ג	ג	PROPN
ejpam-7015	91	6	)	)	PUNCT
ejpam-7015	91	7	and	and	CCONJ
ejpam-7015	91	8	(	(	PUNCT
ejpam-7015	91	9	ξ	ξ	PROPN
ejpam-7015	91	10	,	,	PUNCT
ejpam-7015	91	11	h	h	NOUN
ejpam-7015	91	12	)	)	PUNCT
ejpam-7015	91	13	be	be	VERB
ejpam-7015	91	14	two	two	NUM
ejpam-7015	91	15	afsbrs	afsbrs	ADJ
ejpam-7015	91	16	.	.	PUNCT
ejpam-7015	92	1	if	if	SCONJ
ejpam-7015	92	2	∧(u	∧(u	ADJ
ejpam-7015	92	3	,	,	PUNCT
ejpam-7015	92	4	ג	ג	NOUN
ejpam-7015	92	5	)	)	PUNCT
ejpam-7015	92	6	(	(	PUNCT
ejpam-7015	92	7	ξ	ξ	PROPN
ejpam-7015	92	8	,	,	PUNCT
ejpam-7015	92	9	h	h	NOUN
ejpam-7015	92	10	)	)	PUNCT
ejpam-7015	92	11	is	be	AUX
ejpam-7015	92	12	non	non	ADJ
ejpam-7015	92	13	-	-	ADJ
ejpam-7015	92	14	null	null	ADJ
ejpam-7015	92	15	,	,	PUNCT
ejpam-7015	92	16	then	then	ADV
ejpam-7015	92	17	it	it	PRON
ejpam-7015	92	18	’s	’	VERB
ejpam-7015	92	19	an	an	DET
ejpam-7015	92	20	afsbr	afsbr	NOUN
ejpam-7015	92	21	.	.	PUNCT
ejpam-7015	93	1	proof	proof	NOUN
ejpam-7015	93	2	.	.	PUNCT
ejpam-7015	94	1	let	let	VERB
ejpam-7015	94	2	us	we	PRON
ejpam-7015	94	3	take	take	VERB
ejpam-7015	94	4	(	(	PUNCT
ejpam-7015	94	5	ξ	ξ	PROPN
ejpam-7015	94	6	,	,	PUNCT
ejpam-7015	94	7	h)∧(u	h)∧(u	ADJ
ejpam-7015	94	8	,	,	PUNCT
ejpam-7015	94	9	ג	ג	NOUN
ejpam-7015	94	10	)	)	PUNCT
ejpam-7015	94	11	=	=	SYM
ejpam-7015	94	12	(	(	PUNCT
ejpam-7015	94	13	ω	ω	PROPN
ejpam-7015	94	14	,	,	PUNCT
ejpam-7015	94	15	s	s	PART
ejpam-7015	94	16	)	)	PUNCT
ejpam-7015	94	17	respectively	respectively	ADV
ejpam-7015	94	18	,	,	PUNCT
ejpam-7015	94	19	where	where	SCONJ
ejpam-7015	94	20	s	s	VERB
ejpam-7015	94	21	=	=	SYM
ejpam-7015	94	22	u×h	u×h	PROPN
ejpam-7015	94	23	and	and	CCONJ
ejpam-7015	94	24	ω(a	ω(a	PROPN
ejpam-7015	94	25	,	,	PUNCT
ejpam-7015	94	26	b	b	NOUN
ejpam-7015	94	27	)	)	PUNCT
ejpam-7015	94	28	=	=	SYM
ejpam-7015	94	29	(	(	PUNCT
ejpam-7015	94	30	a)ג	a)ג	NOUN
ejpam-7015	94	31	∧	∧	NOUN
ejpam-7015	94	32	ξ(b	ξ(b	NOUN
ejpam-7015	94	33	)	)	PUNCT
ejpam-7015	94	34	,	,	PUNCT
ejpam-7015	95	1	∀(a	∀(a	PROPN
ejpam-7015	95	2	,	,	PUNCT
ejpam-7015	95	3	b	b	X
ejpam-7015	95	4	)	)	PUNCT
ejpam-7015	95	5	∈	∈	PROPN
ejpam-7015	95	6	s.	s.	PROPN
ejpam-7015	95	7	since	since	SCONJ
ejpam-7015	95	8	(	(	PUNCT
ejpam-7015	95	9	u	u	NOUN
ejpam-7015	95	10	,	,	PUNCT
ejpam-7015	95	11	ג	ג	PROPN
ejpam-7015	95	12	)	)	PUNCT
ejpam-7015	95	13	and	and	CCONJ
ejpam-7015	95	14	(	(	PUNCT
ejpam-7015	95	15	ξ	ξ	PROPN
ejpam-7015	95	16	,	,	PUNCT
ejpam-7015	95	17	h	h	NOUN
ejpam-7015	95	18	)	)	PUNCT
ejpam-7015	95	19	are	be	AUX
ejpam-7015	95	20	afsbrs	afsbr	VERB
ejpam-7015	95	21	of	of	ADP
ejpam-7015	95	22	ℵ	ℵ	NOUN
ejpam-7015	95	23	,	,	PUNCT
ejpam-7015	95	24	we	we	PRON
ejpam-7015	95	25	have	have	AUX
ejpam-7015	95	26	∀x	∀x	NUM
ejpam-7015	95	27	,	,	PUNCT
ejpam-7015	95	28	y	y	PROPN
ejpam-7015	95	29	∈	∈	PROPN
ejpam-7015	95	30	ℵ	ℵ	NOUN
ejpam-7015	95	31	,	,	PUNCT
ejpam-7015	95	32	ω(a	ω(a	NOUN
ejpam-7015	95	33	,	,	PUNCT
ejpam-7015	95	34	b)(x+	b)(x+	NOUN
ejpam-7015	95	35	y	y	NOUN
ejpam-7015	95	36	)	)	PUNCT
ejpam-7015	95	37	=	=	PUNCT
ejpam-7015	96	1	+	+	PROPN
ejpam-7015	96	2	a(xג	a(xג	PROPN
ejpam-7015	96	3	y	y	NOUN
ejpam-7015	96	4	)	)	PUNCT
ejpam-7015	96	5	∧	∧	NOUN
ejpam-7015	96	6	ξb(x	ξb(x	NUM
ejpam-7015	96	7	)	)	PUNCT
ejpam-7015	97	1	+	+	CCONJ
ejpam-7015	97	2	y	y	X
ejpam-7015	97	3	)	)	PUNCT
ejpam-7015	97	4	≤	≤	NUM
ejpam-7015	97	5	a(x)ג	a(x)ג	PROPN
ejpam-7015	97	6	)	)	PUNCT
ejpam-7015	97	7	∨	∨	PROPN
ejpam-7015	97	8	(	(	PUNCT
ejpam-7015	97	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	97	10	∧	∧	PROPN
ejpam-7015	97	11	(	(	PUNCT
ejpam-7015	97	12	ξb(x	ξb(x	NUM
ejpam-7015	97	13	)	)	PUNCT
ejpam-7015	97	14	∨	∨	NUM
ejpam-7015	97	15	ξb(y	ξb(y	NUM
ejpam-7015	97	16	)	)	PUNCT
ejpam-7015	97	17	)	)	PUNCT
ejpam-7015	98	1	=	=	SYM
ejpam-7015	98	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	98	3	)	)	PUNCT
ejpam-7015	98	4	∧	∧	NOUN
ejpam-7015	98	5	ξb(x	ξb(x	NUM
ejpam-7015	98	6	)	)	PUNCT
ejpam-7015	98	7	)	)	PUNCT
ejpam-7015	98	8	∨	∨	PROPN
ejpam-7015	98	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	98	10	)	)	PUNCT
ejpam-7015	98	11	∧	∧	PROPN
ejpam-7015	98	12	ξb(y	ξb(y	NUM
ejpam-7015	98	13	)	)	PUNCT
ejpam-7015	98	14	)	)	PUNCT
ejpam-7015	99	1	=	=	SYM
ejpam-7015	99	2	ω(a	ω(a	PROPN
ejpam-7015	99	3	,	,	PUNCT
ejpam-7015	99	4	b)(x	b)(x	PROPN
ejpam-7015	99	5	)	)	PUNCT
ejpam-7015	99	6	∨	∨	NUM
ejpam-7015	99	7	ω(a	ω(a	PROPN
ejpam-7015	99	8	,	,	PUNCT
ejpam-7015	99	9	b)(y	b)(y	PROPN
ejpam-7015	99	10	)	)	PUNCT
ejpam-7015	99	11	,	,	PUNCT
ejpam-7015	99	12	ω(a	ω(a	PROPN
ejpam-7015	99	13	,	,	PUNCT
ejpam-7015	99	14	b)(xy	b)(xy	NOUN
ejpam-7015	99	15	)	)	PUNCT
ejpam-7015	100	1	=	=	NOUN
ejpam-7015	100	2	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	100	3	∧	∧	PROPN
ejpam-7015	100	4	ξb(xy	ξb(xy	PROPN
ejpam-7015	100	5	)	)	PUNCT
ejpam-7015	100	6	≤	≤	PROPN
ejpam-7015	100	7	a(x)ג	a(x)ג	PROPN
ejpam-7015	100	8	)	)	PUNCT
ejpam-7015	100	9	∨	∨	PROPN
ejpam-7015	100	10	(	(	PUNCT
ejpam-7015	100	11	a(y)ג	a(y)ג	PROPN
ejpam-7015	100	12	∧	∧	PROPN
ejpam-7015	100	13	(	(	PUNCT
ejpam-7015	100	14	ξb(x	ξb(x	NUM
ejpam-7015	100	15	)	)	PUNCT
ejpam-7015	100	16	∨	∨	NUM
ejpam-7015	100	17	ξb(y	ξb(y	NUM
ejpam-7015	100	18	)	)	PUNCT
ejpam-7015	100	19	)	)	PUNCT
ejpam-7015	101	1	=	=	SYM
ejpam-7015	101	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	101	3	)	)	PUNCT
ejpam-7015	101	4	∧	∧	NOUN
ejpam-7015	101	5	ξb(x	ξb(x	NUM
ejpam-7015	101	6	)	)	PUNCT
ejpam-7015	101	7	)	)	PUNCT
ejpam-7015	101	8	∨	∨	PROPN
ejpam-7015	101	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	101	10	)	)	PUNCT
ejpam-7015	101	11	∧	∧	PROPN
ejpam-7015	101	12	ξb(y	ξb(y	NUM
ejpam-7015	101	13	)	)	PUNCT
ejpam-7015	101	14	)	)	PUNCT
ejpam-7015	102	1	=	=	SYM
ejpam-7015	102	2	ω(a	ω(a	PROPN
ejpam-7015	102	3	,	,	PUNCT
ejpam-7015	102	4	b)(x	b)(x	PROPN
ejpam-7015	102	5	)	)	PUNCT
ejpam-7015	102	6	∨	∨	NUM
ejpam-7015	102	7	ω(a	ω(a	PROPN
ejpam-7015	102	8	,	,	PUNCT
ejpam-7015	102	9	b)(y	b)(y	PROPN
ejpam-7015	102	10	)	)	PUNCT
ejpam-7015	102	11	.	.	PUNCT
ejpam-7015	103	1	hence	hence	ADV
ejpam-7015	103	2	,	,	PUNCT
ejpam-7015	103	3	(	(	PUNCT
ejpam-7015	103	4	u	u	NOUN
ejpam-7015	103	5	,	,	PUNCT
ejpam-7015	103	6	ג	ג	NOUN
ejpam-7015	103	7	)	)	PUNCT
ejpam-7015	103	8	∧	∧	PROPN
ejpam-7015	103	9	(	(	PUNCT
ejpam-7015	103	10	ξ	ξ	PROPN
ejpam-7015	103	11	,	,	PUNCT
ejpam-7015	103	12	h	h	NOUN
ejpam-7015	103	13	)	)	PUNCT
ejpam-7015	103	14	is	be	AUX
ejpam-7015	103	15	an	an	DET
ejpam-7015	103	16	afsbr	afsbr	NOUN
ejpam-7015	103	17	of	of	ADP
ejpam-7015	103	18	ℵ.	ℵ.	PROPN
ejpam-7015	103	19	theorem	theorem	ADJ
ejpam-7015	103	20	2	2	X
ejpam-7015	103	21	.	.	PUNCT
ejpam-7015	104	1	let	let	VERB
ejpam-7015	104	2	(	(	PUNCT
ejpam-7015	104	3	u	u	NOUN
ejpam-7015	104	4	,	,	PUNCT
ejpam-7015	104	5	ג	ג	PROPN
ejpam-7015	104	6	)	)	PUNCT
ejpam-7015	104	7	and	and	CCONJ
ejpam-7015	104	8	(	(	PUNCT
ejpam-7015	104	9	ξ	ξ	PROPN
ejpam-7015	104	10	,	,	PUNCT
ejpam-7015	104	11	h	h	NOUN
ejpam-7015	104	12	)	)	PUNCT
ejpam-7015	104	13	be	be	VERB
ejpam-7015	104	14	two	two	NUM
ejpam-7015	104	15	afsbrs	afsbrs	ADJ
ejpam-7015	104	16	.	.	PUNCT
ejpam-7015	105	1	if	if	SCONJ
ejpam-7015	105	2	∨(u	∨(u	PROPN
ejpam-7015	105	3	,	,	PUNCT
ejpam-7015	105	4	ג	ג	NOUN
ejpam-7015	105	5	)	)	PUNCT
ejpam-7015	105	6	(	(	PUNCT
ejpam-7015	105	7	ξ	ξ	PROPN
ejpam-7015	105	8	,	,	PUNCT
ejpam-7015	105	9	h	h	NOUN
ejpam-7015	105	10	)	)	PUNCT
ejpam-7015	105	11	is	be	AUX
ejpam-7015	105	12	non	non	ADJ
ejpam-7015	105	13	-	-	ADJ
ejpam-7015	105	14	null	null	ADJ
ejpam-7015	105	15	,	,	PUNCT
ejpam-7015	105	16	then	then	ADV
ejpam-7015	105	17	it	it	PRON
ejpam-7015	105	18	’s	’	VERB
ejpam-7015	105	19	an	an	DET
ejpam-7015	105	20	afsbr	afsbr	NOUN
ejpam-7015	105	21	.	.	PUNCT
ejpam-7015	106	1	proof	proof	NOUN
ejpam-7015	106	2	.	.	PUNCT
ejpam-7015	107	1	let	let	VERB
ejpam-7015	107	2	us	we	PRON
ejpam-7015	107	3	take	take	VERB
ejpam-7015	107	4	(	(	PUNCT
ejpam-7015	107	5	ξ	ξ	NOUN
ejpam-7015	107	6	,	,	PUNCT
ejpam-7015	107	7	h)∨(u	h)∨(u	NOUN
ejpam-7015	107	8	,	,	PUNCT
ejpam-7015	107	9	ג	ג	NOUN
ejpam-7015	107	10	)	)	PUNCT
ejpam-7015	107	11	=	=	SYM
ejpam-7015	107	12	(	(	PUNCT
ejpam-7015	107	13	ω	ω	PROPN
ejpam-7015	107	14	,	,	PUNCT
ejpam-7015	107	15	s	s	PART
ejpam-7015	107	16	)	)	PUNCT
ejpam-7015	107	17	respectively	respectively	ADV
ejpam-7015	107	18	,	,	PUNCT
ejpam-7015	107	19	where	where	SCONJ
ejpam-7015	107	20	s	s	VERB
ejpam-7015	107	21	=	=	SYM
ejpam-7015	107	22	u×h	u×h	PROPN
ejpam-7015	107	23	and	and	CCONJ
ejpam-7015	107	24	ω(a	ω(a	PROPN
ejpam-7015	107	25	,	,	PUNCT
ejpam-7015	107	26	b	b	NOUN
ejpam-7015	107	27	)	)	PUNCT
ejpam-7015	107	28	=	=	SYM
ejpam-7015	107	29	(	(	PUNCT
ejpam-7015	108	1	a)ג	a)ג	X
ejpam-7015	108	2	∨	∨	NUM
ejpam-7015	108	3	ξ(b	ξ(b	NOUN
ejpam-7015	108	4	)	)	PUNCT
ejpam-7015	108	5	,	,	PUNCT
ejpam-7015	108	6	∀(a	∀(a	PROPN
ejpam-7015	108	7	,	,	PUNCT
ejpam-7015	108	8	b	b	X
ejpam-7015	108	9	)	)	PUNCT
ejpam-7015	108	10	∈	∈	PROPN
ejpam-7015	108	11	s.	s.	PROPN
ejpam-7015	108	12	since	since	SCONJ
ejpam-7015	108	13	(	(	PUNCT
ejpam-7015	108	14	u	u	NOUN
ejpam-7015	108	15	,	,	PUNCT
ejpam-7015	108	16	ג	ג	PROPN
ejpam-7015	108	17	)	)	PUNCT
ejpam-7015	108	18	and	and	CCONJ
ejpam-7015	108	19	(	(	PUNCT
ejpam-7015	108	20	ξ	ξ	PROPN
ejpam-7015	108	21	,	,	PUNCT
ejpam-7015	108	22	h	h	NOUN
ejpam-7015	108	23	)	)	PUNCT
ejpam-7015	108	24	are	be	AUX
ejpam-7015	108	25	afsbrs	afsbr	VERB
ejpam-7015	108	26	of	of	ADP
ejpam-7015	108	27	ℵ	ℵ	NOUN
ejpam-7015	108	28	,	,	PUNCT
ejpam-7015	108	29	we	we	PRON
ejpam-7015	108	30	have	have	VERB
ejpam-7015	108	31	∀x	∀x	NUM
ejpam-7015	108	32	,	,	PUNCT
ejpam-7015	108	33	y	y	PROPN
ejpam-7015	108	34	∈	∈	PROPN
ejpam-7015	108	35	ℵ	ℵ	NOUN
ejpam-7015	108	36	,	,	PUNCT
ejpam-7015	108	37	ω(a	ω(a	NOUN
ejpam-7015	108	38	,	,	PUNCT
ejpam-7015	108	39	b)(x+	b)(x+	NOUN
ejpam-7015	108	40	y	y	NOUN
ejpam-7015	108	41	)	)	PUNCT
ejpam-7015	108	42	=	=	PUNCT
ejpam-7015	109	1	+	+	PROPN
ejpam-7015	109	2	a(xג	a(xג	PROPN
ejpam-7015	109	3	y	y	PROPN
ejpam-7015	109	4	)	)	PUNCT
ejpam-7015	109	5	∨	∨	PROPN
ejpam-7015	109	6	ξb(x+	ξb(x+	PROPN
ejpam-7015	109	7	y	y	PROPN
ejpam-7015	109	8	)	)	PUNCT
ejpam-7015	109	9	≤	≤	PROPN
ejpam-7015	109	10	a(x)ג	a(x)ג	PROPN
ejpam-7015	109	11	)	)	PUNCT
ejpam-7015	109	12	∨	∨	PROPN
ejpam-7015	109	13	(	(	PUNCT
ejpam-7015	109	14	a(y)ג	a(y)ג	PROPN
ejpam-7015	109	15	∨	∨	PROPN
ejpam-7015	109	16	(	(	PUNCT
ejpam-7015	109	17	ξb(x	ξb(x	NUM
ejpam-7015	109	18	)	)	PUNCT
ejpam-7015	109	19	∨	∨	NUM
ejpam-7015	109	20	ξb(y	ξb(y	NUM
ejpam-7015	109	21	)	)	PUNCT
ejpam-7015	109	22	)	)	PUNCT
ejpam-7015	110	1	=	=	SYM
ejpam-7015	110	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	110	3	)	)	PUNCT
ejpam-7015	110	4	∨	∨	NUM
ejpam-7015	110	5	ξb(x	ξb(x	NUM
ejpam-7015	110	6	)	)	PUNCT
ejpam-7015	110	7	)	)	PUNCT
ejpam-7015	110	8	∨	∨	PROPN
ejpam-7015	110	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	110	10	)	)	PUNCT
ejpam-7015	110	11	∨	∨	NUM
ejpam-7015	110	12	ξb(y	ξb(y	NUM
ejpam-7015	110	13	)	)	PUNCT
ejpam-7015	110	14	)	)	PUNCT
ejpam-7015	111	1	=	=	SYM
ejpam-7015	111	2	ω(a	ω(a	PROPN
ejpam-7015	111	3	,	,	PUNCT
ejpam-7015	111	4	b)(x	b)(x	PROPN
ejpam-7015	111	5	)	)	PUNCT
ejpam-7015	111	6	∨	∨	NUM
ejpam-7015	111	7	ω(a	ω(a	PROPN
ejpam-7015	111	8	,	,	PUNCT
ejpam-7015	111	9	b)(y	b)(y	PROPN
ejpam-7015	111	10	)	)	PUNCT
ejpam-7015	111	11	,	,	PUNCT
ejpam-7015	111	12	d.	d.	PROPN
ejpam-7015	111	13	ramesh	ramesh	PROPN
ejpam-7015	111	14	et	et	PROPN
ejpam-7015	111	15	al	al	PROPN
ejpam-7015	111	16	.	.	PUNCT
ejpam-7015	111	17	/	/	SYM
ejpam-7015	111	18	eur	eur	PROPN
ejpam-7015	111	19	.	.	PUNCT
ejpam-7015	112	1	j.	j.	PROPN
ejpam-7015	112	2	pure	pure	PROPN
ejpam-7015	112	3	appl	appl	PROPN
ejpam-7015	112	4	.	.	PROPN
ejpam-7015	112	5	math	math	PROPN
ejpam-7015	112	6	,	,	PUNCT
ejpam-7015	112	7	18	18	NUM
ejpam-7015	112	8	(	(	PUNCT
ejpam-7015	112	9	4	4	NUM
ejpam-7015	112	10	)	)	PUNCT
ejpam-7015	112	11	(	(	PUNCT
ejpam-7015	112	12	2025	2025	NUM
ejpam-7015	112	13	)	)	PUNCT
ejpam-7015	112	14	,	,	PUNCT
ejpam-7015	112	15	7015	7015	NUM
ejpam-7015	112	16	6	6	NUM
ejpam-7015	112	17	of	of	ADP
ejpam-7015	112	18	11	11	NUM
ejpam-7015	112	19	ω(a	ω(a	NOUN
ejpam-7015	112	20	,	,	PUNCT
ejpam-7015	112	21	b)(xy	b)(xy	NOUN
ejpam-7015	112	22	)	)	PUNCT
ejpam-7015	113	1	=	=	SYM
ejpam-7015	113	2	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	113	3	∨	∨	PROPN
ejpam-7015	113	4	ξb(xy	ξb(xy	PROPN
ejpam-7015	113	5	)	)	PUNCT
ejpam-7015	113	6	≤	≤	PROPN
ejpam-7015	113	7	a(x)ג	a(x)ג	PROPN
ejpam-7015	113	8	)	)	PUNCT
ejpam-7015	113	9	∨	∨	PROPN
ejpam-7015	113	10	(	(	PUNCT
ejpam-7015	113	11	a(y)ג	a(y)ג	PROPN
ejpam-7015	113	12	∨	∨	PROPN
ejpam-7015	113	13	(	(	PUNCT
ejpam-7015	113	14	ξb(x	ξb(x	NUM
ejpam-7015	113	15	)	)	PUNCT
ejpam-7015	113	16	∨	∨	NUM
ejpam-7015	113	17	ξb(y	ξb(y	NUM
ejpam-7015	113	18	)	)	PUNCT
ejpam-7015	113	19	)	)	PUNCT
ejpam-7015	114	1	=	=	SYM
ejpam-7015	114	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	114	3	)	)	PUNCT
ejpam-7015	114	4	∨	∨	NUM
ejpam-7015	114	5	ξb(x	ξb(x	NUM
ejpam-7015	114	6	)	)	PUNCT
ejpam-7015	114	7	)	)	PUNCT
ejpam-7015	114	8	∨	∨	PROPN
ejpam-7015	114	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	114	10	)	)	PUNCT
ejpam-7015	114	11	∨	∨	NUM
ejpam-7015	114	12	ξb(y	ξb(y	NUM
ejpam-7015	114	13	)	)	PUNCT
ejpam-7015	114	14	)	)	PUNCT
ejpam-7015	115	1	=	=	SYM
ejpam-7015	115	2	ω(a	ω(a	PROPN
ejpam-7015	115	3	,	,	PUNCT
ejpam-7015	115	4	b)(x	b)(x	PROPN
ejpam-7015	115	5	)	)	PUNCT
ejpam-7015	115	6	∨	∨	NUM
ejpam-7015	115	7	ω(a	ω(a	PROPN
ejpam-7015	115	8	,	,	PUNCT
ejpam-7015	115	9	b)(y	b)(y	PROPN
ejpam-7015	115	10	)	)	PUNCT
ejpam-7015	115	11	.	.	PUNCT
ejpam-7015	116	1	hence	hence	ADV
ejpam-7015	116	2	,	,	PUNCT
ejpam-7015	116	3	(	(	PUNCT
ejpam-7015	116	4	u	u	NOUN
ejpam-7015	116	5	,	,	PUNCT
ejpam-7015	116	6	ג	ג	PROPN
ejpam-7015	116	7	)	)	PUNCT
ejpam-7015	116	8	∨	∨	NOUN
ejpam-7015	116	9	(	(	PUNCT
ejpam-7015	116	10	ξ	ξ	PROPN
ejpam-7015	116	11	,	,	PUNCT
ejpam-7015	116	12	h	h	NOUN
ejpam-7015	116	13	)	)	PUNCT
ejpam-7015	116	14	is	be	AUX
ejpam-7015	116	15	an	an	DET
ejpam-7015	116	16	afsbr	afsbr	NOUN
ejpam-7015	116	17	of	of	ADP
ejpam-7015	116	18	ℵ.	ℵ.	PROPN
ejpam-7015	116	19	theorem	theorem	ADJ
ejpam-7015	116	20	3	3	X
ejpam-7015	116	21	.	.	PUNCT
ejpam-7015	117	1	let	let	VERB
ejpam-7015	117	2	(	(	PUNCT
ejpam-7015	117	3	u	u	NOUN
ejpam-7015	117	4	,	,	PUNCT
ejpam-7015	117	5	ג	ג	PROPN
ejpam-7015	117	6	)	)	PUNCT
ejpam-7015	117	7	and	and	CCONJ
ejpam-7015	117	8	(	(	PUNCT
ejpam-7015	117	9	ξ	ξ	PROPN
ejpam-7015	117	10	,	,	PUNCT
ejpam-7015	117	11	h	h	NOUN
ejpam-7015	117	12	)	)	PUNCT
ejpam-7015	117	13	be	be	VERB
ejpam-7015	117	14	two	two	NUM
ejpam-7015	117	15	afsbrs	afsbrs	ADJ
ejpam-7015	117	16	.	.	PUNCT
ejpam-7015	118	1	if	if	SCONJ
ejpam-7015	118	2	∩(u	∩(u	PROPN
ejpam-7015	118	3	,	,	PUNCT
ejpam-7015	118	4	ג	ג	NOUN
ejpam-7015	118	5	)	)	PUNCT
ejpam-7015	118	6	(	(	PUNCT
ejpam-7015	118	7	ξ	ξ	PROPN
ejpam-7015	118	8	,	,	PUNCT
ejpam-7015	118	9	h	h	NOUN
ejpam-7015	118	10	)	)	PUNCT
ejpam-7015	118	11	is	be	AUX
ejpam-7015	118	12	non	non	ADJ
ejpam-7015	118	13	-	-	ADJ
ejpam-7015	118	14	null	null	ADJ
ejpam-7015	118	15	,	,	PUNCT
ejpam-7015	118	16	then	then	ADV
ejpam-7015	118	17	it	it	PRON
ejpam-7015	118	18	’s	’	VERB
ejpam-7015	118	19	an	an	DET
ejpam-7015	118	20	afsbr	afsbr	NOUN
ejpam-7015	118	21	.	.	PUNCT
ejpam-7015	119	1	proof	proof	NOUN
ejpam-7015	119	2	.	.	PUNCT
ejpam-7015	120	1	let	let	VERB
ejpam-7015	120	2	us	we	PRON
ejpam-7015	120	3	take	take	VERB
ejpam-7015	120	4	∩(u	∩(u	PROPN
ejpam-7015	120	5	,	,	PUNCT
ejpam-7015	120	6	ג	ג	NOUN
ejpam-7015	120	7	)	)	PUNCT
ejpam-7015	120	8	(	(	PUNCT
ejpam-7015	120	9	ξ	ξ	PROPN
ejpam-7015	120	10	,	,	PUNCT
ejpam-7015	120	11	h	h	NOUN
ejpam-7015	120	12	)	)	PUNCT
ejpam-7015	120	13	=	=	SYM
ejpam-7015	120	14	(	(	PUNCT
ejpam-7015	120	15	ω	ω	PROPN
ejpam-7015	120	16	,	,	PUNCT
ejpam-7015	120	17	s	s	PART
ejpam-7015	120	18	)	)	PUNCT
ejpam-7015	120	19	respectively	respectively	ADV
ejpam-7015	120	20	,	,	PUNCT
ejpam-7015	120	21	where	where	SCONJ
ejpam-7015	120	22	s	s	AUX
ejpam-7015	120	23	=	=	X
ejpam-7015	120	24	u∩h	u∩h	ADJ
ejpam-7015	120	25	and	and	CCONJ
ejpam-7015	120	26	ω(a	ω(a	PROPN
ejpam-7015	120	27	,	,	PUNCT
ejpam-7015	120	28	b	b	NOUN
ejpam-7015	120	29	)	)	PUNCT
ejpam-7015	120	30	=	=	SYM
ejpam-7015	120	31	(	(	PUNCT
ejpam-7015	121	1	a)ג	a)ג	NOUN
ejpam-7015	121	2	∩	∩	NOUN
ejpam-7015	121	3	ξ(b	ξ(b	NOUN
ejpam-7015	121	4	)	)	PUNCT
ejpam-7015	121	5	,	,	PUNCT
ejpam-7015	121	6	∀(a	∀(a	PROPN
ejpam-7015	121	7	,	,	PUNCT
ejpam-7015	121	8	b	b	X
ejpam-7015	121	9	)	)	PUNCT
ejpam-7015	121	10	∈	∈	PROPN
ejpam-7015	121	11	s.	s.	PROPN
ejpam-7015	121	12	since	since	SCONJ
ejpam-7015	121	13	(	(	PUNCT
ejpam-7015	121	14	u	u	NOUN
ejpam-7015	121	15	,	,	PUNCT
ejpam-7015	121	16	ג	ג	PROPN
ejpam-7015	121	17	)	)	PUNCT
ejpam-7015	121	18	and	and	CCONJ
ejpam-7015	121	19	(	(	PUNCT
ejpam-7015	121	20	ξ	ξ	PROPN
ejpam-7015	121	21	,	,	PUNCT
ejpam-7015	121	22	h	h	NOUN
ejpam-7015	121	23	)	)	PUNCT
ejpam-7015	121	24	are	be	AUX
ejpam-7015	121	25	afsbrs	afsbr	VERB
ejpam-7015	121	26	of	of	ADP
ejpam-7015	121	27	ℵ	ℵ	NOUN
ejpam-7015	121	28	,	,	PUNCT
ejpam-7015	121	29	we	we	PRON
ejpam-7015	121	30	have	have	AUX
ejpam-7015	121	31	∀x	∀x	NUM
ejpam-7015	121	32	,	,	PUNCT
ejpam-7015	121	33	y	y	PROPN
ejpam-7015	121	34	∈	∈	PROPN
ejpam-7015	121	35	ℵ	ℵ	NOUN
ejpam-7015	121	36	,	,	PUNCT
ejpam-7015	121	37	ω(a	ω(a	NOUN
ejpam-7015	121	38	,	,	PUNCT
ejpam-7015	121	39	b)(x+	b)(x+	NOUN
ejpam-7015	121	40	y	y	NOUN
ejpam-7015	121	41	)	)	PUNCT
ejpam-7015	121	42	=	=	PUNCT
ejpam-7015	122	1	+	+	PROPN
ejpam-7015	122	2	a(xג	a(xג	PROPN
ejpam-7015	122	3	y	y	NOUN
ejpam-7015	122	4	)	)	PUNCT
ejpam-7015	122	5	∩	∩	PROPN
ejpam-7015	122	6	ξb(x+	ξb(x+	PROPN
ejpam-7015	122	7	y	y	PROPN
ejpam-7015	122	8	)	)	PUNCT
ejpam-7015	122	9	≤	≤	PROPN
ejpam-7015	122	10	a(x)ג	a(x)ג	PROPN
ejpam-7015	122	11	)	)	PUNCT
ejpam-7015	122	12	∨	∨	PROPN
ejpam-7015	122	13	(	(	PUNCT
ejpam-7015	122	14	a(y)ג	a(y)ג	PROPN
ejpam-7015	122	15	∩	∩	PROPN
ejpam-7015	122	16	(	(	PUNCT
ejpam-7015	122	17	ξb(x	ξb(x	NUM
ejpam-7015	122	18	)	)	PUNCT
ejpam-7015	122	19	∨	∨	NUM
ejpam-7015	122	20	ξb(y	ξb(y	NUM
ejpam-7015	122	21	)	)	PUNCT
ejpam-7015	122	22	)	)	PUNCT
ejpam-7015	123	1	=	=	SYM
ejpam-7015	123	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	123	3	)	)	PUNCT
ejpam-7015	123	4	∩	∩	NOUN
ejpam-7015	123	5	ξb(x	ξb(x	NUM
ejpam-7015	123	6	)	)	PUNCT
ejpam-7015	123	7	)	)	PUNCT
ejpam-7015	123	8	∨	∨	PROPN
ejpam-7015	123	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	123	10	)	)	PUNCT
ejpam-7015	123	11	∩	∩	NOUN
ejpam-7015	123	12	ξb(y	ξb(y	NUM
ejpam-7015	123	13	)	)	PUNCT
ejpam-7015	123	14	)	)	PUNCT
ejpam-7015	124	1	=	=	SYM
ejpam-7015	124	2	ω(a	ω(a	PROPN
ejpam-7015	124	3	,	,	PUNCT
ejpam-7015	124	4	b)(x	b)(x	PROPN
ejpam-7015	124	5	)	)	PUNCT
ejpam-7015	124	6	∨	∨	NUM
ejpam-7015	124	7	ω(a	ω(a	PROPN
ejpam-7015	124	8	,	,	PUNCT
ejpam-7015	124	9	b)(y	b)(y	PROPN
ejpam-7015	124	10	)	)	PUNCT
ejpam-7015	124	11	,	,	PUNCT
ejpam-7015	124	12	ω(a	ω(a	PROPN
ejpam-7015	124	13	,	,	PUNCT
ejpam-7015	124	14	b)(xy	b)(xy	NOUN
ejpam-7015	124	15	)	)	PUNCT
ejpam-7015	124	16	=	=	SYM
ejpam-7015	125	1	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	125	2	∩	∩	PROPN
ejpam-7015	125	3	ξb(xy	ξb(xy	PROPN
ejpam-7015	125	4	)	)	PUNCT
ejpam-7015	125	5	≤	≤	PROPN
ejpam-7015	125	6	a(x)ג	a(x)ג	PROPN
ejpam-7015	125	7	)	)	PUNCT
ejpam-7015	125	8	∨	∨	PROPN
ejpam-7015	125	9	(	(	PUNCT
ejpam-7015	125	10	a(y)ג	a(y)ג	PROPN
ejpam-7015	125	11	∩	∩	PROPN
ejpam-7015	125	12	(	(	PUNCT
ejpam-7015	125	13	ξb(x	ξb(x	NUM
ejpam-7015	125	14	)	)	PUNCT
ejpam-7015	125	15	∨	∨	NUM
ejpam-7015	125	16	ξb(y	ξb(y	NUM
ejpam-7015	125	17	)	)	PUNCT
ejpam-7015	125	18	)	)	PUNCT
ejpam-7015	126	1	=	=	SYM
ejpam-7015	126	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	126	3	)	)	PUNCT
ejpam-7015	126	4	∩	∩	NOUN
ejpam-7015	126	5	ξb(x	ξb(x	NUM
ejpam-7015	126	6	)	)	PUNCT
ejpam-7015	126	7	)	)	PUNCT
ejpam-7015	126	8	∨	∨	PROPN
ejpam-7015	126	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	126	10	)	)	PUNCT
ejpam-7015	126	11	∩	∩	NOUN
ejpam-7015	126	12	ξb(y	ξb(y	NUM
ejpam-7015	126	13	)	)	PUNCT
ejpam-7015	126	14	)	)	PUNCT
ejpam-7015	127	1	=	=	SYM
ejpam-7015	127	2	ω(a	ω(a	PROPN
ejpam-7015	127	3	,	,	PUNCT
ejpam-7015	127	4	b)(x	b)(x	PROPN
ejpam-7015	127	5	)	)	PUNCT
ejpam-7015	127	6	∨	∨	NUM
ejpam-7015	127	7	ω(a	ω(a	PROPN
ejpam-7015	127	8	,	,	PUNCT
ejpam-7015	127	9	b)(y	b)(y	PROPN
ejpam-7015	127	10	)	)	PUNCT
ejpam-7015	127	11	.	.	PUNCT
ejpam-7015	128	1	hence	hence	ADV
ejpam-7015	128	2	,	,	PUNCT
ejpam-7015	128	3	(	(	PUNCT
ejpam-7015	128	4	u	u	NOUN
ejpam-7015	128	5	,	,	PUNCT
ejpam-7015	128	6	ג	ג	NOUN
ejpam-7015	128	7	)	)	PUNCT
ejpam-7015	128	8	∩	∩	NOUN
ejpam-7015	128	9	(	(	PUNCT
ejpam-7015	128	10	ξ	ξ	PROPN
ejpam-7015	128	11	,	,	PUNCT
ejpam-7015	128	12	h	h	NOUN
ejpam-7015	128	13	)	)	PUNCT
ejpam-7015	128	14	is	be	AUX
ejpam-7015	128	15	an	an	DET
ejpam-7015	128	16	afsbr	afsbr	NOUN
ejpam-7015	128	17	of	of	ADP
ejpam-7015	128	18	ℵ.	ℵ.	PROPN
ejpam-7015	128	19	theorem	theorem	ADJ
ejpam-7015	128	20	4	4	X
ejpam-7015	128	21	.	.	PUNCT
ejpam-7015	129	1	let	let	VERB
ejpam-7015	129	2	(	(	PUNCT
ejpam-7015	129	3	u	u	NOUN
ejpam-7015	129	4	,	,	PUNCT
ejpam-7015	129	5	ג	ג	PROPN
ejpam-7015	129	6	)	)	PUNCT
ejpam-7015	129	7	and	and	CCONJ
ejpam-7015	129	8	(	(	PUNCT
ejpam-7015	129	9	ξ	ξ	PROPN
ejpam-7015	129	10	,	,	PUNCT
ejpam-7015	129	11	h	h	NOUN
ejpam-7015	129	12	)	)	PUNCT
ejpam-7015	129	13	be	be	VERB
ejpam-7015	129	14	two	two	NUM
ejpam-7015	129	15	afsbrs	afsbrs	ADJ
ejpam-7015	129	16	.	.	PUNCT
ejpam-7015	130	1	if	if	SCONJ
ejpam-7015	130	2	∪(u	∪(u	NOUN
ejpam-7015	130	3	,	,	PUNCT
ejpam-7015	130	4	ג	ג	NOUN
ejpam-7015	130	5	)	)	PUNCT
ejpam-7015	130	6	(	(	PUNCT
ejpam-7015	130	7	ξ	ξ	PROPN
ejpam-7015	130	8	,	,	PUNCT
ejpam-7015	130	9	h	h	NOUN
ejpam-7015	130	10	)	)	PUNCT
ejpam-7015	130	11	is	be	AUX
ejpam-7015	130	12	non	non	ADJ
ejpam-7015	130	13	-	-	ADJ
ejpam-7015	130	14	null	null	ADJ
ejpam-7015	130	15	,	,	PUNCT
ejpam-7015	130	16	then	then	ADV
ejpam-7015	130	17	it	it	PRON
ejpam-7015	130	18	’s	’	VERB
ejpam-7015	130	19	an	an	DET
ejpam-7015	130	20	afsbr	afsbr	NOUN
ejpam-7015	130	21	.	.	PUNCT
ejpam-7015	131	1	proof	proof	NOUN
ejpam-7015	131	2	.	.	PUNCT
ejpam-7015	132	1	for	for	ADP
ejpam-7015	132	2	any	any	DET
ejpam-7015	132	3	e	e	PROPN
ejpam-7015	132	4	∈	∈	PROPN
ejpam-7015	132	5	u	u	NOUN
ejpam-7015	132	6	∪	∪	NOUN
ejpam-7015	132	7	h	h	NOUN
ejpam-7015	132	8	,	,	PUNCT
ejpam-7015	132	9	and	and	CCONJ
ejpam-7015	132	10	x	x	X
ejpam-7015	132	11	,	,	PUNCT
ejpam-7015	132	12	y	y	PROPN
ejpam-7015	132	13	∈	∈	PROPN
ejpam-7015	132	14	ℵ	ℵ	NOUN
ejpam-7015	132	15	,	,	PUNCT
ejpam-7015	132	16	we	we	PRON
ejpam-7015	132	17	consider	consider	VERB
ejpam-7015	132	18	the	the	DET
ejpam-7015	132	19	subsequent	subsequent	ADJ
ejpam-7015	132	20	scenarios	scenario	NOUN
ejpam-7015	132	21	.	.	PUNCT
ejpam-7015	133	1	case	case	NOUN
ejpam-7015	134	1	i	i	PRON
ejpam-7015	134	2	:	:	PUNCT
ejpam-7015	134	3	if	if	SCONJ
ejpam-7015	134	4	e	e	PROPN
ejpam-7015	134	5	∈	∈	PROPN
ejpam-7015	134	6	u−	u−	PROPN
ejpam-7015	134	7	h	h	NOUN
ejpam-7015	134	8	,	,	PUNCT
ejpam-7015	134	9	then	then	ADV
ejpam-7015	134	10	ωe(x+	ωe(x+	ADV
ejpam-7015	134	11	y	y	X
ejpam-7015	134	12	)	)	PUNCT
ejpam-7015	134	13	=	=	PUNCT
ejpam-7015	135	1	+	+	VERB
ejpam-7015	135	2	e(xג	e(xג	PROPN
ejpam-7015	135	3	y	y	NOUN
ejpam-7015	135	4	)	)	PUNCT
ejpam-7015	135	5	≤	≤	PUNCT
ejpam-7015	136	1	e(x)ג	e(x)ג	PROPN
ejpam-7015	136	2	∨	∨	NUM
ejpam-7015	136	3	e(y)ג	e(y)ג	PRON
ejpam-7015	136	4	=	=	SYM
ejpam-7015	136	5	ωe(x	ωe(x	X
ejpam-7015	136	6	)	)	PUNCT
ejpam-7015	136	7	∨	∨	NUM
ejpam-7015	136	8	ωe(y	ωe(y	NUM
ejpam-7015	136	9	)	)	PUNCT
ejpam-7015	136	10	,	,	PUNCT
ejpam-7015	136	11	ωe(xy	ωe(xy	NOUN
ejpam-7015	136	12	)	)	PUNCT
ejpam-7015	136	13	=	=	SYM
ejpam-7015	136	14	e(xy)ג	e(xy)ג	PROPN
ejpam-7015	136	15	≤	≤	PUNCT
ejpam-7015	136	16	e(x)ג	e(x)ג	PROPN
ejpam-7015	136	17	∨	∨	NUM
ejpam-7015	136	18	e(y)ג	e(y)ג	PRON
ejpam-7015	136	19	=	=	SYM
ejpam-7015	136	20	ωe(x	ωe(x	X
ejpam-7015	136	21	)	)	PUNCT
ejpam-7015	136	22	∨	∨	NUM
ejpam-7015	136	23	ωe(y	ωe(y	NUM
ejpam-7015	136	24	)	)	PUNCT
ejpam-7015	136	25	.	.	PUNCT
ejpam-7015	137	1	case	case	NOUN
ejpam-7015	137	2	ii	ii	NOUN
ejpam-7015	137	3	:	:	PUNCT
ejpam-7015	137	4	if	if	SCONJ
ejpam-7015	137	5	e	e	PROPN
ejpam-7015	137	6	∈	∈	PROPN
ejpam-7015	137	7	h−	h−	PROPN
ejpam-7015	137	8	u	u	NOUN
ejpam-7015	137	9	,	,	PUNCT
ejpam-7015	137	10	then	then	ADV
ejpam-7015	137	11	ωe(x+	ωe(x+	ADV
ejpam-7015	137	12	y	y	X
ejpam-7015	137	13	)	)	PUNCT
ejpam-7015	137	14	=	=	PUNCT
ejpam-7015	138	1	ξe(x+	ξe(x+	PROPN
ejpam-7015	138	2	y	y	PROPN
ejpam-7015	138	3	)	)	PUNCT
ejpam-7015	138	4	d.	d.	PROPN
ejpam-7015	138	5	ramesh	ramesh	PROPN
ejpam-7015	138	6	et	et	PROPN
ejpam-7015	138	7	al	al	PROPN
ejpam-7015	138	8	.	.	PUNCT
ejpam-7015	138	9	/	/	SYM
ejpam-7015	138	10	eur	eur	PROPN
ejpam-7015	138	11	.	.	PUNCT
ejpam-7015	139	1	j.	j.	PROPN
ejpam-7015	139	2	pure	pure	PROPN
ejpam-7015	139	3	appl	appl	PROPN
ejpam-7015	139	4	.	.	PROPN
ejpam-7015	139	5	math	math	PROPN
ejpam-7015	139	6	,	,	PUNCT
ejpam-7015	139	7	18	18	NUM
ejpam-7015	139	8	(	(	PUNCT
ejpam-7015	139	9	4	4	NUM
ejpam-7015	139	10	)	)	PUNCT
ejpam-7015	139	11	(	(	PUNCT
ejpam-7015	139	12	2025	2025	NUM
ejpam-7015	139	13	)	)	PUNCT
ejpam-7015	139	14	,	,	PUNCT
ejpam-7015	139	15	7015	7015	NUM
ejpam-7015	139	16	7	7	NUM
ejpam-7015	139	17	of	of	ADP
ejpam-7015	139	18	11	11	NUM
ejpam-7015	139	19	≤	≤	NOUN
ejpam-7015	139	20	ξe(x	ξe(x	PUNCT
ejpam-7015	139	21	)	)	PUNCT
ejpam-7015	139	22	∨	∨	NUM
ejpam-7015	139	23	ξe(y	ξe(y	NUM
ejpam-7015	139	24	)	)	PUNCT
ejpam-7015	139	25	=	=	SYM
ejpam-7015	139	26	ωe(x	ωe(x	X
ejpam-7015	139	27	)	)	PUNCT
ejpam-7015	139	28	∨	∨	NUM
ejpam-7015	139	29	ωe(y	ωe(y	NUM
ejpam-7015	139	30	)	)	PUNCT
ejpam-7015	139	31	,	,	PUNCT
ejpam-7015	139	32	ωe(xy	ωe(xy	NOUN
ejpam-7015	139	33	)	)	PUNCT
ejpam-7015	139	34	=	=	SYM
ejpam-7015	139	35	ξe(xy	ξe(xy	PROPN
ejpam-7015	139	36	)	)	PUNCT
ejpam-7015	139	37	≤	≤	NOUN
ejpam-7015	139	38	ξe(x	ξe(x	PUNCT
ejpam-7015	139	39	)	)	PUNCT
ejpam-7015	139	40	∨	∨	NUM
ejpam-7015	139	41	ξe(y	ξe(y	NUM
ejpam-7015	139	42	)	)	PUNCT
ejpam-7015	139	43	=	=	SYM
ejpam-7015	139	44	ωe(x	ωe(x	X
ejpam-7015	139	45	)	)	PUNCT
ejpam-7015	139	46	∨	∨	NUM
ejpam-7015	139	47	ωe(y	ωe(y	NUM
ejpam-7015	139	48	)	)	PUNCT
ejpam-7015	139	49	.	.	PUNCT
ejpam-7015	140	1	case	case	NOUN
ejpam-7015	140	2	iii	iii	X
ejpam-7015	140	3	:	:	PUNCT
ejpam-7015	140	4	if	if	SCONJ
ejpam-7015	140	5	e	e	PROPN
ejpam-7015	140	6	∈	∈	PROPN
ejpam-7015	140	7	u	u	NOUN
ejpam-7015	140	8	∩	∩	ADJ
ejpam-7015	140	9	h	h	NOUN
ejpam-7015	140	10	,	,	PUNCT
ejpam-7015	140	11	then	then	ADV
ejpam-7015	140	12	ωe(x+	ωe(x+	ADV
ejpam-7015	140	13	y	y	X
ejpam-7015	140	14	)	)	PUNCT
ejpam-7015	140	15	=	=	PUNCT
ejpam-7015	141	1	+	+	ADJ
ejpam-7015	141	2	e(xג	e(xג	PROPN
ejpam-7015	141	3	y	y	NOUN
ejpam-7015	141	4	)	)	PUNCT
ejpam-7015	141	5	∪	∪	VERB
ejpam-7015	141	6	ξe(x+	ξe(x+	PROPN
ejpam-7015	141	7	y	y	NOUN
ejpam-7015	141	8	)	)	PUNCT
ejpam-7015	141	9	≤	≤	NUM
ejpam-7015	141	10	e(x)ג	e(x)ג	NOUN
ejpam-7015	141	11	)	)	PUNCT
ejpam-7015	141	12	∨	∨	PROPN
ejpam-7015	141	13	(	(	PUNCT
ejpam-7015	141	14	e(y)ג	e(y)ג	PROPN
ejpam-7015	141	15	∪	∪	ADJ
ejpam-7015	141	16	(	(	PUNCT
ejpam-7015	141	17	ξe(x	ξe(x	NOUN
ejpam-7015	141	18	)	)	PUNCT
ejpam-7015	141	19	∨	∨	NUM
ejpam-7015	141	20	ξe(y	ξe(y	NUM
ejpam-7015	141	21	)	)	PUNCT
ejpam-7015	141	22	)	)	PUNCT
ejpam-7015	142	1	=	=	PUNCT
ejpam-7015	142	2	e(x)ג	e(x)ג	NOUN
ejpam-7015	142	3	)	)	PUNCT
ejpam-7015	142	4	∪	∪	ADP
ejpam-7015	142	5	ξe(x	ξe(x	NUM
ejpam-7015	142	6	)	)	PUNCT
ejpam-7015	142	7	)	)	PUNCT
ejpam-7015	142	8	∨	∨	NUM
ejpam-7015	142	9	e(y)ג	e(y)ג	PROPN
ejpam-7015	142	10	)	)	PUNCT
ejpam-7015	142	11	∪	∪	ADP
ejpam-7015	142	12	ξe(y	ξe(y	NUM
ejpam-7015	142	13	)	)	PUNCT
ejpam-7015	142	14	)	)	PUNCT
ejpam-7015	142	15	=	=	SYM
ejpam-7015	142	16	ωe(x	ωe(x	X
ejpam-7015	142	17	)	)	PUNCT
ejpam-7015	142	18	∨	∨	NUM
ejpam-7015	142	19	ωe(y	ωe(y	NUM
ejpam-7015	142	20	)	)	PUNCT
ejpam-7015	142	21	,	,	PUNCT
ejpam-7015	142	22	ωe(xy	ωe(xy	NOUN
ejpam-7015	142	23	)	)	PUNCT
ejpam-7015	142	24	=	=	SYM
ejpam-7015	142	25	e(xy)ג	e(xy)ג	PROPN
ejpam-7015	142	26	∪	∪	PROPN
ejpam-7015	142	27	ξe(xy	ξe(xy	PROPN
ejpam-7015	142	28	)	)	PUNCT
ejpam-7015	142	29	≤	≤	NUM
ejpam-7015	142	30	e(x)ג	e(x)ג	NOUN
ejpam-7015	142	31	)	)	PUNCT
ejpam-7015	142	32	∨	∨	PROPN
ejpam-7015	142	33	(	(	PUNCT
ejpam-7015	142	34	e(y)ג	e(y)ג	PROPN
ejpam-7015	142	35	∪	∪	ADJ
ejpam-7015	142	36	(	(	PUNCT
ejpam-7015	142	37	ξe(x	ξe(x	NOUN
ejpam-7015	142	38	)	)	PUNCT
ejpam-7015	142	39	∨	∨	NUM
ejpam-7015	142	40	ξe(y	ξe(y	NUM
ejpam-7015	142	41	)	)	PUNCT
ejpam-7015	142	42	)	)	PUNCT
ejpam-7015	143	1	=	=	PUNCT
ejpam-7015	143	2	e(x)ג	e(x)ג	NOUN
ejpam-7015	143	3	)	)	PUNCT
ejpam-7015	143	4	∪	∪	ADP
ejpam-7015	143	5	ξe(x	ξe(x	NUM
ejpam-7015	143	6	)	)	PUNCT
ejpam-7015	143	7	)	)	PUNCT
ejpam-7015	143	8	∨	∨	NUM
ejpam-7015	143	9	e(y)ג	e(y)ג	PROPN
ejpam-7015	143	10	)	)	PUNCT
ejpam-7015	143	11	∪	∪	ADP
ejpam-7015	143	12	ξe(y	ξe(y	NUM
ejpam-7015	143	13	)	)	PUNCT
ejpam-7015	143	14	)	)	PUNCT
ejpam-7015	143	15	=	=	SYM
ejpam-7015	143	16	ωe(x	ωe(x	X
ejpam-7015	143	17	)	)	PUNCT
ejpam-7015	143	18	∨	∨	NUM
ejpam-7015	143	19	ωe(y	ωe(y	NUM
ejpam-7015	143	20	)	)	PUNCT
ejpam-7015	143	21	.	.	PUNCT
ejpam-7015	144	1	hence	hence	ADV
ejpam-7015	144	2	,	,	PUNCT
ejpam-7015	144	3	(	(	PUNCT
ejpam-7015	144	4	u	u	NOUN
ejpam-7015	144	5	,	,	PUNCT
ejpam-7015	144	6	ג	ג	NOUN
ejpam-7015	144	7	)	)	PUNCT
ejpam-7015	144	8	∪	∪	NOUN
ejpam-7015	144	9	(	(	PUNCT
ejpam-7015	144	10	ξ	ξ	PROPN
ejpam-7015	144	11	,	,	PUNCT
ejpam-7015	144	12	h	h	NOUN
ejpam-7015	144	13	)	)	PUNCT
ejpam-7015	144	14	is	be	AUX
ejpam-7015	144	15	an	an	DET
ejpam-7015	144	16	afsbr	afsbr	NOUN
ejpam-7015	144	17	of	of	ADP
ejpam-7015	144	18	ℵ.	ℵ.	PROPN
ejpam-7015	144	19	4	4	X
ejpam-7015	144	20	.	.	X
ejpam-7015	144	21	anti	anti	ADJ
ejpam-7015	144	22	-	-	ADJ
ejpam-7015	144	23	fuzzy	fuzzy	ADJ
ejpam-7015	144	24	soft	soft	ADJ
ejpam-7015	144	25	ideals	ideal	NOUN
ejpam-7015	144	26	over	over	ADP
ejpam-7015	144	27	boolean	boolean	ADJ
ejpam-7015	144	28	rings	ring	NOUN
ejpam-7015	144	29	in	in	ADP
ejpam-7015	144	30	this	this	DET
ejpam-7015	144	31	section	section	NOUN
ejpam-7015	144	32	,	,	PUNCT
ejpam-7015	144	33	we	we	PRON
ejpam-7015	144	34	define	define	VERB
ejpam-7015	144	35	afsis	afsis	NOUN
ejpam-7015	144	36	and	and	CCONJ
ejpam-7015	144	37	discuss	discuss	VERB
ejpam-7015	144	38	some	some	PRON
ejpam-7015	144	39	of	of	ADP
ejpam-7015	144	40	their	their	PRON
ejpam-7015	144	41	fundamental	fundamental	ADJ
ejpam-7015	144	42	properties	property	NOUN
ejpam-7015	144	43	.	.	PUNCT
ejpam-7015	145	1	definition	definition	NOUN
ejpam-7015	145	2	12	12	NUM
ejpam-7015	145	3	.	.	PUNCT
ejpam-7015	146	1	an	an	DET
ejpam-7015	146	2	fss	fss	ADJ
ejpam-7015	146	3	(	(	PUNCT
ejpam-7015	146	4	u	u	NOUN
ejpam-7015	146	5	,	,	PUNCT
ejpam-7015	146	6	ג	ג	NOUN
ejpam-7015	146	7	)	)	PUNCT
ejpam-7015	146	8	over	over	ADP
ejpam-7015	146	9	ℵ	ℵ	NOUN
ejpam-7015	146	10	is	be	AUX
ejpam-7015	146	11	called	call	VERB
ejpam-7015	146	12	an	an	DET
ejpam-7015	146	13	anti	anti	ADJ
ejpam-7015	146	14	-	-	ADJ
ejpam-7015	146	15	fuzzy	fuzzy	ADJ
ejpam-7015	146	16	soft	soft	ADJ
ejpam-7015	146	17	ideal	ideal	NOUN
ejpam-7015	146	18	(	(	PUNCT
ejpam-7015	146	19	afsi	afsi	ADV
ejpam-7015	146	20	)	)	PUNCT
ejpam-7015	146	21	of	of	ADP
ejpam-7015	146	22	ℵ	ℵ	NOUN
ejpam-7015	146	23	if	if	SCONJ
ejpam-7015	146	24	(	(	PUNCT
ejpam-7015	146	25	i	i	NOUN
ejpam-7015	146	26	)	)	PUNCT
ejpam-7015	147	1	+	+	ADP
ejpam-7015	147	2	a(xג	a(xג	PROPN
ejpam-7015	147	3	y	y	NOUN
ejpam-7015	147	4	)	)	PUNCT
ejpam-7015	147	5	≤	≤	PART
ejpam-7015	147	6	a(x)ג	a(x)ג	PROPN
ejpam-7015	147	7	∨	∨	NUM
ejpam-7015	147	8	,	,	PUNCT
ejpam-7015	147	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	147	10	(	(	PUNCT
ejpam-7015	147	11	ii	ii	PROPN
ejpam-7015	147	12	)	)	PUNCT
ejpam-7015	147	13	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	147	14	≥	≥	NOUN
ejpam-7015	147	15	a(x)ג	a(x)ג	PROPN
ejpam-7015	147	16	∧	∧	PROPN
ejpam-7015	147	17	,	,	PUNCT
ejpam-7015	147	18	a(y)ג	a(y)ג	PROPN
ejpam-7015	147	19	∀x	∀x	NUM
ejpam-7015	147	20	,	,	PUNCT
ejpam-7015	147	21	y	y	PROPN
ejpam-7015	147	22	∈	∈	PROPN
ejpam-7015	147	23	ℵ.	ℵ.	PROPN
ejpam-7015	147	24	example	example	NOUN
ejpam-7015	148	1	2	2	X
ejpam-7015	148	2	.	.	PUNCT
ejpam-7015	148	3	let	let	VERB
ejpam-7015	148	4	ℵ	ℵ	NOUN
ejpam-7015	148	5	=	=	SYM
ejpam-7015	148	6	{	{	PUNCT
ejpam-7015	148	7	0	0	NUM
ejpam-7015	148	8	,	,	PUNCT
ejpam-7015	148	9	a∗	a∗	ADJ
ejpam-7015	148	10	,	,	PUNCT
ejpam-7015	148	11	c∗	c∗	PROPN
ejpam-7015	148	12	,	,	PUNCT
ejpam-7015	148	13	n∗	n∗	PROPN
ejpam-7015	148	14	}	}	PUNCT
ejpam-7015	148	15	be	be	VERB
ejpam-7015	148	16	a	a	DET
ejpam-7015	148	17	non	non	ADJ
ejpam-7015	148	18	-	-	ADJ
ejpam-7015	148	19	empty	empty	ADJ
ejpam-7015	148	20	set	set	NOUN
ejpam-7015	148	21	with	with	ADP
ejpam-7015	148	22	two	two	NUM
ejpam-7015	148	23	binary	binary	ADJ
ejpam-7015	148	24	operations	operation	NOUN
ejpam-7015	148	25	+	+	CCONJ
ejpam-7015	148	26	and	and	CCONJ
ejpam-7015	148	27	·	·	PUNCT
ejpam-7015	148	28	defined	define	VERB
ejpam-7015	148	29	as	as	SCONJ
ejpam-7015	148	30	follows	follow	VERB
ejpam-7015	148	31	:	:	PUNCT
ejpam-7015	148	32	+	+	SYM
ejpam-7015	148	33	0	0	NUM
ejpam-7015	148	34	a∗	a∗	PROPN
ejpam-7015	148	35	c∗	c∗	PROPN
ejpam-7015	148	36	n∗	n∗	PROPN
ejpam-7015	148	37	0	0	NUM
ejpam-7015	148	38	0	0	NUM
ejpam-7015	148	39	a∗	a∗	PROPN
ejpam-7015	148	40	c∗	c∗	PROPN
ejpam-7015	148	41	n∗	n∗	VERB
ejpam-7015	148	42	a∗	a∗	PROPN
ejpam-7015	148	43	a∗	a∗	PROPN
ejpam-7015	148	44	0	0	NUM
ejpam-7015	148	45	c∗	c∗	PROPN
ejpam-7015	148	46	n∗	n∗	PROPN
ejpam-7015	148	47	c∗	c∗	PROPN
ejpam-7015	148	48	c∗	c∗	PROPN
ejpam-7015	148	49	c∗	c∗	PROPN
ejpam-7015	148	50	0	0	NUM
ejpam-7015	148	51	a∗	a∗	PROPN
ejpam-7015	148	52	n∗	n∗	PROPN
ejpam-7015	148	53	n∗	n∗	PROPN
ejpam-7015	148	54	n∗	n∗	VERB
ejpam-7015	148	55	a∗	a∗	PROPN
ejpam-7015	148	56	0	0	NUM
ejpam-7015	148	57	·	·	SYM
ejpam-7015	148	58	0	0	NUM
ejpam-7015	148	59	a∗	a∗	PROPN
ejpam-7015	148	60	c∗	c∗	PROPN
ejpam-7015	148	61	n∗	n∗	PROPN
ejpam-7015	148	62	0	0	NUM
ejpam-7015	148	63	0	0	NUM
ejpam-7015	148	64	0	0	NUM
ejpam-7015	148	65	0	0	NUM
ejpam-7015	148	66	0	0	NUM
ejpam-7015	148	67	a∗	a∗	PROPN
ejpam-7015	148	68	0	0	NUM
ejpam-7015	148	69	a∗	a∗	PROPN
ejpam-7015	148	70	0	0	NUM
ejpam-7015	148	71	a∗	a∗	PROPN
ejpam-7015	148	72	c∗	c∗	PROPN
ejpam-7015	148	73	0	0	NUM
ejpam-7015	148	74	0	0	NUM
ejpam-7015	148	75	c∗	c∗	PROPN
ejpam-7015	148	76	c∗	c∗	PROPN
ejpam-7015	148	77	n∗	n∗	PROPN
ejpam-7015	148	78	0	0	NUM
ejpam-7015	148	79	a∗	a∗	PROPN
ejpam-7015	148	80	c∗	c∗	PROPN
ejpam-7015	148	81	n∗	n∗	PROPN
ejpam-7015	148	82	let	let	VERB
ejpam-7015	148	83	u	u	PRON
ejpam-7015	148	84	=	=	X
ejpam-7015	148	85	{	{	PUNCT
ejpam-7015	148	86	ι11	ι11	NOUN
ejpam-7015	148	87	,	,	PUNCT
ejpam-7015	148	88	ι12	ι12	NOUN
ejpam-7015	148	89	,	,	PUNCT
ejpam-7015	148	90	ι13	ι13	NOUN
ejpam-7015	148	91	}	}	PUNCT
ejpam-7015	148	92	be	be	VERB
ejpam-7015	148	93	the	the	DET
ejpam-7015	148	94	set	set	NOUN
ejpam-7015	148	95	of	of	ADP
ejpam-7015	148	96	parameters	parameter	NOUN
ejpam-7015	148	97	and	and	CCONJ
ejpam-7015	148	98	now	now	ADV
ejpam-7015	148	99	define	define	VERB
ejpam-7015	148	100	a	a	DET
ejpam-7015	148	101	fss	fss	ADJ
ejpam-7015	148	102	(	(	PUNCT
ejpam-7015	148	103	u	u	NOUN
ejpam-7015	148	104	,	,	PUNCT
ejpam-7015	148	105	ג	ג	NOUN
ejpam-7015	148	106	)	)	PUNCT
ejpam-7015	148	107	over	over	ADP
ejpam-7015	148	108	ℵ	ℵ	NOUN
ejpam-7015	148	109	as	as	SCONJ
ejpam-7015	148	110	follows	follow	VERB
ejpam-7015	148	111	:	:	PUNCT
ejpam-7015	149	1	d.	d.	PROPN
ejpam-7015	149	2	ramesh	ramesh	PROPN
ejpam-7015	149	3	et	et	PROPN
ejpam-7015	149	4	al	al	PROPN
ejpam-7015	149	5	.	.	PUNCT
ejpam-7015	149	6	/	/	SYM
ejpam-7015	149	7	eur	eur	PROPN
ejpam-7015	149	8	.	.	PUNCT
ejpam-7015	150	1	j.	j.	PROPN
ejpam-7015	150	2	pure	pure	PROPN
ejpam-7015	150	3	appl	appl	PROPN
ejpam-7015	150	4	.	.	PROPN
ejpam-7015	150	5	math	math	PROPN
ejpam-7015	150	6	,	,	PUNCT
ejpam-7015	150	7	18	18	NUM
ejpam-7015	150	8	(	(	PUNCT
ejpam-7015	150	9	4	4	NUM
ejpam-7015	150	10	)	)	PUNCT
ejpam-7015	150	11	(	(	PUNCT
ejpam-7015	150	12	2025	2025	NUM
ejpam-7015	150	13	)	)	PUNCT
ejpam-7015	150	14	,	,	PUNCT
ejpam-7015	150	15	7015	7015	NUM
ejpam-7015	150	16	8	8	NUM
ejpam-7015	150	17	of	of	ADP
ejpam-7015	150	18	11	11	NUM
ejpam-7015	150	19	(	(	PUNCT
ejpam-7015	150	20	ι11)ג	ι11)ג	NOUN
ejpam-7015	150	21	=	=	X
ejpam-7015	150	22	{	{	PUNCT
ejpam-7015	150	23	(	(	PUNCT
ejpam-7015	150	24	0	0	NUM
ejpam-7015	150	25	,	,	PUNCT
ejpam-7015	150	26	0.9	0.9	NUM
ejpam-7015	150	27	)	)	PUNCT
ejpam-7015	150	28	,	,	PUNCT
ejpam-7015	150	29	(	(	PUNCT
ejpam-7015	150	30	a∗	a∗	PROPN
ejpam-7015	150	31	,	,	PUNCT
ejpam-7015	150	32	0.7	0.7	NUM
ejpam-7015	150	33	)	)	PUNCT
ejpam-7015	150	34	,	,	PUNCT
ejpam-7015	150	35	(	(	PUNCT
ejpam-7015	150	36	c∗	c∗	PROPN
ejpam-7015	150	37	,	,	PUNCT
ejpam-7015	150	38	0.8	0.8	NUM
ejpam-7015	150	39	)	)	PUNCT
ejpam-7015	150	40	,	,	PUNCT
ejpam-7015	150	41	(	(	PUNCT
ejpam-7015	150	42	n∗	n∗	PROPN
ejpam-7015	150	43	,	,	PUNCT
ejpam-7015	150	44	0.7	0.7	NUM
ejpam-7015	150	45	)	)	PUNCT
ejpam-7015	150	46	}	}	PUNCT
ejpam-7015	150	47	(	(	PUNCT
ejpam-7015	150	48	ι12)ג	ι12)ג	PUNCT
ejpam-7015	150	49	=	=	SYM
ejpam-7015	150	50	{	{	PUNCT
ejpam-7015	150	51	(	(	PUNCT
ejpam-7015	150	52	0	0	NUM
ejpam-7015	150	53	,	,	PUNCT
ejpam-7015	150	54	0.8	0.8	NUM
ejpam-7015	150	55	)	)	PUNCT
ejpam-7015	150	56	,	,	PUNCT
ejpam-7015	150	57	(	(	PUNCT
ejpam-7015	150	58	a∗	a∗	PROPN
ejpam-7015	150	59	,	,	PUNCT
ejpam-7015	150	60	0.5	0.5	NUM
ejpam-7015	150	61	)	)	PUNCT
ejpam-7015	150	62	,	,	PUNCT
ejpam-7015	150	63	(	(	PUNCT
ejpam-7015	150	64	c∗	c∗	PROPN
ejpam-7015	150	65	,	,	PUNCT
ejpam-7015	150	66	0.5	0.5	NUM
ejpam-7015	150	67	)	)	PUNCT
ejpam-7015	150	68	,	,	PUNCT
ejpam-7015	150	69	(	(	PUNCT
ejpam-7015	150	70	n∗	n∗	PROPN
ejpam-7015	150	71	,	,	PUNCT
ejpam-7015	150	72	0.8	0.8	NUM
ejpam-7015	150	73	)	)	PUNCT
ejpam-7015	150	74	}	}	PUNCT
ejpam-7015	150	75	(	(	PUNCT
ejpam-7015	150	76	ι13)ג	ι13)ג	PUNCT
ejpam-7015	150	77	=	=	X
ejpam-7015	150	78	{	{	PUNCT
ejpam-7015	150	79	(	(	PUNCT
ejpam-7015	150	80	0	0	NUM
ejpam-7015	150	81	,	,	PUNCT
ejpam-7015	150	82	0.4	0.4	NUM
ejpam-7015	150	83	)	)	PUNCT
ejpam-7015	150	84	,	,	PUNCT
ejpam-7015	150	85	(	(	PUNCT
ejpam-7015	150	86	a∗	a∗	PROPN
ejpam-7015	150	87	,	,	PUNCT
ejpam-7015	150	88	0.4	0.4	NUM
ejpam-7015	150	89	)	)	PUNCT
ejpam-7015	150	90	,	,	PUNCT
ejpam-7015	150	91	(	(	PUNCT
ejpam-7015	150	92	c∗	c∗	NOUN
ejpam-7015	150	93	,	,	PUNCT
ejpam-7015	150	94	0.6	0.6	NUM
ejpam-7015	150	95	)	)	PUNCT
ejpam-7015	150	96	,	,	PUNCT
ejpam-7015	150	97	(	(	PUNCT
ejpam-7015	150	98	n∗	n∗	PROPN
ejpam-7015	150	99	,	,	PUNCT
ejpam-7015	150	100	0.8	0.8	NUM
ejpam-7015	150	101	)	)	PUNCT
ejpam-7015	150	102	}	}	PUNCT
ejpam-7015	150	103	hence	hence	ADV
ejpam-7015	150	104	,	,	PUNCT
ejpam-7015	150	105	(	(	PUNCT
ejpam-7015	150	106	u	u	NOUN
ejpam-7015	150	107	,	,	PUNCT
ejpam-7015	150	108	ג	ג	NOUN
ejpam-7015	150	109	)	)	PUNCT
ejpam-7015	150	110	is	be	AUX
ejpam-7015	150	111	an	an	DET
ejpam-7015	150	112	afsi	afsi	NOUN
ejpam-7015	150	113	of	of	ADP
ejpam-7015	150	114	ℵ.	ℵ.	PROPN
ejpam-7015	150	115	theorem	theorem	VERB
ejpam-7015	150	116	5	5	NUM
ejpam-7015	150	117	.	.	PUNCT
ejpam-7015	151	1	let	let	VERB
ejpam-7015	151	2	(	(	PUNCT
ejpam-7015	151	3	u	u	NOUN
ejpam-7015	151	4	,	,	PUNCT
ejpam-7015	151	5	ג	ג	PROPN
ejpam-7015	151	6	)	)	PUNCT
ejpam-7015	151	7	and	and	CCONJ
ejpam-7015	151	8	(	(	PUNCT
ejpam-7015	151	9	ξ	ξ	PROPN
ejpam-7015	151	10	,	,	PUNCT
ejpam-7015	151	11	h	h	NOUN
ejpam-7015	151	12	)	)	PUNCT
ejpam-7015	151	13	be	be	VERB
ejpam-7015	151	14	two	two	NUM
ejpam-7015	151	15	afsis	afsis	NOUN
ejpam-7015	151	16	.	.	PUNCT
ejpam-7015	152	1	if	if	SCONJ
ejpam-7015	152	2	(	(	PUNCT
ejpam-7015	152	3	u	u	NOUN
ejpam-7015	152	4	,	,	PUNCT
ejpam-7015	152	5	ג	ג	NOUN
ejpam-7015	152	6	)	)	PUNCT
ejpam-7015	152	7	∧	∧	PROPN
ejpam-7015	152	8	(	(	PUNCT
ejpam-7015	152	9	ξ	ξ	PROPN
ejpam-7015	152	10	,	,	PUNCT
ejpam-7015	152	11	h	h	NOUN
ejpam-7015	152	12	)	)	PUNCT
ejpam-7015	152	13	is	be	AUX
ejpam-7015	152	14	non	non	ADJ
ejpam-7015	152	15	-	-	ADJ
ejpam-7015	152	16	null	null	ADJ
ejpam-7015	152	17	,	,	PUNCT
ejpam-7015	152	18	then	then	ADV
ejpam-7015	152	19	it	it	PRON
ejpam-7015	152	20	’s	’	VERB
ejpam-7015	152	21	an	an	DET
ejpam-7015	152	22	afsi	afsi	NOUN
ejpam-7015	152	23	.	.	PUNCT
ejpam-7015	153	1	proof	proof	NOUN
ejpam-7015	153	2	.	.	PUNCT
ejpam-7015	154	1	let	let	VERB
ejpam-7015	154	2	us	we	PRON
ejpam-7015	154	3	take	take	VERB
ejpam-7015	154	4	(	(	PUNCT
ejpam-7015	154	5	ξ	ξ	PROPN
ejpam-7015	154	6	,	,	PUNCT
ejpam-7015	154	7	h)∧(u	h)∧(u	ADJ
ejpam-7015	154	8	,	,	PUNCT
ejpam-7015	154	9	ג	ג	NOUN
ejpam-7015	154	10	)	)	PUNCT
ejpam-7015	154	11	=	=	SYM
ejpam-7015	154	12	(	(	PUNCT
ejpam-7015	154	13	ω	ω	PROPN
ejpam-7015	154	14	,	,	PUNCT
ejpam-7015	154	15	s	s	PART
ejpam-7015	154	16	)	)	PUNCT
ejpam-7015	154	17	respectively	respectively	ADV
ejpam-7015	154	18	,	,	PUNCT
ejpam-7015	154	19	where	where	SCONJ
ejpam-7015	154	20	s	s	VERB
ejpam-7015	154	21	=	=	SYM
ejpam-7015	154	22	u×h	u×h	PROPN
ejpam-7015	154	23	and	and	CCONJ
ejpam-7015	154	24	ω(a	ω(a	PROPN
ejpam-7015	154	25	,	,	PUNCT
ejpam-7015	154	26	b	b	NOUN
ejpam-7015	154	27	)	)	PUNCT
ejpam-7015	154	28	=	=	SYM
ejpam-7015	154	29	(	(	PUNCT
ejpam-7015	154	30	a)ג	a)ג	NOUN
ejpam-7015	154	31	∧	∧	NOUN
ejpam-7015	154	32	ξ(b	ξ(b	NOUN
ejpam-7015	154	33	)	)	PUNCT
ejpam-7015	154	34	,	,	PUNCT
ejpam-7015	155	1	∀(a	∀(a	PROPN
ejpam-7015	155	2	,	,	PUNCT
ejpam-7015	155	3	b	b	X
ejpam-7015	155	4	)	)	PUNCT
ejpam-7015	155	5	∈	∈	PROPN
ejpam-7015	155	6	s.	s.	PROPN
ejpam-7015	155	7	since	since	SCONJ
ejpam-7015	155	8	(	(	PUNCT
ejpam-7015	155	9	u	u	NOUN
ejpam-7015	155	10	,	,	PUNCT
ejpam-7015	155	11	ג	ג	PROPN
ejpam-7015	155	12	)	)	PUNCT
ejpam-7015	155	13	and	and	CCONJ
ejpam-7015	155	14	(	(	PUNCT
ejpam-7015	155	15	ξ	ξ	PROPN
ejpam-7015	155	16	,	,	PUNCT
ejpam-7015	155	17	h	h	NOUN
ejpam-7015	155	18	)	)	PUNCT
ejpam-7015	155	19	are	be	AUX
ejpam-7015	155	20	afsis	afsis	NOUN
ejpam-7015	155	21	of	of	ADP
ejpam-7015	155	22	ℵ	ℵ	NOUN
ejpam-7015	155	23	,	,	PUNCT
ejpam-7015	155	24	we	we	PRON
ejpam-7015	155	25	have	have	VERB
ejpam-7015	155	26	∀x	∀x	NUM
ejpam-7015	155	27	,	,	PUNCT
ejpam-7015	155	28	y	y	PROPN
ejpam-7015	155	29	∈	∈	PROPN
ejpam-7015	155	30	ℵ	ℵ	NOUN
ejpam-7015	155	31	,	,	PUNCT
ejpam-7015	155	32	ω(a	ω(a	NOUN
ejpam-7015	155	33	,	,	PUNCT
ejpam-7015	155	34	b)(x+	b)(x+	NOUN
ejpam-7015	155	35	y	y	NOUN
ejpam-7015	155	36	)	)	PUNCT
ejpam-7015	155	37	=	=	PUNCT
ejpam-7015	156	1	+	+	PROPN
ejpam-7015	156	2	a(xג	a(xג	PROPN
ejpam-7015	156	3	y	y	NOUN
ejpam-7015	156	4	)	)	PUNCT
ejpam-7015	156	5	∧	∧	PROPN
ejpam-7015	156	6	ξb(x+	ξb(x+	PROPN
ejpam-7015	156	7	y	y	PROPN
ejpam-7015	156	8	)	)	PUNCT
ejpam-7015	156	9	≤	≤	PROPN
ejpam-7015	156	10	a(x)ג	a(x)ג	PROPN
ejpam-7015	156	11	)	)	PUNCT
ejpam-7015	156	12	∨	∨	PROPN
ejpam-7015	156	13	(	(	PUNCT
ejpam-7015	156	14	a(y)ג	a(y)ג	PROPN
ejpam-7015	156	15	∧	∧	PROPN
ejpam-7015	156	16	(	(	PUNCT
ejpam-7015	156	17	ξb(x	ξb(x	NUM
ejpam-7015	156	18	)	)	PUNCT
ejpam-7015	156	19	∨	∨	NUM
ejpam-7015	156	20	ξb(y	ξb(y	NUM
ejpam-7015	156	21	)	)	PUNCT
ejpam-7015	156	22	)	)	PUNCT
ejpam-7015	157	1	=	=	SYM
ejpam-7015	157	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	157	3	)	)	PUNCT
ejpam-7015	157	4	∧	∧	NOUN
ejpam-7015	157	5	ξb(x	ξb(x	NUM
ejpam-7015	157	6	)	)	PUNCT
ejpam-7015	157	7	)	)	PUNCT
ejpam-7015	157	8	∨	∨	PROPN
ejpam-7015	157	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	157	10	)	)	PUNCT
ejpam-7015	157	11	∧	∧	PROPN
ejpam-7015	157	12	ξb(y	ξb(y	NUM
ejpam-7015	157	13	)	)	PUNCT
ejpam-7015	157	14	)	)	PUNCT
ejpam-7015	158	1	=	=	SYM
ejpam-7015	158	2	ω(a	ω(a	PROPN
ejpam-7015	158	3	,	,	PUNCT
ejpam-7015	158	4	b)(x	b)(x	PROPN
ejpam-7015	158	5	)	)	PUNCT
ejpam-7015	158	6	∨	∨	NUM
ejpam-7015	158	7	ω(a	ω(a	PROPN
ejpam-7015	158	8	,	,	PUNCT
ejpam-7015	158	9	b)(y	b)(y	PROPN
ejpam-7015	158	10	)	)	PUNCT
ejpam-7015	158	11	,	,	PUNCT
ejpam-7015	158	12	ω(a	ω(a	PROPN
ejpam-7015	158	13	,	,	PUNCT
ejpam-7015	158	14	b)(xy	b)(xy	NOUN
ejpam-7015	158	15	)	)	PUNCT
ejpam-7015	159	1	=	=	NOUN
ejpam-7015	159	2	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	159	3	∧	∧	PROPN
ejpam-7015	159	4	ξb(xy	ξb(xy	PROPN
ejpam-7015	159	5	)	)	PUNCT
ejpam-7015	159	6	≥	≥	NOUN
ejpam-7015	159	7	a(x)ג	a(x)ג	PROPN
ejpam-7015	159	8	)	)	PUNCT
ejpam-7015	159	9	∧	∧	PROPN
ejpam-7015	159	10	(	(	PUNCT
ejpam-7015	159	11	a(y)ג	a(y)ג	PROPN
ejpam-7015	159	12	∧	∧	PROPN
ejpam-7015	159	13	(	(	PUNCT
ejpam-7015	159	14	ξb(x	ξb(x	NUM
ejpam-7015	159	15	)	)	PUNCT
ejpam-7015	159	16	∧	∧	NOUN
ejpam-7015	159	17	ξb(y	ξb(y	NUM
ejpam-7015	159	18	)	)	PUNCT
ejpam-7015	159	19	)	)	PUNCT
ejpam-7015	160	1	=	=	SYM
ejpam-7015	160	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	160	3	)	)	PUNCT
ejpam-7015	160	4	∧	∧	NOUN
ejpam-7015	160	5	ξb(x	ξb(x	NUM
ejpam-7015	160	6	)	)	PUNCT
ejpam-7015	160	7	)	)	PUNCT
ejpam-7015	160	8	∧	∧	PROPN
ejpam-7015	160	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	160	10	)	)	PUNCT
ejpam-7015	160	11	∧	∧	PROPN
ejpam-7015	160	12	ξb(y	ξb(y	NUM
ejpam-7015	160	13	)	)	PUNCT
ejpam-7015	160	14	)	)	PUNCT
ejpam-7015	161	1	=	=	SYM
ejpam-7015	161	2	ω(a	ω(a	PROPN
ejpam-7015	161	3	,	,	PUNCT
ejpam-7015	161	4	b)(x	b)(x	PROPN
ejpam-7015	161	5	)	)	PUNCT
ejpam-7015	161	6	∨	∨	NUM
ejpam-7015	161	7	ω(a	ω(a	PROPN
ejpam-7015	161	8	,	,	PUNCT
ejpam-7015	161	9	b)(y	b)(y	PROPN
ejpam-7015	161	10	)	)	PUNCT
ejpam-7015	161	11	.	.	PUNCT
ejpam-7015	162	1	hence	hence	ADV
ejpam-7015	162	2	,	,	PUNCT
ejpam-7015	162	3	(	(	PUNCT
ejpam-7015	162	4	u	u	NOUN
ejpam-7015	162	5	,	,	PUNCT
ejpam-7015	162	6	ג	ג	NOUN
ejpam-7015	162	7	)	)	PUNCT
ejpam-7015	162	8	∧	∧	PROPN
ejpam-7015	162	9	(	(	PUNCT
ejpam-7015	162	10	ξ	ξ	PROPN
ejpam-7015	162	11	,	,	PUNCT
ejpam-7015	162	12	h	h	NOUN
ejpam-7015	162	13	)	)	PUNCT
ejpam-7015	162	14	is	be	AUX
ejpam-7015	162	15	an	an	DET
ejpam-7015	162	16	afsi	afsi	NOUN
ejpam-7015	162	17	of	of	ADP
ejpam-7015	162	18	ℵ.	ℵ.	PROPN
ejpam-7015	162	19	theorem	theorem	VERB
ejpam-7015	162	20	6	6	NUM
ejpam-7015	162	21	.	.	PUNCT
ejpam-7015	163	1	let	let	VERB
ejpam-7015	163	2	(	(	PUNCT
ejpam-7015	163	3	u	u	NOUN
ejpam-7015	163	4	,	,	PUNCT
ejpam-7015	163	5	ג	ג	PROPN
ejpam-7015	163	6	)	)	PUNCT
ejpam-7015	163	7	and	and	CCONJ
ejpam-7015	163	8	(	(	PUNCT
ejpam-7015	163	9	ξ	ξ	PROPN
ejpam-7015	163	10	,	,	PUNCT
ejpam-7015	163	11	h	h	NOUN
ejpam-7015	163	12	)	)	PUNCT
ejpam-7015	163	13	be	be	VERB
ejpam-7015	163	14	two	two	NUM
ejpam-7015	163	15	afsis	afsis	NOUN
ejpam-7015	163	16	.	.	PUNCT
ejpam-7015	164	1	if	if	SCONJ
ejpam-7015	164	2	(	(	PUNCT
ejpam-7015	164	3	u	u	NOUN
ejpam-7015	164	4	,	,	PUNCT
ejpam-7015	164	5	ג	ג	NOUN
ejpam-7015	164	6	)	)	PUNCT
ejpam-7015	164	7	∨	∨	NOUN
ejpam-7015	164	8	(	(	PUNCT
ejpam-7015	164	9	ξ	ξ	PROPN
ejpam-7015	164	10	,	,	PUNCT
ejpam-7015	164	11	h	h	NOUN
ejpam-7015	164	12	)	)	PUNCT
ejpam-7015	164	13	is	be	AUX
ejpam-7015	164	14	non	non	ADJ
ejpam-7015	164	15	-	-	ADJ
ejpam-7015	164	16	null	null	ADJ
ejpam-7015	164	17	,	,	PUNCT
ejpam-7015	164	18	then	then	ADV
ejpam-7015	164	19	it	it	PRON
ejpam-7015	164	20	’s	’	VERB
ejpam-7015	164	21	an	an	DET
ejpam-7015	164	22	afsi	afsi	NOUN
ejpam-7015	164	23	.	.	PUNCT
ejpam-7015	165	1	proof	proof	NOUN
ejpam-7015	165	2	.	.	PUNCT
ejpam-7015	166	1	let	let	VERB
ejpam-7015	166	2	us	we	PRON
ejpam-7015	166	3	take	take	VERB
ejpam-7015	166	4	∨(u	∨(u	PROPN
ejpam-7015	166	5	,	,	PUNCT
ejpam-7015	166	6	ג	ג	NOUN
ejpam-7015	166	7	)	)	PUNCT
ejpam-7015	166	8	(	(	PUNCT
ejpam-7015	166	9	ξ	ξ	PROPN
ejpam-7015	166	10	,	,	PUNCT
ejpam-7015	166	11	h	h	NOUN
ejpam-7015	166	12	)	)	PUNCT
ejpam-7015	166	13	=	=	SYM
ejpam-7015	166	14	ω	ω	PROPN
ejpam-7015	166	15	,	,	PUNCT
ejpam-7015	166	16	s	s	PART
ejpam-7015	166	17	)	)	PUNCT
ejpam-7015	166	18	respectively	respectively	ADV
ejpam-7015	166	19	,	,	PUNCT
ejpam-7015	166	20	where	where	SCONJ
ejpam-7015	166	21	s	s	VERB
ejpam-7015	166	22	=	=	SYM
ejpam-7015	166	23	u×h	u×h	PROPN
ejpam-7015	166	24	and	and	CCONJ
ejpam-7015	166	25	ω(a	ω(a	PROPN
ejpam-7015	166	26	,	,	PUNCT
ejpam-7015	166	27	b	b	NOUN
ejpam-7015	166	28	)	)	PUNCT
ejpam-7015	166	29	=	=	SYM
ejpam-7015	166	30	(	(	PUNCT
ejpam-7015	166	31	a)ג	a)ג	X
ejpam-7015	166	32	∨	∨	NUM
ejpam-7015	166	33	ξ(b	ξ(b	NOUN
ejpam-7015	166	34	)	)	PUNCT
ejpam-7015	166	35	,	,	PUNCT
ejpam-7015	166	36	∀(a	∀(a	PROPN
ejpam-7015	166	37	,	,	PUNCT
ejpam-7015	166	38	b	b	X
ejpam-7015	166	39	)	)	PUNCT
ejpam-7015	166	40	∈	∈	PROPN
ejpam-7015	166	41	s.	s.	PROPN
ejpam-7015	166	42	since	since	SCONJ
ejpam-7015	166	43	(	(	PUNCT
ejpam-7015	166	44	u	u	NOUN
ejpam-7015	166	45	,	,	PUNCT
ejpam-7015	166	46	ג	ג	PROPN
ejpam-7015	166	47	)	)	PUNCT
ejpam-7015	166	48	and	and	CCONJ
ejpam-7015	166	49	(	(	PUNCT
ejpam-7015	166	50	ξ	ξ	PROPN
ejpam-7015	166	51	,	,	PUNCT
ejpam-7015	166	52	h	h	NOUN
ejpam-7015	166	53	)	)	PUNCT
ejpam-7015	166	54	are	be	AUX
ejpam-7015	166	55	afsis	afsis	NOUN
ejpam-7015	166	56	of	of	ADP
ejpam-7015	166	57	ℵ	ℵ	NOUN
ejpam-7015	166	58	,	,	PUNCT
ejpam-7015	166	59	we	we	PRON
ejpam-7015	166	60	have	have	VERB
ejpam-7015	166	61	∀x	∀x	NUM
ejpam-7015	166	62	,	,	PUNCT
ejpam-7015	166	63	y	y	PROPN
ejpam-7015	166	64	∈	∈	PROPN
ejpam-7015	166	65	ℵ	ℵ	NOUN
ejpam-7015	166	66	,	,	PUNCT
ejpam-7015	166	67	ω(a	ω(a	NOUN
ejpam-7015	166	68	,	,	PUNCT
ejpam-7015	166	69	b)(x+	b)(x+	NOUN
ejpam-7015	166	70	y	y	NOUN
ejpam-7015	166	71	)	)	PUNCT
ejpam-7015	166	72	=	=	PUNCT
ejpam-7015	167	1	+	+	PROPN
ejpam-7015	167	2	a(xג	a(xג	PROPN
ejpam-7015	167	3	y	y	PROPN
ejpam-7015	167	4	)	)	PUNCT
ejpam-7015	167	5	∨	∨	PROPN
ejpam-7015	167	6	ξb(x+	ξb(x+	PROPN
ejpam-7015	167	7	y	y	PROPN
ejpam-7015	167	8	)	)	PUNCT
ejpam-7015	167	9	≤	≤	PROPN
ejpam-7015	167	10	a(x)ג	a(x)ג	PROPN
ejpam-7015	167	11	)	)	PUNCT
ejpam-7015	167	12	∨	∨	PROPN
ejpam-7015	167	13	(	(	PUNCT
ejpam-7015	167	14	a(y)ג	a(y)ג	PROPN
ejpam-7015	167	15	∨	∨	PROPN
ejpam-7015	167	16	(	(	PUNCT
ejpam-7015	167	17	ξb(x	ξb(x	NUM
ejpam-7015	167	18	)	)	PUNCT
ejpam-7015	167	19	∨	∨	NUM
ejpam-7015	167	20	ξb(y	ξb(y	NUM
ejpam-7015	167	21	)	)	PUNCT
ejpam-7015	167	22	)	)	PUNCT
ejpam-7015	168	1	=	=	SYM
ejpam-7015	168	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	168	3	)	)	PUNCT
ejpam-7015	168	4	∨	∨	NUM
ejpam-7015	168	5	ξb(x	ξb(x	NUM
ejpam-7015	168	6	)	)	PUNCT
ejpam-7015	168	7	)	)	PUNCT
ejpam-7015	168	8	∨	∨	PROPN
ejpam-7015	168	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	168	10	)	)	PUNCT
ejpam-7015	168	11	∨	∨	NUM
ejpam-7015	168	12	ξb(y	ξb(y	NUM
ejpam-7015	168	13	)	)	PUNCT
ejpam-7015	168	14	)	)	PUNCT
ejpam-7015	169	1	=	=	SYM
ejpam-7015	169	2	ω(a	ω(a	PROPN
ejpam-7015	169	3	,	,	PUNCT
ejpam-7015	169	4	b)(x	b)(x	PROPN
ejpam-7015	169	5	)	)	PUNCT
ejpam-7015	169	6	∨	∨	NUM
ejpam-7015	169	7	ω(a	ω(a	PROPN
ejpam-7015	169	8	,	,	PUNCT
ejpam-7015	169	9	b)(y	b)(y	PROPN
ejpam-7015	169	10	)	)	PUNCT
ejpam-7015	169	11	,	,	PUNCT
ejpam-7015	169	12	ω(a	ω(a	PROPN
ejpam-7015	169	13	,	,	PUNCT
ejpam-7015	169	14	b)(xy	b)(xy	NOUN
ejpam-7015	169	15	)	)	PUNCT
ejpam-7015	169	16	=	=	SYM
ejpam-7015	170	1	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	170	2	∨	∨	PROPN
ejpam-7015	170	3	ξb(xy	ξb(xy	PROPN
ejpam-7015	170	4	)	)	PUNCT
ejpam-7015	170	5	≥	≥	NOUN
ejpam-7015	170	6	a(x)ג	a(x)ג	PROPN
ejpam-7015	170	7	)	)	PUNCT
ejpam-7015	170	8	∧	∧	PROPN
ejpam-7015	170	9	(	(	PUNCT
ejpam-7015	170	10	a(y)ג	a(y)ג	PROPN
ejpam-7015	170	11	∨	∨	PROPN
ejpam-7015	170	12	(	(	PUNCT
ejpam-7015	170	13	ξb(x	ξb(x	NUM
ejpam-7015	170	14	)	)	PUNCT
ejpam-7015	170	15	∧	∧	NOUN
ejpam-7015	170	16	ξb(y	ξb(y	NUM
ejpam-7015	170	17	)	)	PUNCT
ejpam-7015	170	18	)	)	PUNCT
ejpam-7015	171	1	=	=	SYM
ejpam-7015	171	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	171	3	)	)	PUNCT
ejpam-7015	171	4	∨	∨	NUM
ejpam-7015	171	5	ξb(x	ξb(x	NUM
ejpam-7015	171	6	)	)	PUNCT
ejpam-7015	171	7	)	)	PUNCT
ejpam-7015	172	1	∧	∧	PROPN
ejpam-7015	172	2	a(y)ג	a(y)ג	PROPN
ejpam-7015	172	3	)	)	PUNCT
ejpam-7015	172	4	∨	∨	NUM
ejpam-7015	172	5	ξb(y	ξb(y	NUM
ejpam-7015	172	6	)	)	PUNCT
ejpam-7015	172	7	)	)	PUNCT
ejpam-7015	173	1	=	=	SYM
ejpam-7015	173	2	ω(a	ω(a	PROPN
ejpam-7015	173	3	,	,	PUNCT
ejpam-7015	173	4	b)(x	b)(x	PROPN
ejpam-7015	173	5	)	)	PUNCT
ejpam-7015	173	6	∧	∧	PROPN
ejpam-7015	173	7	ω(a	ω(a	PROPN
ejpam-7015	173	8	,	,	PUNCT
ejpam-7015	173	9	b)(y	b)(y	PROPN
ejpam-7015	173	10	)	)	PUNCT
ejpam-7015	173	11	.	.	PUNCT
ejpam-7015	174	1	hence	hence	ADV
ejpam-7015	174	2	,	,	PUNCT
ejpam-7015	174	3	(	(	PUNCT
ejpam-7015	174	4	u	u	NOUN
ejpam-7015	174	5	,	,	PUNCT
ejpam-7015	174	6	ג	ג	PROPN
ejpam-7015	174	7	)	)	PUNCT
ejpam-7015	174	8	∨	∨	NOUN
ejpam-7015	174	9	(	(	PUNCT
ejpam-7015	174	10	ξ	ξ	PROPN
ejpam-7015	174	11	,	,	PUNCT
ejpam-7015	174	12	h	h	NOUN
ejpam-7015	174	13	)	)	PUNCT
ejpam-7015	174	14	is	be	AUX
ejpam-7015	174	15	an	an	DET
ejpam-7015	174	16	afsi	afsi	NOUN
ejpam-7015	174	17	of	of	ADP
ejpam-7015	174	18	ℵ.	ℵ.	PROPN
ejpam-7015	174	19	d.	d.	PROPN
ejpam-7015	174	20	ramesh	ramesh	PROPN
ejpam-7015	174	21	et	et	PROPN
ejpam-7015	174	22	al	al	PROPN
ejpam-7015	174	23	.	.	PUNCT
ejpam-7015	174	24	/	/	SYM
ejpam-7015	174	25	eur	eur	PROPN
ejpam-7015	174	26	.	.	PUNCT
ejpam-7015	175	1	j.	j.	PROPN
ejpam-7015	175	2	pure	pure	PROPN
ejpam-7015	175	3	appl	appl	PROPN
ejpam-7015	175	4	.	.	PROPN
ejpam-7015	175	5	math	math	PROPN
ejpam-7015	175	6	,	,	PUNCT
ejpam-7015	175	7	18	18	NUM
ejpam-7015	175	8	(	(	PUNCT
ejpam-7015	175	9	4	4	NUM
ejpam-7015	175	10	)	)	PUNCT
ejpam-7015	175	11	(	(	PUNCT
ejpam-7015	175	12	2025	2025	NUM
ejpam-7015	175	13	)	)	PUNCT
ejpam-7015	175	14	,	,	PUNCT
ejpam-7015	175	15	7015	7015	NUM
ejpam-7015	175	16	9	9	NUM
ejpam-7015	175	17	of	of	ADP
ejpam-7015	175	18	11	11	NUM
ejpam-7015	175	19	theorem	theorem	NOUN
ejpam-7015	175	20	7	7	NUM
ejpam-7015	175	21	.	.	PUNCT
ejpam-7015	176	1	let	let	VERB
ejpam-7015	176	2	(	(	PUNCT
ejpam-7015	176	3	u	u	NOUN
ejpam-7015	176	4	,	,	PUNCT
ejpam-7015	176	5	ג	ג	PROPN
ejpam-7015	176	6	)	)	PUNCT
ejpam-7015	176	7	and	and	CCONJ
ejpam-7015	176	8	(	(	PUNCT
ejpam-7015	176	9	ξ	ξ	PROPN
ejpam-7015	176	10	,	,	PUNCT
ejpam-7015	176	11	h	h	NOUN
ejpam-7015	176	12	)	)	PUNCT
ejpam-7015	176	13	be	be	VERB
ejpam-7015	176	14	two	two	NUM
ejpam-7015	176	15	afsis	afsis	NOUN
ejpam-7015	176	16	.	.	PUNCT
ejpam-7015	177	1	if	if	SCONJ
ejpam-7015	177	2	(	(	PUNCT
ejpam-7015	177	3	u	u	NOUN
ejpam-7015	177	4	,	,	PUNCT
ejpam-7015	177	5	ג	ג	NOUN
ejpam-7015	177	6	)	)	PUNCT
ejpam-7015	177	7	∩	∩	NOUN
ejpam-7015	177	8	(	(	PUNCT
ejpam-7015	177	9	ξ	ξ	PROPN
ejpam-7015	177	10	,	,	PUNCT
ejpam-7015	177	11	h	h	NOUN
ejpam-7015	177	12	)	)	PUNCT
ejpam-7015	177	13	is	be	AUX
ejpam-7015	177	14	non	non	ADJ
ejpam-7015	177	15	-	-	ADJ
ejpam-7015	177	16	null	null	ADJ
ejpam-7015	177	17	,	,	PUNCT
ejpam-7015	177	18	then	then	ADV
ejpam-7015	177	19	it	it	PRON
ejpam-7015	177	20	’s	’	VERB
ejpam-7015	177	21	an	an	DET
ejpam-7015	177	22	afsi	afsi	NOUN
ejpam-7015	177	23	.	.	PUNCT
ejpam-7015	178	1	proof	proof	NOUN
ejpam-7015	178	2	.	.	PUNCT
ejpam-7015	179	1	let	let	VERB
ejpam-7015	179	2	us	we	PRON
ejpam-7015	179	3	take	take	VERB
ejpam-7015	179	4	∩(u	∩(u	PROPN
ejpam-7015	179	5	,	,	PUNCT
ejpam-7015	179	6	ג	ג	NOUN
ejpam-7015	179	7	)	)	PUNCT
ejpam-7015	179	8	(	(	PUNCT
ejpam-7015	179	9	ξ	ξ	PROPN
ejpam-7015	179	10	,	,	PUNCT
ejpam-7015	179	11	h	h	NOUN
ejpam-7015	179	12	)	)	PUNCT
ejpam-7015	179	13	=	=	SYM
ejpam-7015	179	14	(	(	PUNCT
ejpam-7015	179	15	ω	ω	PROPN
ejpam-7015	179	16	,	,	PUNCT
ejpam-7015	179	17	s	s	PART
ejpam-7015	179	18	)	)	PUNCT
ejpam-7015	179	19	respectively	respectively	ADV
ejpam-7015	179	20	,	,	PUNCT
ejpam-7015	179	21	where	where	SCONJ
ejpam-7015	179	22	s	s	AUX
ejpam-7015	179	23	=	=	X
ejpam-7015	179	24	u∩h	u∩h	ADJ
ejpam-7015	179	25	and	and	CCONJ
ejpam-7015	179	26	ω(a	ω(a	PROPN
ejpam-7015	179	27	,	,	PUNCT
ejpam-7015	179	28	b	b	NOUN
ejpam-7015	179	29	)	)	PUNCT
ejpam-7015	179	30	=	=	SYM
ejpam-7015	179	31	(	(	PUNCT
ejpam-7015	180	1	a)ג	a)ג	NOUN
ejpam-7015	180	2	∩	∩	NOUN
ejpam-7015	180	3	ξ(b	ξ(b	NOUN
ejpam-7015	180	4	)	)	PUNCT
ejpam-7015	180	5	,	,	PUNCT
ejpam-7015	180	6	∀(a	∀(a	PROPN
ejpam-7015	180	7	,	,	PUNCT
ejpam-7015	180	8	b	b	X
ejpam-7015	180	9	)	)	PUNCT
ejpam-7015	180	10	∈	∈	PROPN
ejpam-7015	180	11	s.	s.	PROPN
ejpam-7015	180	12	since	since	SCONJ
ejpam-7015	180	13	(	(	PUNCT
ejpam-7015	180	14	u	u	NOUN
ejpam-7015	180	15	,	,	PUNCT
ejpam-7015	180	16	ג	ג	PROPN
ejpam-7015	180	17	)	)	PUNCT
ejpam-7015	180	18	and	and	CCONJ
ejpam-7015	180	19	(	(	PUNCT
ejpam-7015	180	20	ξ	ξ	PROPN
ejpam-7015	180	21	,	,	PUNCT
ejpam-7015	180	22	h	h	NOUN
ejpam-7015	180	23	)	)	PUNCT
ejpam-7015	180	24	are	be	AUX
ejpam-7015	180	25	afsis	afsis	NOUN
ejpam-7015	180	26	of	of	ADP
ejpam-7015	180	27	ℵ	ℵ	NOUN
ejpam-7015	180	28	,	,	PUNCT
ejpam-7015	180	29	we	we	PRON
ejpam-7015	180	30	have	have	VERB
ejpam-7015	180	31	∀x	∀x	NUM
ejpam-7015	180	32	,	,	PUNCT
ejpam-7015	180	33	y	y	PROPN
ejpam-7015	180	34	∈	∈	PROPN
ejpam-7015	180	35	ℵ	ℵ	NOUN
ejpam-7015	180	36	,	,	PUNCT
ejpam-7015	180	37	ω(a	ω(a	NOUN
ejpam-7015	180	38	,	,	PUNCT
ejpam-7015	180	39	b)(x+	b)(x+	NOUN
ejpam-7015	180	40	y	y	NOUN
ejpam-7015	180	41	)	)	PUNCT
ejpam-7015	180	42	=	=	PUNCT
ejpam-7015	181	1	+	+	PROPN
ejpam-7015	181	2	a(xג	a(xג	PROPN
ejpam-7015	181	3	y	y	NOUN
ejpam-7015	181	4	)	)	PUNCT
ejpam-7015	181	5	∩	∩	PROPN
ejpam-7015	181	6	ξb(x+	ξb(x+	PROPN
ejpam-7015	181	7	y	y	PROPN
ejpam-7015	181	8	)	)	PUNCT
ejpam-7015	181	9	≤	≤	PROPN
ejpam-7015	181	10	a(x)ג	a(x)ג	PROPN
ejpam-7015	181	11	)	)	PUNCT
ejpam-7015	181	12	∨	∨	PROPN
ejpam-7015	181	13	(	(	PUNCT
ejpam-7015	181	14	a(y)ג	a(y)ג	PROPN
ejpam-7015	181	15	∩	∩	PROPN
ejpam-7015	181	16	(	(	PUNCT
ejpam-7015	181	17	ξb(x	ξb(x	NUM
ejpam-7015	181	18	)	)	PUNCT
ejpam-7015	181	19	∨	∨	NUM
ejpam-7015	181	20	ξb(y	ξb(y	NUM
ejpam-7015	181	21	)	)	PUNCT
ejpam-7015	181	22	)	)	PUNCT
ejpam-7015	182	1	=	=	SYM
ejpam-7015	182	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	182	3	)	)	PUNCT
ejpam-7015	182	4	∩	∩	NOUN
ejpam-7015	182	5	ξb(x	ξb(x	NUM
ejpam-7015	182	6	)	)	PUNCT
ejpam-7015	182	7	)	)	PUNCT
ejpam-7015	182	8	∨	∨	PROPN
ejpam-7015	182	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	182	10	)	)	PUNCT
ejpam-7015	182	11	∩	∩	NOUN
ejpam-7015	182	12	ξb(y	ξb(y	NUM
ejpam-7015	182	13	)	)	PUNCT
ejpam-7015	182	14	)	)	PUNCT
ejpam-7015	183	1	=	=	SYM
ejpam-7015	183	2	ω(a	ω(a	PROPN
ejpam-7015	183	3	,	,	PUNCT
ejpam-7015	183	4	b)(x	b)(x	PROPN
ejpam-7015	183	5	)	)	PUNCT
ejpam-7015	183	6	∨	∨	NUM
ejpam-7015	183	7	ω(a	ω(a	PROPN
ejpam-7015	183	8	,	,	PUNCT
ejpam-7015	183	9	b)(y	b)(y	PROPN
ejpam-7015	183	10	)	)	PUNCT
ejpam-7015	183	11	,	,	PUNCT
ejpam-7015	183	12	ω(a	ω(a	PROPN
ejpam-7015	183	13	,	,	PUNCT
ejpam-7015	183	14	b)(xy	b)(xy	NOUN
ejpam-7015	183	15	)	)	PUNCT
ejpam-7015	183	16	=	=	SYM
ejpam-7015	184	1	a(xy)ג	a(xy)ג	PROPN
ejpam-7015	184	2	∩	∩	PROPN
ejpam-7015	184	3	ξb(xy	ξb(xy	PROPN
ejpam-7015	184	4	)	)	PUNCT
ejpam-7015	184	5	≥	≥	NOUN
ejpam-7015	184	6	a(x)ג	a(x)ג	PROPN
ejpam-7015	184	7	)	)	PUNCT
ejpam-7015	185	1	∧	∧	PROPN
ejpam-7015	185	2	(	(	PUNCT
ejpam-7015	185	3	a(y)ג	a(y)ג	PROPN
ejpam-7015	185	4	∩	∩	PROPN
ejpam-7015	185	5	(	(	PUNCT
ejpam-7015	185	6	ξb(x	ξb(x	NUM
ejpam-7015	185	7	)	)	PUNCT
ejpam-7015	185	8	∧	∧	NOUN
ejpam-7015	185	9	ξb(y	ξb(y	NUM
ejpam-7015	185	10	)	)	PUNCT
ejpam-7015	185	11	)	)	PUNCT
ejpam-7015	186	1	=	=	SYM
ejpam-7015	186	2	a(x)ג	a(x)ג	PROPN
ejpam-7015	186	3	)	)	PUNCT
ejpam-7015	186	4	∩	∩	NOUN
ejpam-7015	186	5	ξb(x	ξb(x	NUM
ejpam-7015	186	6	)	)	PUNCT
ejpam-7015	186	7	)	)	PUNCT
ejpam-7015	186	8	∧	∧	PROPN
ejpam-7015	186	9	a(y)ג	a(y)ג	PROPN
ejpam-7015	186	10	)	)	PUNCT
ejpam-7015	186	11	∩	∩	NOUN
ejpam-7015	186	12	ξb(y	ξb(y	NUM
ejpam-7015	186	13	)	)	PUNCT
ejpam-7015	186	14	)	)	PUNCT
ejpam-7015	187	1	=	=	SYM
ejpam-7015	187	2	ω(a	ω(a	PROPN
ejpam-7015	187	3	,	,	PUNCT
ejpam-7015	187	4	b)(x	b)(x	PROPN
ejpam-7015	187	5	)	)	PUNCT
ejpam-7015	187	6	∧	∧	PROPN
ejpam-7015	187	7	ω(a	ω(a	PROPN
ejpam-7015	187	8	,	,	PUNCT
ejpam-7015	187	9	b)(y	b)(y	PROPN
ejpam-7015	187	10	)	)	PUNCT
ejpam-7015	187	11	.	.	PUNCT
ejpam-7015	188	1	hence	hence	ADV
ejpam-7015	188	2	,	,	PUNCT
ejpam-7015	188	3	(	(	PUNCT
ejpam-7015	188	4	u	u	NOUN
ejpam-7015	188	5	,	,	PUNCT
ejpam-7015	188	6	ג	ג	NOUN
ejpam-7015	188	7	)	)	PUNCT
ejpam-7015	188	8	∩	∩	NOUN
ejpam-7015	188	9	(	(	PUNCT
ejpam-7015	188	10	ξ	ξ	PROPN
ejpam-7015	188	11	,	,	PUNCT
ejpam-7015	188	12	h	h	NOUN
ejpam-7015	188	13	)	)	PUNCT
ejpam-7015	188	14	is	be	AUX
ejpam-7015	188	15	an	an	DET
ejpam-7015	188	16	afsi	afsi	NOUN
ejpam-7015	188	17	of	of	ADP
ejpam-7015	188	18	ℵ.	ℵ.	PROPN
ejpam-7015	188	19	theorem	theorem	VERB
ejpam-7015	188	20	8	8	NUM
ejpam-7015	188	21	.	.	PUNCT
ejpam-7015	189	1	let	let	VERB
ejpam-7015	189	2	(	(	PUNCT
ejpam-7015	189	3	u	u	NOUN
ejpam-7015	189	4	,	,	PUNCT
ejpam-7015	189	5	ג	ג	PROPN
ejpam-7015	189	6	)	)	PUNCT
ejpam-7015	189	7	and	and	CCONJ
ejpam-7015	189	8	(	(	PUNCT
ejpam-7015	189	9	ξ	ξ	PROPN
ejpam-7015	189	10	,	,	PUNCT
ejpam-7015	189	11	h	h	NOUN
ejpam-7015	189	12	)	)	PUNCT
ejpam-7015	189	13	be	be	VERB
ejpam-7015	189	14	two	two	NUM
ejpam-7015	189	15	afsis	afsis	NOUN
ejpam-7015	189	16	.	.	PUNCT
ejpam-7015	190	1	if	if	SCONJ
ejpam-7015	190	2	(	(	PUNCT
ejpam-7015	190	3	u	u	NOUN
ejpam-7015	190	4	,	,	PUNCT
ejpam-7015	190	5	ג	ג	NOUN
ejpam-7015	190	6	)	)	PUNCT
ejpam-7015	190	7	∪	∪	NOUN
ejpam-7015	190	8	(	(	PUNCT
ejpam-7015	190	9	ξ	ξ	PROPN
ejpam-7015	190	10	,	,	PUNCT
ejpam-7015	190	11	h	h	NOUN
ejpam-7015	190	12	)	)	PUNCT
ejpam-7015	190	13	is	be	AUX
ejpam-7015	190	14	non	non	ADJ
ejpam-7015	190	15	-	-	ADJ
ejpam-7015	190	16	null	null	ADJ
ejpam-7015	190	17	,	,	PUNCT
ejpam-7015	190	18	then	then	ADV
ejpam-7015	190	19	it	it	PRON
ejpam-7015	190	20	’s	’	VERB
ejpam-7015	190	21	an	an	DET
ejpam-7015	190	22	afsi	afsi	NOUN
ejpam-7015	190	23	.	.	PUNCT
ejpam-7015	191	1	proof	proof	NOUN
ejpam-7015	191	2	.	.	PUNCT
ejpam-7015	192	1	for	for	ADP
ejpam-7015	192	2	any	any	DET
ejpam-7015	192	3	e	e	PROPN
ejpam-7015	192	4	∈	∈	PROPN
ejpam-7015	192	5	u	u	NOUN
ejpam-7015	192	6	∪	∪	NOUN
ejpam-7015	192	7	h	h	NOUN
ejpam-7015	192	8	,	,	PUNCT
ejpam-7015	192	9	and	and	CCONJ
ejpam-7015	192	10	x	x	X
ejpam-7015	192	11	,	,	PUNCT
ejpam-7015	192	12	y	y	PROPN
ejpam-7015	192	13	∈	∈	PROPN
ejpam-7015	192	14	ℵ	ℵ	NOUN
ejpam-7015	192	15	,	,	PUNCT
ejpam-7015	192	16	we	we	PRON
ejpam-7015	192	17	consider	consider	VERB
ejpam-7015	192	18	the	the	DET
ejpam-7015	192	19	subsequent	subsequent	ADJ
ejpam-7015	192	20	scenarios	scenario	NOUN
ejpam-7015	192	21	.	.	PUNCT
ejpam-7015	193	1	case	case	NOUN
ejpam-7015	194	1	i	i	PRON
ejpam-7015	194	2	:	:	PUNCT
ejpam-7015	194	3	if	if	SCONJ
ejpam-7015	194	4	e	e	PROPN
ejpam-7015	194	5	∈	∈	PROPN
ejpam-7015	194	6	u−	u−	PROPN
ejpam-7015	194	7	h	h	NOUN
ejpam-7015	194	8	,	,	PUNCT
ejpam-7015	194	9	then	then	ADV
ejpam-7015	194	10	ωe(x+	ωe(x+	ADV
ejpam-7015	194	11	y	y	X
ejpam-7015	194	12	)	)	PUNCT
ejpam-7015	194	13	=	=	PUNCT
ejpam-7015	195	1	+	+	VERB
ejpam-7015	195	2	e(xג	e(xג	PROPN
ejpam-7015	195	3	y	y	NOUN
ejpam-7015	195	4	)	)	PUNCT
ejpam-7015	195	5	≤	≤	PUNCT
ejpam-7015	196	1	e(x)ג	e(x)ג	PROPN
ejpam-7015	196	2	∨	∨	NUM
ejpam-7015	196	3	e(y)ג	e(y)ג	PRON
ejpam-7015	196	4	=	=	SYM
ejpam-7015	196	5	ωe(x	ωe(x	X
ejpam-7015	196	6	)	)	PUNCT
ejpam-7015	196	7	∨	∨	NUM
ejpam-7015	196	8	ωe(y	ωe(y	NUM
ejpam-7015	196	9	)	)	PUNCT
ejpam-7015	196	10	,	,	PUNCT
ejpam-7015	196	11	ωe(xy	ωe(xy	NOUN
ejpam-7015	196	12	)	)	PUNCT
ejpam-7015	196	13	=	=	SYM
ejpam-7015	196	14	e(xy)ג	e(xy)ג	PROPN
ejpam-7015	196	15	≥	≥	NOUN
ejpam-7015	196	16	e(x)ג	e(x)ג	PROPN
ejpam-7015	196	17	∧	∧	PROPN
ejpam-7015	196	18	e(y)ג	e(y)ג	ADJ
ejpam-7015	196	19	=	=	SYM
ejpam-7015	196	20	ωe(x	ωe(x	X
ejpam-7015	196	21	)	)	PUNCT
ejpam-7015	196	22	∧	∧	NOUN
ejpam-7015	196	23	ωe(y	ωe(y	NUM
ejpam-7015	196	24	)	)	PUNCT
ejpam-7015	196	25	.	.	PUNCT
ejpam-7015	197	1	case	case	NOUN
ejpam-7015	197	2	ii	ii	NOUN
ejpam-7015	197	3	:	:	PUNCT
ejpam-7015	197	4	if	if	SCONJ
ejpam-7015	197	5	e	e	PROPN
ejpam-7015	197	6	∈	∈	PROPN
ejpam-7015	197	7	h−	h−	PROPN
ejpam-7015	197	8	u	u	NOUN
ejpam-7015	197	9	,	,	PUNCT
ejpam-7015	197	10	then	then	ADV
ejpam-7015	197	11	ωe(x+	ωe(x+	ADV
ejpam-7015	197	12	y	y	X
ejpam-7015	197	13	)	)	PUNCT
ejpam-7015	197	14	=	=	PUNCT
ejpam-7015	198	1	ξe(x+	ξe(x+	ADV
ejpam-7015	198	2	y	y	NOUN
ejpam-7015	198	3	)	)	PUNCT
ejpam-7015	198	4	≤	≤	NOUN
ejpam-7015	198	5	ξe(x	ξe(x	PUNCT
ejpam-7015	198	6	)	)	PUNCT
ejpam-7015	198	7	∨	∨	NUM
ejpam-7015	198	8	ξe(y	ξe(y	NUM
ejpam-7015	198	9	)	)	PUNCT
ejpam-7015	198	10	=	=	SYM
ejpam-7015	198	11	ωe(x	ωe(x	X
ejpam-7015	198	12	)	)	PUNCT
ejpam-7015	198	13	∨	∨	NUM
ejpam-7015	198	14	ωe(y	ωe(y	NUM
ejpam-7015	198	15	)	)	PUNCT
ejpam-7015	198	16	,	,	PUNCT
ejpam-7015	198	17	ωe(xy	ωe(xy	NOUN
ejpam-7015	198	18	)	)	PUNCT
ejpam-7015	198	19	=	=	SYM
ejpam-7015	198	20	ξe(xy	ξe(xy	PROPN
ejpam-7015	198	21	)	)	PUNCT
ejpam-7015	198	22	≥	≥	NOUN
ejpam-7015	198	23	ξe(x	ξe(x	NUM
ejpam-7015	198	24	)	)	PUNCT
ejpam-7015	198	25	∧	∧	PROPN
ejpam-7015	198	26	ξe(y	ξe(y	NUM
ejpam-7015	198	27	)	)	PUNCT
ejpam-7015	198	28	d.	d.	PROPN
ejpam-7015	198	29	ramesh	ramesh	PROPN
ejpam-7015	198	30	et	et	PROPN
ejpam-7015	198	31	al	al	PROPN
ejpam-7015	198	32	.	.	PUNCT
ejpam-7015	198	33	/	/	SYM
ejpam-7015	198	34	eur	eur	PROPN
ejpam-7015	198	35	.	.	PUNCT
ejpam-7015	199	1	j.	j.	PROPN
ejpam-7015	199	2	pure	pure	PROPN
ejpam-7015	199	3	appl	appl	PROPN
ejpam-7015	199	4	.	.	PROPN
ejpam-7015	199	5	math	math	PROPN
ejpam-7015	199	6	,	,	PUNCT
ejpam-7015	199	7	18	18	NUM
ejpam-7015	199	8	(	(	PUNCT
ejpam-7015	199	9	4	4	NUM
ejpam-7015	199	10	)	)	PUNCT
ejpam-7015	199	11	(	(	PUNCT
ejpam-7015	199	12	2025	2025	NUM
ejpam-7015	199	13	)	)	PUNCT
ejpam-7015	199	14	,	,	PUNCT
ejpam-7015	199	15	7015	7015	NUM
ejpam-7015	199	16	10	10	NUM
ejpam-7015	199	17	of	of	ADP
ejpam-7015	199	18	11	11	NUM
ejpam-7015	199	19	=	=	SYM
ejpam-7015	199	20	ωe(x	ωe(x	X
ejpam-7015	199	21	)	)	PUNCT
ejpam-7015	199	22	∧	∧	NOUN
ejpam-7015	199	23	ωe(y	ωe(y	NUM
ejpam-7015	199	24	)	)	PUNCT
ejpam-7015	199	25	.	.	PUNCT
ejpam-7015	200	1	case	case	NOUN
ejpam-7015	200	2	iii	iii	X
ejpam-7015	200	3	:	:	PUNCT
ejpam-7015	200	4	if	if	SCONJ
ejpam-7015	200	5	e	e	PROPN
ejpam-7015	200	6	∈	∈	PROPN
ejpam-7015	200	7	u	u	NOUN
ejpam-7015	200	8	∩	∩	ADJ
ejpam-7015	200	9	h	h	NOUN
ejpam-7015	200	10	,	,	PUNCT
ejpam-7015	200	11	then	then	ADV
ejpam-7015	200	12	ωe(x+	ωe(x+	ADV
ejpam-7015	200	13	y	y	X
ejpam-7015	200	14	)	)	PUNCT
ejpam-7015	200	15	=	=	PUNCT
ejpam-7015	201	1	+	+	ADJ
ejpam-7015	201	2	e(xג	e(xג	PROPN
ejpam-7015	201	3	y	y	NOUN
ejpam-7015	201	4	)	)	PUNCT
ejpam-7015	201	5	∪	∪	VERB
ejpam-7015	201	6	ξe(x+	ξe(x+	PROPN
ejpam-7015	201	7	y	y	NOUN
ejpam-7015	201	8	)	)	PUNCT
ejpam-7015	201	9	≤	≤	NUM
ejpam-7015	201	10	e(x)ג	e(x)ג	NOUN
ejpam-7015	201	11	)	)	PUNCT
ejpam-7015	201	12	∨	∨	PROPN
ejpam-7015	201	13	(	(	PUNCT
ejpam-7015	201	14	e(y)ג	e(y)ג	PROPN
ejpam-7015	201	15	∪	∪	ADJ
ejpam-7015	201	16	(	(	PUNCT
ejpam-7015	201	17	ξe(x	ξe(x	NOUN
ejpam-7015	201	18	)	)	PUNCT
ejpam-7015	201	19	∨	∨	NUM
ejpam-7015	201	20	ξe(y	ξe(y	NUM
ejpam-7015	201	21	)	)	PUNCT
ejpam-7015	201	22	)	)	PUNCT
ejpam-7015	202	1	=	=	PUNCT
ejpam-7015	202	2	e(x)ג	e(x)ג	NOUN
ejpam-7015	202	3	)	)	PUNCT
ejpam-7015	202	4	∪	∪	ADP
ejpam-7015	202	5	ξe(x	ξe(x	NUM
ejpam-7015	202	6	)	)	PUNCT
ejpam-7015	202	7	)	)	PUNCT
ejpam-7015	202	8	∨	∨	NUM
ejpam-7015	202	9	e(y)ג	e(y)ג	PROPN
ejpam-7015	202	10	)	)	PUNCT
ejpam-7015	202	11	∪	∪	ADP
ejpam-7015	202	12	ξe(y	ξe(y	NUM
ejpam-7015	202	13	)	)	PUNCT
ejpam-7015	202	14	)	)	PUNCT
ejpam-7015	202	15	=	=	SYM
ejpam-7015	202	16	ωe(x	ωe(x	X
ejpam-7015	202	17	)	)	PUNCT
ejpam-7015	202	18	∨	∨	NUM
ejpam-7015	202	19	ωe(y	ωe(y	NUM
ejpam-7015	202	20	)	)	PUNCT
ejpam-7015	202	21	,	,	PUNCT
ejpam-7015	202	22	ωe(xy	ωe(xy	NOUN
ejpam-7015	202	23	)	)	PUNCT
ejpam-7015	202	24	=	=	SYM
ejpam-7015	202	25	e(xy)ג	e(xy)ג	PROPN
ejpam-7015	202	26	∪	∪	PROPN
ejpam-7015	202	27	ξe(xy	ξe(xy	PROPN
ejpam-7015	202	28	)	)	PUNCT
ejpam-7015	202	29	≥	≥	NOUN
ejpam-7015	202	30	e(x)ג	e(x)ג	NOUN
ejpam-7015	202	31	)	)	PUNCT
ejpam-7015	202	32	∧	∧	PROPN
ejpam-7015	202	33	(	(	PUNCT
ejpam-7015	202	34	e(y)ג	e(y)ג	PROPN
ejpam-7015	202	35	∪	∪	ADJ
ejpam-7015	202	36	(	(	PUNCT
ejpam-7015	202	37	ξe(x	ξe(x	NOUN
ejpam-7015	202	38	)	)	PUNCT
ejpam-7015	202	39	∧	∧	PROPN
ejpam-7015	202	40	ξe(y	ξe(y	NUM
ejpam-7015	202	41	)	)	PUNCT
ejpam-7015	202	42	)	)	PUNCT
ejpam-7015	203	1	=	=	PUNCT
ejpam-7015	203	2	e(x)ג	e(x)ג	NOUN
ejpam-7015	203	3	)	)	PUNCT
ejpam-7015	203	4	∪	∪	ADP
ejpam-7015	203	5	ξe(x	ξe(x	NUM
ejpam-7015	203	6	)	)	PUNCT
ejpam-7015	203	7	)	)	PUNCT
ejpam-7015	204	1	∧	∧	NOUN
ejpam-7015	204	2	e(y)ג	e(y)ג	PROPN
ejpam-7015	204	3	)	)	PUNCT
ejpam-7015	204	4	∪	∪	ADP
ejpam-7015	204	5	ξe(y	ξe(y	NUM
ejpam-7015	204	6	)	)	PUNCT
ejpam-7015	204	7	)	)	PUNCT
ejpam-7015	205	1	=	=	SYM
ejpam-7015	205	2	ωe(x	ωe(x	X
ejpam-7015	205	3	)	)	PUNCT
ejpam-7015	205	4	∧	∧	NOUN
ejpam-7015	205	5	ωe(y	ωe(y	NUM
ejpam-7015	205	6	)	)	PUNCT
ejpam-7015	205	7	.	.	PUNCT
ejpam-7015	206	1	hence	hence	ADV
ejpam-7015	206	2	,	,	PUNCT
ejpam-7015	206	3	(	(	PUNCT
ejpam-7015	206	4	u	u	NOUN
ejpam-7015	206	5	,	,	PUNCT
ejpam-7015	206	6	ג	ג	NOUN
ejpam-7015	206	7	)	)	PUNCT
ejpam-7015	206	8	∪	∪	NOUN
ejpam-7015	206	9	(	(	PUNCT
ejpam-7015	206	10	ξ	ξ	PROPN
ejpam-7015	206	11	,	,	PUNCT
ejpam-7015	206	12	h	h	NOUN
ejpam-7015	206	13	)	)	PUNCT
ejpam-7015	206	14	is	be	AUX
ejpam-7015	206	15	an	an	DET
ejpam-7015	206	16	afsi	afsi	NOUN
ejpam-7015	206	17	of	of	ADP
ejpam-7015	206	18	ℵ.	ℵ.	PROPN
ejpam-7015	206	19	5	5	NUM
ejpam-7015	206	20	.	.	PUNCT
ejpam-7015	206	21	conclusion	conclusion	NOUN
ejpam-7015	206	22	in	in	ADP
ejpam-7015	206	23	this	this	DET
ejpam-7015	206	24	work	work	NOUN
ejpam-7015	206	25	,	,	PUNCT
ejpam-7015	206	26	we	we	PRON
ejpam-7015	206	27	introduced	introduce	VERB
ejpam-7015	206	28	and	and	CCONJ
ejpam-7015	206	29	rigorously	rigorously	ADV
ejpam-7015	206	30	investigated	investigate	VERB
ejpam-7015	206	31	the	the	DET
ejpam-7015	206	32	theory	theory	NOUN
ejpam-7015	206	33	of	of	ADP
ejpam-7015	206	34	anti	anti	ADJ
ejpam-7015	206	35	-	-	ADJ
ejpam-7015	206	36	fuzzy	fuzzy	ADJ
ejpam-7015	206	37	soft	soft	ADJ
ejpam-7015	206	38	boolean	boolean	ADJ
ejpam-7015	206	39	rings	ring	NOUN
ejpam-7015	206	40	(	(	PUNCT
ejpam-7015	206	41	afsbrs	afsbrs	PROPN
ejpam-7015	206	42	)	)	PUNCT
ejpam-7015	206	43	and	and	CCONJ
ejpam-7015	206	44	anti	anti	ADJ
ejpam-7015	206	45	-	-	ADJ
ejpam-7015	206	46	fuzzy	fuzzy	ADJ
ejpam-7015	206	47	soft	soft	ADJ
ejpam-7015	206	48	ideals	ideal	NOUN
ejpam-7015	206	49	(	(	PUNCT
ejpam-7015	206	50	afsis	afsis	NOUN
ejpam-7015	206	51	)	)	PUNCT
ejpam-7015	206	52	,	,	PUNCT
ejpam-7015	206	53	defining	define	VERB
ejpam-7015	206	54	their	their	PRON
ejpam-7015	206	55	structure	structure	NOUN
ejpam-7015	206	56	,	,	PUNCT
ejpam-7015	206	57	algebraic	algebraic	ADJ
ejpam-7015	206	58	operations	operation	NOUN
ejpam-7015	206	59	,	,	PUNCT
ejpam-7015	206	60	and	and	CCONJ
ejpam-7015	206	61	core	core	NOUN
ejpam-7015	206	62	properties	property	NOUN
ejpam-7015	206	63	.	.	PUNCT
ejpam-7015	207	1	motivated	motivate	VERB
ejpam-7015	207	2	by	by	ADP
ejpam-7015	207	3	the	the	DET
ejpam-7015	207	4	need	need	NOUN
ejpam-7015	207	5	to	to	PART
ejpam-7015	207	6	formally	formally	ADV
ejpam-7015	207	7	capture	capture	VERB
ejpam-7015	207	8	nonmembership	nonmembership	NOUN
ejpam-7015	207	9	and	and	CCONJ
ejpam-7015	207	10	opposing	oppose	VERB
ejpam-7015	207	11	information	information	NOUN
ejpam-7015	207	12	—	—	PUNCT
ejpam-7015	207	13	often	often	ADV
ejpam-7015	207	14	overlooked	overlook	VERB
ejpam-7015	207	15	in	in	ADP
ejpam-7015	207	16	classical	classical	ADJ
ejpam-7015	207	17	fuzzy	fuzzy	ADJ
ejpam-7015	207	18	soft	soft	ADJ
ejpam-7015	207	19	frameworks	framework	NOUN
ejpam-7015	207	20	—	—	PUNCT
ejpam-7015	207	21	this	this	DET
ejpam-7015	207	22	study	study	NOUN
ejpam-7015	207	23	provides	provide	VERB
ejpam-7015	207	24	a	a	DET
ejpam-7015	207	25	dual	dual	ADJ
ejpam-7015	207	26	extension	extension	NOUN
ejpam-7015	207	27	that	that	PRON
ejpam-7015	207	28	enriches	enrich	VERB
ejpam-7015	207	29	the	the	DET
ejpam-7015	207	30	algebraic	algebraic	ADJ
ejpam-7015	207	31	modeling	modeling	NOUN
ejpam-7015	207	32	of	of	ADP
ejpam-7015	207	33	uncertainty	uncertainty	NOUN
ejpam-7015	207	34	.	.	PUNCT
ejpam-7015	208	1	through	through	ADP
ejpam-7015	208	2	precise	precise	ADJ
ejpam-7015	208	3	definitions	definition	NOUN
ejpam-7015	208	4	,	,	PUNCT
ejpam-7015	208	5	illustrative	illustrative	ADJ
ejpam-7015	208	6	examples	example	NOUN
ejpam-7015	208	7	,	,	PUNCT
ejpam-7015	208	8	and	and	CCONJ
ejpam-7015	208	9	closure	closure	NOUN
ejpam-7015	208	10	theorems	theorem	NOUN
ejpam-7015	208	11	,	,	PUNCT
ejpam-7015	208	12	we	we	PRON
ejpam-7015	208	13	established	establish	VERB
ejpam-7015	208	14	the	the	DET
ejpam-7015	208	15	internal	internal	ADJ
ejpam-7015	208	16	consistency	consistency	NOUN
ejpam-7015	208	17	and	and	CCONJ
ejpam-7015	208	18	structural	structural	ADJ
ejpam-7015	208	19	robustness	robustness	NOUN
ejpam-7015	208	20	of	of	ADP
ejpam-7015	208	21	afsbrs	afsbrs	NOUN
ejpam-7015	208	22	under	under	ADP
ejpam-7015	208	23	standard	standard	ADJ
ejpam-7015	208	24	set	set	NOUN
ejpam-7015	208	25	-	-	PUNCT
ejpam-7015	208	26	theoretic	theoretic	NOUN
ejpam-7015	208	27	operations	operation	NOUN
ejpam-7015	208	28	.	.	PUNCT
ejpam-7015	209	1	these	these	DET
ejpam-7015	209	2	findings	finding	NOUN
ejpam-7015	209	3	affirm	affirm	VERB
ejpam-7015	209	4	the	the	DET
ejpam-7015	209	5	potential	potential	NOUN
ejpam-7015	209	6	of	of	ADP
ejpam-7015	209	7	anti	anti	ADJ
ejpam-7015	209	8	-	-	ADJ
ejpam-7015	209	9	fuzzy	fuzzy	ADJ
ejpam-7015	209	10	soft	soft	ADJ
ejpam-7015	209	11	algebraic	algebraic	ADJ
ejpam-7015	209	12	systems	system	NOUN
ejpam-7015	209	13	as	as	ADP
ejpam-7015	209	14	foundational	foundational	ADJ
ejpam-7015	209	15	tools	tool	NOUN
ejpam-7015	209	16	for	for	ADP
ejpam-7015	209	17	representing	represent	VERB
ejpam-7015	209	18	rejection	rejection	NOUN
ejpam-7015	209	19	,	,	PUNCT
ejpam-7015	209	20	contradiction	contradiction	NOUN
ejpam-7015	209	21	,	,	PUNCT
ejpam-7015	209	22	and	and	CCONJ
ejpam-7015	209	23	negative	negative	ADJ
ejpam-7015	209	24	knowledge	knowledge	NOUN
ejpam-7015	209	25	in	in	ADP
ejpam-7015	209	26	decision	decision	NOUN
ejpam-7015	209	27	-	-	PUNCT
ejpam-7015	209	28	making	make	VERB
ejpam-7015	209	29	scenarios	scenario	NOUN
ejpam-7015	209	30	.	.	PUNCT
ejpam-7015	210	1	future	future	ADJ
ejpam-7015	210	2	work	work	NOUN
ejpam-7015	210	3	may	may	AUX
ejpam-7015	210	4	expand	expand	VERB
ejpam-7015	210	5	on	on	ADP
ejpam-7015	210	6	this	this	DET
ejpam-7015	210	7	foundation	foundation	NOUN
ejpam-7015	210	8	by	by	ADP
ejpam-7015	210	9	exploring	explore	VERB
ejpam-7015	210	10	morphisms	morphism	NOUN
ejpam-7015	210	11	,	,	PUNCT
ejpam-7015	210	12	deeper	deep	ADJ
ejpam-7015	210	13	characterizations	characterization	NOUN
ejpam-7015	210	14	,	,	PUNCT
ejpam-7015	210	15	and	and	CCONJ
ejpam-7015	210	16	algorithmic	algorithmic	ADJ
ejpam-7015	210	17	implementations	implementation	NOUN
ejpam-7015	210	18	,	,	PUNCT
ejpam-7015	210	19	as	as	ADV
ejpam-7015	210	20	well	well	ADV
ejpam-7015	210	21	as	as	ADP
ejpam-7015	210	22	practical	practical	ADJ
ejpam-7015	210	23	applications	application	NOUN
ejpam-7015	210	24	in	in	ADP
ejpam-7015	210	25	non	non	ADJ
ejpam-7015	210	26	-	-	ADJ
ejpam-7015	210	27	classical	classical	ADJ
ejpam-7015	210	28	logic	logic	NOUN
ejpam-7015	210	29	,	,	PUNCT
ejpam-7015	210	30	artificial	artificial	ADJ
ejpam-7015	210	31	intelligence	intelligence	NOUN
ejpam-7015	210	32	,	,	PUNCT
ejpam-7015	210	33	and	and	CCONJ
ejpam-7015	210	34	soft	soft	ADJ
ejpam-7015	210	35	computing	computing	NOUN
ejpam-7015	210	36	environments	environment	NOUN
ejpam-7015	210	37	.	.	PUNCT
ejpam-7015	211	1	acknowledgements	acknowledgement	NOUN
ejpam-7015	211	2	this	this	DET
ejpam-7015	211	3	research	research	NOUN
ejpam-7015	211	4	was	be	AUX
ejpam-7015	211	5	supported	support	VERB
ejpam-7015	211	6	by	by	ADP
ejpam-7015	211	7	university	university	NOUN
ejpam-7015	211	8	of	of	ADP
ejpam-7015	211	9	phayao	phayao	NOUN
ejpam-7015	211	10	and	and	CCONJ
ejpam-7015	211	11	thailand	thailand	PROPN
ejpam-7015	211	12	science	science	PROPN
ejpam-7015	211	13	research	research	PROPN
ejpam-7015	211	14	and	and	CCONJ
ejpam-7015	211	15	innovation	innovation	NOUN
ejpam-7015	211	16	fund	fund	NOUN
ejpam-7015	211	17	(	(	PUNCT
ejpam-7015	211	18	fundamental	fundamental	ADJ
ejpam-7015	211	19	fund	fund	NOUN
ejpam-7015	211	20	2026	2026	NUM
ejpam-7015	211	21	,	,	PUNCT
ejpam-7015	211	22	grant	grant	VERB
ejpam-7015	211	23	no	no	NOUN
ejpam-7015	211	24	.	.	PUNCT
ejpam-7015	211	25	2252/2568	2252/2568	NUM
ejpam-7015	211	26	)	)	PUNCT
ejpam-7015	211	27	.	.	PUNCT
ejpam-7015	212	1	references	reference	NOUN
ejpam-7015	212	2	[	[	X
ejpam-7015	212	3	1	1	NUM
ejpam-7015	212	4	]	]	PUNCT
ejpam-7015	212	5	l.	l.	PROPN
ejpam-7015	212	6	a.	a.	PROPN
ejpam-7015	212	7	zadeh	zadeh	PROPN
ejpam-7015	212	8	.	.	PUNCT
ejpam-7015	213	1	fuzzy	fuzzy	ADJ
ejpam-7015	213	2	sets	set	NOUN
ejpam-7015	213	3	.	.	PUNCT
ejpam-7015	214	1	information	information	NOUN
ejpam-7015	214	2	and	and	CCONJ
ejpam-7015	214	3	control	control	NOUN
ejpam-7015	214	4	,	,	PUNCT
ejpam-7015	214	5	8(3):338–353	8(3):338–353	NUM
ejpam-7015	214	6	,	,	PUNCT
ejpam-7015	214	7	1965	1965	NUM
ejpam-7015	214	8	.	.	PUNCT
ejpam-7015	215	1	[	[	X
ejpam-7015	215	2	2	2	NUM
ejpam-7015	215	3	]	]	PUNCT
ejpam-7015	215	4	d.	d.	PROPN
ejpam-7015	215	5	molodtsov	molodtsov	PROPN
ejpam-7015	215	6	.	.	PUNCT
ejpam-7015	216	1	soft	soft	ADJ
ejpam-7015	216	2	set	set	ADJ
ejpam-7015	216	3	theory	theory	NOUN
ejpam-7015	216	4	first	first	ADJ
ejpam-7015	216	5	results	result	NOUN
ejpam-7015	216	6	.	.	PUNCT
ejpam-7015	217	1	computers	computer	NOUN
ejpam-7015	217	2	and	and	CCONJ
ejpam-7015	217	3	mathematics	mathematic	NOUN
ejpam-7015	217	4	with	with	ADP
ejpam-7015	217	5	applications	application	NOUN
ejpam-7015	217	6	,	,	PUNCT
ejpam-7015	217	7	37(4	37(4	PROPN
ejpam-7015	217	8	-	-	PUNCT
ejpam-7015	217	9	5):19–31	5):19–31	NUM
ejpam-7015	217	10	,	,	PUNCT
ejpam-7015	217	11	1999	1999	NUM
ejpam-7015	217	12	.	.	PUNCT
ejpam-7015	218	1	d.	d.	PROPN
ejpam-7015	218	2	ramesh	ramesh	PROPN
ejpam-7015	218	3	et	et	PROPN
ejpam-7015	218	4	al	al	PROPN
ejpam-7015	218	5	.	.	PUNCT
ejpam-7015	218	6	/	/	SYM
ejpam-7015	218	7	eur	eur	PROPN
ejpam-7015	218	8	.	.	PUNCT
ejpam-7015	219	1	j.	j.	PROPN
ejpam-7015	219	2	pure	pure	PROPN
ejpam-7015	219	3	appl	appl	PROPN
ejpam-7015	219	4	.	.	PROPN
ejpam-7015	219	5	math	math	PROPN
ejpam-7015	219	6	,	,	PUNCT
ejpam-7015	219	7	18	18	NUM
ejpam-7015	219	8	(	(	PUNCT
ejpam-7015	219	9	4	4	NUM
ejpam-7015	219	10	)	)	PUNCT
ejpam-7015	219	11	(	(	PUNCT
ejpam-7015	219	12	2025	2025	NUM
ejpam-7015	219	13	)	)	PUNCT
ejpam-7015	219	14	,	,	PUNCT
ejpam-7015	219	15	7015	7015	NUM
ejpam-7015	219	16	11	11	NUM
ejpam-7015	219	17	of	of	ADP
ejpam-7015	219	18	11	11	NUM
ejpam-7015	220	1	[	[	X
ejpam-7015	220	2	3	3	NUM
ejpam-7015	220	3	]	]	PUNCT
ejpam-7015	220	4	p.	p.	NOUN
ejpam-7015	220	5	k.	k.	PROPN
ejpam-7015	221	1	maji	maji	PROPN
ejpam-7015	221	2	,	,	PUNCT
ejpam-7015	221	3	r.	r.	PROPN
ejpam-7015	221	4	biswas	biswas	PROPN
ejpam-7015	221	5	,	,	PUNCT
ejpam-7015	221	6	and	and	CCONJ
ejpam-7015	222	1	a.	a.	PROPN
ejpam-7015	222	2	r.	r.	PROPN
ejpam-7015	222	3	roy	roy	PROPN
ejpam-7015	222	4	.	.	PROPN
ejpam-7015	222	5	fuzzy	fuzzy	ADJ
ejpam-7015	222	6	soft	soft	ADJ
ejpam-7015	222	7	sets	set	NOUN
ejpam-7015	222	8	.	.	PUNCT
ejpam-7015	223	1	journal	journal	NOUN
ejpam-7015	223	2	of	of	ADP
ejpam-7015	223	3	fuzzy	fuzzy	ADJ
ejpam-7015	223	4	mathematics	mathematic	NOUN
ejpam-7015	223	5	,	,	PUNCT
ejpam-7015	223	6	9(3):589–602	9(3):589–602	NOUN
ejpam-7015	223	7	,	,	PUNCT
ejpam-7015	223	8	2001	2001	NUM
ejpam-7015	223	9	.	.	PUNCT
ejpam-7015	224	1	[	[	X
ejpam-7015	224	2	4	4	X
ejpam-7015	224	3	]	]	PUNCT
ejpam-7015	224	4	p.	p.	NOUN
ejpam-7015	224	5	k.	k.	PROPN
ejpam-7015	225	1	maji	maji	PROPN
ejpam-7015	225	2	,	,	PUNCT
ejpam-7015	225	3	r.	r.	PROPN
ejpam-7015	225	4	biswas	biswas	PROPN
ejpam-7015	225	5	,	,	PUNCT
ejpam-7015	225	6	and	and	CCONJ
ejpam-7015	225	7	a.	a.	PROPN
ejpam-7015	225	8	r.	r.	PROPN
ejpam-7015	225	9	roy	roy	PROPN
ejpam-7015	225	10	.	.	PROPN
ejpam-7015	225	11	soft	soft	ADJ
ejpam-7015	225	12	set	set	NOUN
ejpam-7015	225	13	theory	theory	NOUN
ejpam-7015	225	14	.	.	PUNCT
ejpam-7015	226	1	computers	computer	NOUN
ejpam-7015	226	2	and	and	CCONJ
ejpam-7015	226	3	mathematics	mathematic	NOUN
ejpam-7015	226	4	with	with	ADP
ejpam-7015	226	5	applications	application	NOUN
ejpam-7015	226	6	,	,	PUNCT
ejpam-7015	226	7	45(4	45(4	NOUN
ejpam-7015	226	8	-	-	PUNCT
ejpam-7015	226	9	5):555–562	5):555–562	NUM
ejpam-7015	226	10	,	,	PUNCT
ejpam-7015	226	11	2003	2003	NUM
ejpam-7015	226	12	.	.	PUNCT
ejpam-7015	227	1	[	[	X
ejpam-7015	227	2	5	5	X
ejpam-7015	227	3	]	]	PUNCT
ejpam-7015	227	4	v.	v.	ADP
ejpam-7015	227	5	n.	n.	PROPN
ejpam-7015	227	6	dixit	dixit	PROPN
ejpam-7015	227	7	,	,	PUNCT
ejpam-7015	227	8	r.	r.	PROPN
ejpam-7015	227	9	kumar	kumar	PROPN
ejpam-7015	227	10	,	,	PUNCT
ejpam-7015	227	11	and	and	CCONJ
ejpam-7015	227	12	n.	n.	PROPN
ejpam-7015	227	13	ajmal	ajmal	PROPN
ejpam-7015	227	14	.	.	PUNCT
ejpam-7015	228	1	on	on	ADP
ejpam-7015	228	2	fuzzy	fuzzy	ADJ
ejpam-7015	228	3	rings	ring	NOUN
ejpam-7015	228	4	.	.	PUNCT
ejpam-7015	229	1	fuzzy	fuzzy	ADJ
ejpam-7015	229	2	sets	set	NOUN
ejpam-7015	229	3	and	and	CCONJ
ejpam-7015	229	4	systems	system	NOUN
ejpam-7015	229	5	,	,	PUNCT
ejpam-7015	229	6	49(2):205–213	49(2):205–213	NUM
ejpam-7015	229	7	,	,	PUNCT
ejpam-7015	229	8	1992	1992	NUM
ejpam-7015	229	9	.	.	PUNCT
ejpam-7015	230	1	[	[	X
ejpam-7015	230	2	6	6	NUM
ejpam-7015	230	3	]	]	PUNCT
ejpam-7015	230	4	b.	b.	NOUN
ejpam-7015	230	5	ahmat	ahmat	NOUN
ejpam-7015	230	6	and	and	CCONJ
ejpam-7015	230	7	a.	a.	NOUN
ejpam-7015	230	8	kharal	kharal	PROPN
ejpam-7015	230	9	.	.	PUNCT
ejpam-7015	231	1	on	on	ADP
ejpam-7015	231	2	fuzzy	fuzzy	ADJ
ejpam-7015	231	3	soft	soft	ADJ
ejpam-7015	231	4	sets	set	NOUN
ejpam-7015	231	5	.	.	PUNCT
ejpam-7015	232	1	advances	advance	NOUN
ejpam-7015	232	2	in	in	ADP
ejpam-7015	232	3	fuzzy	fuzzy	ADJ
ejpam-7015	232	4	systems	system	NOUN
ejpam-7015	232	5	,	,	PUNCT
ejpam-7015	232	6	2009	2009	NUM
ejpam-7015	232	7	:	:	PUNCT
ejpam-7015	232	8	article	article	NOUN
ejpam-7015	232	9	i	i	PROPN
ejpam-7015	232	10	d	d	PROPN
ejpam-7015	232	11	586507	586507	NUM
ejpam-7015	232	12	,	,	PUNCT
ejpam-7015	232	13	6	6	NUM
ejpam-7015	232	14	pages	page	NOUN
ejpam-7015	232	15	,	,	PUNCT
ejpam-7015	232	16	2009	2009	NUM
ejpam-7015	232	17	.	.	PUNCT
ejpam-7015	233	1	[	[	X
ejpam-7015	233	2	7	7	X
ejpam-7015	233	3	]	]	X
ejpam-7015	233	4	u.	u.	NOUN
ejpam-7015	233	5	acar	acar	PROPN
ejpam-7015	233	6	,	,	PUNCT
ejpam-7015	233	7	f.	f.	PROPN
ejpam-7015	233	8	koyuncu	koyuncu	PROPN
ejpam-7015	233	9	,	,	PUNCT
ejpam-7015	233	10	and	and	CCONJ
ejpam-7015	233	11	b.	b.	PROPN
ejpam-7015	233	12	tanay	tanay	PROPN
ejpam-7015	233	13	.	.	PUNCT
ejpam-7015	234	1	soft	soft	ADJ
ejpam-7015	234	2	sets	set	NOUN
ejpam-7015	234	3	and	and	CCONJ
ejpam-7015	234	4	soft	soft	ADJ
ejpam-7015	234	5	rings	ring	NOUN
ejpam-7015	234	6	.	.	PUNCT
ejpam-7015	235	1	computers	computer	NOUN
ejpam-7015	235	2	and	and	CCONJ
ejpam-7015	235	3	mathematics	mathematic	NOUN
ejpam-7015	235	4	with	with	ADP
ejpam-7015	235	5	applications	application	NOUN
ejpam-7015	235	6	,	,	PUNCT
ejpam-7015	235	7	59:3458–3463	59:3458–3463	NUM
ejpam-7015	235	8	,	,	PUNCT
ejpam-7015	235	9	2010	2010	NUM
ejpam-7015	235	10	.	.	PUNCT
ejpam-7015	236	1	[	[	X
ejpam-7015	236	2	8	8	NUM
ejpam-7015	236	3	]	]	PUNCT
ejpam-7015	236	4	m.	m.	NOUN
ejpam-7015	236	5	akram	akram	PROPN
ejpam-7015	236	6	and	and	CCONJ
ejpam-7015	236	7	k.	k.	PROPN
ejpam-7015	236	8	h.	h.	PROPN
ejpam-7015	236	9	dar	dar	PROPN
ejpam-7015	236	10	.	.	PUNCT
ejpam-7015	237	1	on	on	ADP
ejpam-7015	237	2	anti	anti	X
ejpam-7015	237	3	fuzzy	fuzzy	ADJ
ejpam-7015	237	4	left	leave	VERB
ejpam-7015	237	5	h	h	NOUN
ejpam-7015	237	6	-	-	PUNCT
ejpam-7015	237	7	ideals	ideal	NOUN
ejpam-7015	237	8	in	in	ADP
ejpam-7015	237	9	hemirings	hemiring	NOUN
ejpam-7015	237	10	.	.	PUNCT
ejpam-7015	238	1	international	international	ADJ
ejpam-7015	238	2	mathematical	mathematical	PROPN
ejpam-7015	238	3	forum	forum	PROPN
ejpam-7015	238	4	,	,	PUNCT
ejpam-7015	238	5	2(46):2295–2304	2(46):2295–2304	NUM
ejpam-7015	238	6	,	,	PUNCT
ejpam-7015	238	7	2007	2007	NUM
ejpam-7015	238	8	.	.	PUNCT
ejpam-7015	239	1	[	[	X
ejpam-7015	239	2	9	9	NUM
ejpam-7015	239	3	]	]	PUNCT
ejpam-7015	239	4	s.	s.	PROPN
ejpam-7015	239	5	m.	m.	PROPN
ejpam-7015	239	6	hong	hong	PROPN
ejpam-7015	239	7	and	and	CCONJ
ejpam-7015	239	8	y.	y.	PROPN
ejpam-7015	239	9	b.	b.	PROPN
ejpam-7015	239	10	jun	jun	PROPN
ejpam-7015	239	11	.	.	PUNCT
ejpam-7015	240	1	anti	anti	PROPN
ejpam-7015	240	2	fuzzy	fuzzy	ADJ
ejpam-7015	240	3	ideals	ideal	NOUN
ejpam-7015	240	4	in	in	ADP
ejpam-7015	240	5	bck	bck	NOUN
ejpam-7015	240	6	-	-	PUNCT
ejpam-7015	240	7	algebras	algebras	PROPN
ejpam-7015	240	8	.	.	PUNCT
ejpam-7015	241	1	kyungpook	kyungpook	PROPN
ejpam-7015	241	2	mathematical	mathematical	PROPN
ejpam-7015	241	3	journal	journal	PROPN
ejpam-7015	241	4	,	,	PUNCT
ejpam-7015	241	5	38(1):145–150	38(1):145–150	PROPN
ejpam-7015	241	6	,	,	PUNCT
ejpam-7015	241	7	1998	1998	NUM
ejpam-7015	241	8	.	.	PUNCT
ejpam-7015	242	1	[	[	X
ejpam-7015	242	2	10	10	NUM
ejpam-7015	242	3	]	]	X
ejpam-7015	242	4	g.	g.	PROPN
ejpam-7015	242	5	s.	s.	PROPN
ejpam-7015	242	6	rao	rao	PROPN
ejpam-7015	242	7	,	,	PUNCT
ejpam-7015	242	8	p.	p.	PROPN
ejpam-7015	242	9	kolluru	kolluru	PROPN
ejpam-7015	242	10	,	,	PUNCT
ejpam-7015	242	11	and	and	CCONJ
ejpam-7015	242	12	b.	b.	PROPN
ejpam-7015	242	13	p.	p.	NOUN
ejpam-7015	242	14	munagala	munagala	PROPN
ejpam-7015	242	15	.	.	PUNCT
ejpam-7015	243	1	a	a	DET
ejpam-7015	243	2	note	note	NOUN
ejpam-7015	243	3	on	on	ADP
ejpam-7015	243	4	soft	soft	ADJ
ejpam-7015	243	5	boolean	boolean	ADJ
ejpam-7015	243	6	near	near	ADJ
ejpam-7015	243	7	-	-	PUNCT
ejpam-7015	243	8	rings	ring	NOUN
ejpam-7015	243	9	.	.	PUNCT
ejpam-7015	244	1	aip	aip	PROPN
ejpam-7015	244	2	conference	conference	NOUN
ejpam-7015	244	3	proceedings	proceeding	NOUN
ejpam-7015	244	4	,	,	PUNCT
ejpam-7015	244	5	2707:020013	2707:020013	NUM
ejpam-7015	244	6	,	,	PUNCT
ejpam-7015	244	7	2023	2023	NUM
ejpam-7015	244	8	.	.	PUNCT
ejpam-7015	245	1	[	[	X
ejpam-7015	245	2	11	11	NUM
ejpam-7015	245	3	]	]	X
ejpam-7015	245	4	g.	g.	PROPN
ejpam-7015	245	5	s.	s.	PROPN
ejpam-7015	245	6	rao	rao	PROPN
ejpam-7015	245	7	,	,	PUNCT
ejpam-7015	245	8	d.	d.	PROPN
ejpam-7015	245	9	ramesh	ramesh	PROPN
ejpam-7015	245	10	,	,	PUNCT
ejpam-7015	245	11	a.	a.	NOUN
ejpam-7015	245	12	iampan	iampan	PROPN
ejpam-7015	245	13	,	,	PUNCT
ejpam-7015	245	14	and	and	CCONJ
ejpam-7015	245	15	b.	b.	PROPN
ejpam-7015	245	16	satyanarayana	satyanarayana	PROPN
ejpam-7015	245	17	.	.	PUNCT
ejpam-7015	246	1	fuzzy	fuzzy	ADJ
ejpam-7015	246	2	soft	soft	ADJ
ejpam-7015	246	3	boolean	boolean	ADJ
ejpam-7015	246	4	rings	ring	NOUN
ejpam-7015	246	5	.	.	PUNCT
ejpam-7015	247	1	international	international	ADJ
ejpam-7015	247	2	journal	journal	NOUN
ejpam-7015	247	3	of	of	ADP
ejpam-7015	247	4	analysis	analysis	NOUN
ejpam-7015	247	5	and	and	CCONJ
ejpam-7015	247	6	applications	application	NOUN
ejpam-7015	247	7	,	,	PUNCT
ejpam-7015	247	8	21:60	21:60	NUM
ejpam-7015	247	9	,	,	PUNCT
ejpam-7015	247	10	2023	2023	NUM
ejpam-7015	247	11	.	.	PUNCT
ejpam-7015	248	1	[	[	X
ejpam-7015	248	2	12	12	NUM
ejpam-7015	248	3	]	]	X
ejpam-7015	248	4	g.	g.	PROPN
ejpam-7015	248	5	s.	s.	PROPN
ejpam-7015	248	6	rao	rao	PROPN
ejpam-7015	248	7	,	,	PUNCT
ejpam-7015	248	8	p.	p.	PROPN
ejpam-7015	248	9	kolluru	kolluru	PROPN
ejpam-7015	248	10	,	,	PUNCT
ejpam-7015	248	11	and	and	CCONJ
ejpam-7015	248	12	n.	n.	NOUN
ejpam-7015	248	13	thandu	thandu	NOUN
ejpam-7015	248	14	.	.	PUNCT
ejpam-7015	249	1	soft	soft	ADJ
ejpam-7015	249	2	intersection	intersection	NOUN
ejpam-7015	249	3	boolean	boolean	ADJ
ejpam-7015	249	4	near	near	ADP
ejpam-7015	249	5	-	-	PUNCT
ejpam-7015	249	6	rings	ring	NOUN
ejpam-7015	249	7	with	with	ADP
ejpam-7015	249	8	its	its	PRON
ejpam-7015	249	9	applications	application	NOUN
ejpam-7015	249	10	.	.	PUNCT
ejpam-7015	250	1	aip	aip	PROPN
ejpam-7015	250	2	conference	conference	NOUN
ejpam-7015	250	3	proceedings	proceeding	NOUN
ejpam-7015	250	4	,	,	PUNCT
ejpam-7015	250	5	2707:020012	2707:020012	NUM
ejpam-7015	250	6	,	,	PUNCT
ejpam-7015	250	7	2023	2023	NUM
ejpam-7015	250	8	.	.	PUNCT
ejpam-7015	251	1	[	[	X
ejpam-7015	251	2	13	13	NUM
ejpam-7015	251	3	]	]	X
ejpam-7015	251	4	g.	g.	PROPN
ejpam-7015	251	5	s.	s.	PROPN
ejpam-7015	251	6	rao	rao	PROPN
ejpam-7015	251	7	,	,	PUNCT
ejpam-7015	251	8	d.	d.	PROPN
ejpam-7015	251	9	ramesh	ramesh	PROPN
ejpam-7015	251	10	,	,	PUNCT
ejpam-7015	251	11	and	and	CCONJ
ejpam-7015	251	12	b.	b.	PROPN
ejpam-7015	251	13	satyanarayana	satyanarayana	PROPN
ejpam-7015	251	14	.	.	PUNCT
ejpam-7015	252	1	(	(	PUNCT
ejpam-7015	252	2	∈,∈	∈,∈	X
ejpam-7015	252	3	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-7015	252	4	soft	soft	ADJ
ejpam-7015	252	5	boolean	boolean	NOUN
ejpam-7015	252	6	near	near	ADP
ejpam-7015	252	7	rings	ring	NOUN
ejpam-7015	252	8	.	.	PUNCT
ejpam-7015	253	1	asia	asia	PROPN
ejpam-7015	253	2	pacific	pacific	PROPN
ejpam-7015	253	3	journal	journal	PROPN
ejpam-7015	253	4	of	of	ADP
ejpam-7015	253	5	mathematics	mathematic	NOUN
ejpam-7015	253	6	,	,	PUNCT
ejpam-7015	253	7	10:50	10:50	NUM
ejpam-7015	253	8	,	,	PUNCT
ejpam-7015	253	9	2023	2023	NUM
ejpam-7015	253	10	.	.	PUNCT
ejpam-7015	254	1	[	[	X
ejpam-7015	254	2	14	14	NUM
ejpam-7015	254	3	]	]	X
ejpam-7015	254	4	g.	g.	PROPN
ejpam-7015	254	5	s.	s.	PROPN
ejpam-7015	254	6	rao	rao	PROPN
ejpam-7015	254	7	,	,	PUNCT
ejpam-7015	254	8	d.	d.	PROPN
ejpam-7015	254	9	ramesh	ramesh	PROPN
ejpam-7015	254	10	,	,	PUNCT
ejpam-7015	254	11	a.	a.	NOUN
ejpam-7015	254	12	iampan	iampan	PROPN
ejpam-7015	254	13	,	,	PUNCT
ejpam-7015	254	14	and	and	CCONJ
ejpam-7015	254	15	b.	b.	PROPN
ejpam-7015	254	16	satyanarayana	satyanarayana	PROPN
ejpam-7015	254	17	.	.	PUNCT
ejpam-7015	255	1	fuzzy	fuzzy	ADJ
ejpam-7015	255	2	soft	soft	ADJ
ejpam-7015	255	3	boolean	boolean	ADJ
ejpam-7015	255	4	near	near	ADJ
ejpam-7015	255	5	-	-	PUNCT
ejpam-7015	255	6	rings	ring	NOUN
ejpam-7015	255	7	and	and	CCONJ
ejpam-7015	255	8	idealistic	idealistic	ADJ
ejpam-7015	255	9	fuzzy	fuzzy	ADJ
ejpam-7015	255	10	soft	soft	ADJ
ejpam-7015	255	11	boolean	boolean	ADJ
ejpam-7015	255	12	near	near	ADJ
ejpam-7015	255	13	-	-	PUNCT
ejpam-7015	255	14	rings	ring	NOUN
ejpam-7015	255	15	.	.	PUNCT
ejpam-7015	256	1	icic	icic	PROPN
ejpam-7015	256	2	express	express	PROPN
ejpam-7015	256	3	letters	letter	NOUN
ejpam-7015	256	4	,	,	PUNCT
ejpam-7015	256	5	18(7):677–684	18(7):677–684	NUM
ejpam-7015	256	6	,	,	PUNCT
ejpam-7015	256	7	2024	2024	NUM
ejpam-7015	256	8	.	.	PUNCT
ejpam-7015	257	1	[	[	X
ejpam-7015	257	2	15	15	NUM
ejpam-7015	257	3	]	]	X
ejpam-7015	257	4	g.	g.	PROPN
ejpam-7015	257	5	s.	s.	PROPN
ejpam-7015	257	6	rao	rao	PROPN
ejpam-7015	257	7	,	,	PUNCT
ejpam-7015	257	8	d.	d.	PROPN
ejpam-7015	257	9	ramesh	ramesh	PROPN
ejpam-7015	257	10	,	,	PUNCT
ejpam-7015	257	11	a.	a.	PROPN
ejpam-7015	257	12	iampan	iampan	PROPN
ejpam-7015	257	13	,	,	PUNCT
ejpam-7015	257	14	g.	g.	PROPN
ejpam-7015	257	15	vijaya	vijaya	PROPN
ejpam-7015	257	16	lakshmi	lakshmi	PROPN
ejpam-7015	257	17	,	,	PUNCT
ejpam-7015	257	18	and	and	CCONJ
ejpam-7015	257	19	b.	b.	PROPN
ejpam-7015	257	20	satyanarayana	satyanarayana	PROPN
ejpam-7015	257	21	.	.	PUNCT
ejpam-7015	258	1	(	(	PUNCT
ejpam-7015	258	2	∈,∈	∈,∈	X
ejpam-7015	258	3	∨qk)-intuitionistic	∨qk)-intuitionistic	ADJ
ejpam-7015	258	4	fuzzy	fuzzy	ADJ
ejpam-7015	258	5	soft	soft	ADJ
ejpam-7015	258	6	boolean	boolean	ADJ
ejpam-7015	258	7	near	near	ADJ
ejpam-7015	258	8	-	-	PUNCT
ejpam-7015	258	9	rings	ring	NOUN
ejpam-7015	258	10	.	.	PUNCT
ejpam-7015	259	1	international	international	ADJ
ejpam-7015	259	2	journal	journal	NOUN
ejpam-7015	259	3	of	of	ADP
ejpam-7015	259	4	analysis	analysis	NOUN
ejpam-7015	259	5	and	and	CCONJ
ejpam-7015	259	6	applications	application	NOUN
ejpam-7015	259	7	,	,	PUNCT
ejpam-7015	259	8	23:91	23:91	NUM
ejpam-7015	259	9	,	,	PUNCT
ejpam-7015	259	10	2025	2025	NUM
ejpam-7015	259	11	.	.	PUNCT
ejpam-7015	260	1	[	[	X
ejpam-7015	260	2	16	16	NUM
ejpam-7015	260	3	]	]	X
ejpam-7015	260	4	g.	g.	PROPN
ejpam-7015	260	5	s.	s.	PROPN
ejpam-7015	260	6	rao	rao	PROPN
ejpam-7015	260	7	,	,	PUNCT
ejpam-7015	260	8	d.	d.	PROPN
ejpam-7015	260	9	ramesh	ramesh	PROPN
ejpam-7015	260	10	,	,	PUNCT
ejpam-7015	260	11	a.	a.	PROPN
ejpam-7015	260	12	iampan	iampan	PROPN
ejpam-7015	260	13	,	,	PUNCT
ejpam-7015	260	14	b.	b.	PROPN
ejpam-7015	260	15	satyanarayana	satyanarayana	PROPN
ejpam-7015	260	16	,	,	PUNCT
ejpam-7015	260	17	and	and	CCONJ
ejpam-7015	260	18	p.	p.	PROPN
ejpam-7015	260	19	rajani	rajani	PROPN
ejpam-7015	260	20	.	.	PUNCT
ejpam-7015	261	1	intuitionistic	intuitionistic	ADJ
ejpam-7015	261	2	fuzzy	fuzzy	ADJ
ejpam-7015	261	3	soft	soft	ADJ
ejpam-7015	261	4	boolean	boolean	ADJ
ejpam-7015	261	5	rings	ring	NOUN
ejpam-7015	261	6	.	.	PUNCT
ejpam-7015	262	1	international	international	ADJ
ejpam-7015	262	2	journal	journal	NOUN
ejpam-7015	262	3	of	of	ADP
ejpam-7015	262	4	analysis	analysis	NOUN
ejpam-7015	262	5	and	and	CCONJ
ejpam-7015	262	6	applications	application	NOUN
ejpam-7015	262	7	,	,	PUNCT
ejpam-7015	262	8	23:43	23:43	NUM
ejpam-7015	262	9	,	,	PUNCT
ejpam-7015	262	10	2025	2025	NUM
ejpam-7015	262	11	.	.	PUNCT
ejpam-7015	263	1	[	[	X
ejpam-7015	263	2	17	17	NUM
ejpam-7015	263	3	]	]	X
ejpam-7015	263	4	g.	g.	PROPN
ejpam-7015	263	5	s.	s.	PROPN
ejpam-7015	263	6	rao	rao	PROPN
ejpam-7015	263	7	,	,	PUNCT
ejpam-7015	263	8	v.	v.	PROPN
ejpam-7015	263	9	p.	p.	PROPN
ejpam-7015	263	10	kolanchinathan	kolanchinathan	PROPN
ejpam-7015	263	11	,	,	PUNCT
ejpam-7015	263	12	k.	k.	PROPN
ejpam-7015	263	13	jhansi	jhansi	PROPN
ejpam-7015	263	14	rani	rani	PROPN
ejpam-7015	263	15	,	,	PUNCT
ejpam-7015	263	16	a.	a.	NOUN
ejpam-7015	263	17	iampan	iampan	PROPN
ejpam-7015	263	18	,	,	PUNCT
ejpam-7015	263	19	k.	k.	PROPN
ejpam-7015	263	20	hemabala	hemabala	PROPN
ejpam-7015	263	21	,	,	PUNCT
ejpam-7015	263	22	d.	d.	PROPN
ejpam-7015	263	23	ramesh	ramesh	PROPN
ejpam-7015	263	24	,	,	PUNCT
ejpam-7015	263	25	and	and	CCONJ
ejpam-7015	263	26	b.	b.	PROPN
ejpam-7015	263	27	satyanarayana	satyanarayana	PROPN
ejpam-7015	263	28	.	.	PUNCT
ejpam-7015	264	1	algebraic	algebraic	ADJ
ejpam-7015	264	2	aspects	aspect	NOUN
ejpam-7015	264	3	of	of	ADP
ejpam-7015	264	4	bipolar	bipolar	ADJ
ejpam-7015	264	5	fuzzy	fuzzy	ADJ
ejpam-7015	264	6	soft	soft	ADJ
ejpam-7015	264	7	boolean	boolean	ADJ
ejpam-7015	264	8	rings	ring	NOUN
ejpam-7015	264	9	.	.	PUNCT
ejpam-7015	265	1	european	european	PROPN
ejpam-7015	265	2	journal	journal	PROPN
ejpam-7015	265	3	of	of	ADP
ejpam-7015	265	4	pure	pure	ADJ
ejpam-7015	265	5	and	and	CCONJ
ejpam-7015	265	6	applied	applied	ADJ
ejpam-7015	265	7	mathematics	mathematic	NOUN
ejpam-7015	265	8	,	,	PUNCT
ejpam-7015	265	9	18(3):6459	18(3):6459	NUM
ejpam-7015	265	10	,	,	PUNCT
ejpam-7015	265	11	2025	2025	NUM
ejpam-7015	265	12	.	.	PUNCT
ejpam-7015	266	1	[	[	X
ejpam-7015	266	2	18	18	NUM
ejpam-7015	266	3	]	]	X
ejpam-7015	266	4	n.	n.	PROPN
ejpam-7015	266	5	hamsa	hamsa	PROPN
ejpam-7015	266	6	,	,	PUNCT
ejpam-7015	266	7	k.	k.	PROPN
ejpam-7015	266	8	b.	b.	PROPN
ejpam-7015	266	9	srinivas	srinivas	PROPN
ejpam-7015	266	10	,	,	PUNCT
ejpam-7015	266	11	and	and	CCONJ
ejpam-7015	266	12	k.	k.	PROPN
ejpam-7015	266	13	s.	s.	PROPN
ejpam-7015	266	14	prasad	prasad	PROPN
ejpam-7015	266	15	.	.	PUNCT
ejpam-7015	267	1	on	on	ADP
ejpam-7015	267	2	central	central	ADJ
ejpam-7015	267	3	boolean	boolean	ADJ
ejpam-7015	267	4	rings	ring	NOUN
ejpam-7015	267	5	and	and	CCONJ
ejpam-7015	267	6	boolean	boolean	ADJ
ejpam-7015	267	7	type	type	NOUN
ejpam-7015	267	8	fuzzy	fuzzy	ADJ
ejpam-7015	267	9	ideals	ideal	NOUN
ejpam-7015	267	10	.	.	PUNCT
ejpam-7015	268	1	kuwait	kuwait	PROPN
ejpam-7015	268	2	journal	journal	PROPN
ejpam-7015	268	3	of	of	ADP
ejpam-7015	268	4	science	science	PROPN
ejpam-7015	268	5	,	,	PUNCT
ejpam-7015	268	6	46(4):23–32	46(4):23–32	NUM
ejpam-7015	268	7	,	,	PUNCT
ejpam-7015	268	8	2019	2019	NUM
ejpam-7015	268	9	.	.	PUNCT
ejpam-7015	269	1	[	[	X
ejpam-7015	269	2	19	19	NUM
ejpam-7015	269	3	]	]	PUNCT
ejpam-7015	269	4	t.	t.	NOUN
ejpam-7015	269	5	chalapathi	chalapathi	NOUN
ejpam-7015	269	6	and	and	CCONJ
ejpam-7015	269	7	l.	l.	PROPN
ejpam-7015	269	8	madhavi	madhavi	PROPN
ejpam-7015	269	9	.	.	PROPN
ejpam-7015	269	10	neutrosophic	neutrosophic	ADJ
ejpam-7015	269	11	boolean	boolean	ADJ
ejpam-7015	269	12	rings	ring	NOUN
ejpam-7015	269	13	.	.	PUNCT
ejpam-7015	270	1	neutrosophic	neutrosophic	ADJ
ejpam-7015	270	2	sets	set	NOUN
ejpam-7015	270	3	and	and	CCONJ
ejpam-7015	270	4	systems	system	NOUN
ejpam-7015	270	5	,	,	PUNCT
ejpam-7015	270	6	33:59–66	33:59–66	NUM
ejpam-7015	270	7	,	,	PUNCT
ejpam-7015	270	8	2020	2020	NUM
ejpam-7015	270	9	.	.	PUNCT
ejpam-7015	271	1	[	[	X
ejpam-7015	271	2	20	20	NUM
ejpam-7015	271	3	]	]	X
ejpam-7015	271	4	r.	r.	PROPN
ejpam-7015	271	5	ameri	ameri	PROPN
ejpam-7015	271	6	,	,	PUNCT
ejpam-7015	271	7	m.	m.	NOUN
ejpam-7015	271	8	hamidi	hamidi	PROPN
ejpam-7015	271	9	,	,	PUNCT
ejpam-7015	271	10	and	and	CCONJ
ejpam-7015	271	11	a.	a.	NOUN
ejpam-7015	271	12	a.	a.	NOUN
ejpam-7015	271	13	tavakoli	tavakoli	PROPN
ejpam-7015	271	14	.	.	PUNCT
ejpam-7015	272	1	boolean	boolean	ADJ
ejpam-7015	272	2	rings	ring	NOUN
ejpam-7015	272	3	based	base	VERB
ejpam-7015	272	4	on	on	ADP
ejpam-7015	272	5	multirings	multiring	NOUN
ejpam-7015	272	6	.	.	PUNCT
ejpam-7015	273	1	journal	journal	PROPN
ejpam-7015	273	2	of	of	ADP
ejpam-7015	273	3	sciences	sciences	PROPN
ejpam-7015	273	4	,	,	PUNCT
ejpam-7015	273	5	islamic	islamic	PROPN
ejpam-7015	273	6	republic	republic	PROPN
ejpam-7015	273	7	of	of	ADP
ejpam-7015	273	8	iran	iran	PROPN
ejpam-7015	273	9	,	,	PUNCT
ejpam-7015	273	10	32(2):159–168	32(2):159–168	PROPN
ejpam-7015	273	11	,	,	PUNCT
ejpam-7015	273	12	2021	2021	NUM
ejpam-7015	273	13	.	.	PUNCT