id	sid	tid	token	lemma	pos
ejpam-6226	1	1	european	european	PROPN
ejpam-6226	1	2	journal	journal	PROPN
ejpam-6226	1	3	of	of	ADP
ejpam-6226	1	4	pure	pure	ADJ
ejpam-6226	1	5	and	and	CCONJ
ejpam-6226	1	6	applied	applied	ADJ
ejpam-6226	1	7	mathematics	mathematic	NOUN
ejpam-6226	1	8	2025	2025	NUM
ejpam-6226	1	9	,	,	PUNCT
ejpam-6226	1	10	vol	vol	NOUN
ejpam-6226	1	11	.	.	PROPN
ejpam-6226	1	12	18	18	NUM
ejpam-6226	1	13	,	,	PUNCT
ejpam-6226	1	14	issue	issue	NOUN
ejpam-6226	1	15	3	3	NUM
ejpam-6226	1	16	,	,	PUNCT
ejpam-6226	1	17	article	article	NOUN
ejpam-6226	1	18	number	number	NOUN
ejpam-6226	1	19	6226	6226	NUM
ejpam-6226	1	20	issn	issn	VERB
ejpam-6226	1	21	1307	1307	NUM
ejpam-6226	1	22	-	-	SYM
ejpam-6226	1	23	5543	5543	NUM
ejpam-6226	1	24	–	–	PUNCT
ejpam-6226	1	25	ejpam.com	ejpam.com	X
ejpam-6226	1	26	published	publish	VERB
ejpam-6226	1	27	by	by	ADP
ejpam-6226	1	28	new	new	PROPN
ejpam-6226	1	29	york	york	PROPN
ejpam-6226	1	30	business	business	PROPN
ejpam-6226	1	31	global	global	PROPN
ejpam-6226	1	32	implicative	implicative	ADJ
ejpam-6226	1	33	and	and	CCONJ
ejpam-6226	1	34	positive	positive	ADJ
ejpam-6226	1	35	implicative	implicative	ADJ
ejpam-6226	1	36	ink	ink	NOUN
ejpam-6226	1	37	-	-	PUNCT
ejpam-6226	1	38	ideals	ideal	NOUN
ejpam-6226	1	39	of	of	ADP
ejpam-6226	1	40	neutrosophic	neutrosophic	ADJ
ejpam-6226	1	41	ink	ink	NOUN
ejpam-6226	1	42	-	-	PUNCT
ejpam-6226	1	43	algebras	algebras	NOUN
ejpam-6226	1	44	remala	remala	NOUN
ejpam-6226	1	45	mounikalakshmi1	mounikalakshmi1	PROPN
ejpam-6226	1	46	,	,	PUNCT
ejpam-6226	1	47	eswarlal	eswarlal	PROPN
ejpam-6226	1	48	tamma1	tamma1	PROPN
ejpam-6226	1	49	,	,	PUNCT
ejpam-6226	1	50	venkata	venkata	PROPN
ejpam-6226	1	51	kalyani	kalyani	PROPN
ejpam-6226	1	52	uppuluri2	uppuluri2	PROPN
ejpam-6226	1	53	,	,	PUNCT
ejpam-6226	1	54	aiyared	aiyare	VERB
ejpam-6226	1	55	iampan3,∗	iampan3,∗	NOUN
ejpam-6226	1	56	,	,	PUNCT
ejpam-6226	1	57	t.	t.	PROPN
ejpam-6226	1	58	srinivasa	srinivasa	PROPN
ejpam-6226	1	59	rao1	rao1	PROPN
ejpam-6226	1	60	1	1	NUM
ejpam-6226	1	61	department	department	NOUN
ejpam-6226	1	62	of	of	ADP
ejpam-6226	1	63	engineering	engineering	NOUN
ejpam-6226	1	64	mathematics	mathematic	NOUN
ejpam-6226	1	65	,	,	PUNCT
ejpam-6226	1	66	college	college	NOUN
ejpam-6226	1	67	of	of	ADP
ejpam-6226	1	68	engineering	engineering	PROPN
ejpam-6226	1	69	,	,	PUNCT
ejpam-6226	1	70	koneru	koneru	PROPN
ejpam-6226	1	71	lakshmaiah	lakshmaiah	PROPN
ejpam-6226	1	72	education	education	PROPN
ejpam-6226	1	73	foundation	foundation	PROPN
ejpam-6226	1	74	,	,	PUNCT
ejpam-6226	1	75	vaddeswaram	vaddeswaram	PROPN
ejpam-6226	1	76	,	,	PUNCT
ejpam-6226	1	77	andhra	andhra	PROPN
ejpam-6226	1	78	pradesh	pradesh	PROPN
ejpam-6226	1	79	522302	522302	NUM
ejpam-6226	1	80	,	,	PUNCT
ejpam-6226	1	81	india	india	PROPN
ejpam-6226	1	82	2	2	NUM
ejpam-6226	1	83	freshman	freshman	NOUN
ejpam-6226	1	84	engineering	engineering	NOUN
ejpam-6226	1	85	department	department	PROPN
ejpam-6226	1	86	,	,	PUNCT
ejpam-6226	1	87	nri	nri	PROPN
ejpam-6226	1	88	institute	institute	PROPN
ejpam-6226	1	89	of	of	ADP
ejpam-6226	1	90	technology	technology	PROPN
ejpam-6226	1	91	,	,	PUNCT
ejpam-6226	1	92	pothavarapadu	pothavarapadu	NOUN
ejpam-6226	1	93	,	,	PUNCT
ejpam-6226	1	94	nunna	nunna	NOUN
ejpam-6226	1	95	,	,	PUNCT
ejpam-6226	1	96	agiripalli	agiripalli	NOUN
ejpam-6226	1	97	,	,	PUNCT
ejpam-6226	1	98	vijayawada-521212	vijayawada-521212	NOUN
ejpam-6226	1	99	,	,	PUNCT
ejpam-6226	1	100	india	india	PROPN
ejpam-6226	1	101	3	3	NUM
ejpam-6226	1	102	department	department	NOUN
ejpam-6226	1	103	of	of	ADP
ejpam-6226	1	104	mathematics	mathematic	NOUN
ejpam-6226	1	105	,	,	PUNCT
ejpam-6226	1	106	school	school	NOUN
ejpam-6226	1	107	of	of	ADP
ejpam-6226	1	108	science	science	NOUN
ejpam-6226	1	109	,	,	PUNCT
ejpam-6226	1	110	university	university	NOUN
ejpam-6226	1	111	of	of	ADP
ejpam-6226	1	112	phayao	phayao	NOUN
ejpam-6226	1	113	,	,	PUNCT
ejpam-6226	1	114	mae	mae	PROPN
ejpam-6226	1	115	ka	ka	PROPN
ejpam-6226	1	116	,	,	PUNCT
ejpam-6226	1	117	mueang	mueang	PROPN
ejpam-6226	1	118	,	,	PUNCT
ejpam-6226	1	119	phayao	phayao	NOUN
ejpam-6226	1	120	56000	56000	NUM
ejpam-6226	1	121	,	,	PUNCT
ejpam-6226	1	122	thailand	thailand	PROPN
ejpam-6226	1	123	abstract	abstract	NOUN
ejpam-6226	1	124	.	.	PUNCT
ejpam-6226	2	1	this	this	DET
ejpam-6226	2	2	paper	paper	NOUN
ejpam-6226	2	3	introduces	introduce	NOUN
ejpam-6226	2	4	and	and	CCONJ
ejpam-6226	2	5	develops	develop	VERB
ejpam-6226	2	6	the	the	DET
ejpam-6226	2	7	concepts	concept	NOUN
ejpam-6226	2	8	of	of	ADP
ejpam-6226	2	9	implicative	implicative	ADJ
ejpam-6226	2	10	ink	ink	NOUN
ejpam-6226	2	11	-	-	PUNCT
ejpam-6226	2	12	ideals	ideal	NOUN
ejpam-6226	2	13	(	(	PUNCT
ejpam-6226	2	14	mink	mink	NOUN
ejpam-6226	2	15	-	-	PUNCT
ejpam-6226	2	16	is	be	AUX
ejpam-6226	2	17	)	)	PUNCT
ejpam-6226	2	18	and	and	CCONJ
ejpam-6226	2	19	positive	positive	ADJ
ejpam-6226	2	20	implicative	implicative	ADJ
ejpam-6226	2	21	ink	ink	NOUN
ejpam-6226	2	22	-	-	PUNCT
ejpam-6226	2	23	ideals	ideal	NOUN
ejpam-6226	2	24	(	(	PUNCT
ejpam-6226	2	25	pmink	pmink	NOUN
ejpam-6226	2	26	-	-	PUNCT
ejpam-6226	2	27	is	be	AUX
ejpam-6226	2	28	)	)	PUNCT
ejpam-6226	2	29	within	within	ADP
ejpam-6226	2	30	the	the	DET
ejpam-6226	2	31	framework	framework	NOUN
ejpam-6226	2	32	of	of	ADP
ejpam-6226	2	33	ink	ink	NOUN
ejpam-6226	2	34	-	-	PUNCT
ejpam-6226	2	35	algebras	algebras	PROPN
ejpam-6226	2	36	.	.	PUNCT
ejpam-6226	3	1	these	these	DET
ejpam-6226	3	2	notions	notion	NOUN
ejpam-6226	3	3	are	be	AUX
ejpam-6226	3	4	subsequently	subsequently	ADV
ejpam-6226	3	5	extended	extend	VERB
ejpam-6226	3	6	to	to	ADP
ejpam-6226	3	7	fuzzy	fuzzy	ADJ
ejpam-6226	3	8	and	and	CCONJ
ejpam-6226	3	9	neutrosophic	neutrosophic	ADJ
ejpam-6226	3	10	contexts	contexts	NOUN
ejpam-6226	3	11	,	,	PUNCT
ejpam-6226	3	12	resulting	result	VERB
ejpam-6226	3	13	in	in	ADP
ejpam-6226	3	14	the	the	DET
ejpam-6226	3	15	definitions	definition	NOUN
ejpam-6226	3	16	of	of	ADP
ejpam-6226	3	17	fuzzy	fuzzy	ADJ
ejpam-6226	3	18	implicative	implicative	ADJ
ejpam-6226	3	19	ink	ink	NOUN
ejpam-6226	3	20	-	-	PUNCT
ejpam-6226	3	21	ideals	ideal	NOUN
ejpam-6226	3	22	(	(	PUNCT
ejpam-6226	3	23	fmink	fmink	NOUN
ejpam-6226	3	24	-	-	PUNCT
ejpam-6226	3	25	is	be	AUX
ejpam-6226	3	26	)	)	PUNCT
ejpam-6226	3	27	,	,	PUNCT
ejpam-6226	3	28	fuzzy	fuzzy	ADJ
ejpam-6226	3	29	positive	positive	ADJ
ejpam-6226	3	30	implicative	implicative	ADJ
ejpam-6226	3	31	ink	ink	NOUN
ejpam-6226	3	32	-	-	PUNCT
ejpam-6226	3	33	ideals	ideal	NOUN
ejpam-6226	3	34	(	(	PUNCT
ejpam-6226	3	35	fpmink	fpmink	NOUN
ejpam-6226	3	36	-	-	PUNCT
ejpam-6226	3	37	is	be	AUX
ejpam-6226	3	38	)	)	PUNCT
ejpam-6226	3	39	,	,	PUNCT
ejpam-6226	3	40	neutrosophic	neutrosophic	ADJ
ejpam-6226	3	41	implicative	implicative	ADJ
ejpam-6226	3	42	ink	ink	NOUN
ejpam-6226	3	43	-	-	PUNCT
ejpam-6226	3	44	ideals	ideal	NOUN
ejpam-6226	3	45	(	(	PUNCT
ejpam-6226	3	46	nmink	nmink	NOUN
ejpam-6226	3	47	-	-	PUNCT
ejpam-6226	3	48	is	be	AUX
ejpam-6226	3	49	)	)	PUNCT
ejpam-6226	3	50	,	,	PUNCT
ejpam-6226	3	51	and	and	CCONJ
ejpam-6226	3	52	neutrosophic	neutrosophic	ADJ
ejpam-6226	3	53	positive	positive	ADJ
ejpam-6226	3	54	implicative	implicative	ADJ
ejpam-6226	3	55	ink	ink	NOUN
ejpam-6226	3	56	-	-	PUNCT
ejpam-6226	3	57	ideals	ideal	NOUN
ejpam-6226	3	58	(	(	PUNCT
ejpam-6226	3	59	npmink	npmink	NOUN
ejpam-6226	3	60	-	-	PUNCT
ejpam-6226	3	61	is	be	AUX
ejpam-6226	3	62	)	)	PUNCT
ejpam-6226	3	63	.	.	PUNCT
ejpam-6226	4	1	the	the	DET
ejpam-6226	4	2	structural	structural	ADJ
ejpam-6226	4	3	properties	property	NOUN
ejpam-6226	4	4	of	of	ADP
ejpam-6226	4	5	these	these	DET
ejpam-6226	4	6	ideals	ideal	NOUN
ejpam-6226	4	7	are	be	AUX
ejpam-6226	4	8	investigated	investigate	VERB
ejpam-6226	4	9	,	,	PUNCT
ejpam-6226	4	10	including	include	VERB
ejpam-6226	4	11	their	their	PRON
ejpam-6226	4	12	behavior	behavior	NOUN
ejpam-6226	4	13	under	under	ADP
ejpam-6226	4	14	intersection	intersection	NOUN
ejpam-6226	4	15	and	and	CCONJ
ejpam-6226	4	16	union	union	NOUN
ejpam-6226	4	17	,	,	PUNCT
ejpam-6226	4	18	where	where	SCONJ
ejpam-6226	4	19	it	it	PRON
ejpam-6226	4	20	is	be	AUX
ejpam-6226	4	21	shown	show	VERB
ejpam-6226	4	22	that	that	SCONJ
ejpam-6226	4	23	intersection	intersection	NOUN
ejpam-6226	4	24	preserves	preserve	VERB
ejpam-6226	4	25	the	the	DET
ejpam-6226	4	26	respective	respective	ADJ
ejpam-6226	4	27	implicative	implicative	ADJ
ejpam-6226	4	28	properties	property	NOUN
ejpam-6226	4	29	,	,	PUNCT
ejpam-6226	4	30	while	while	SCONJ
ejpam-6226	4	31	union	union	NOUN
ejpam-6226	4	32	does	do	AUX
ejpam-6226	4	33	not	not	PART
ejpam-6226	4	34	in	in	ADP
ejpam-6226	4	35	general	general	ADJ
ejpam-6226	4	36	.	.	PUNCT
ejpam-6226	5	1	furthermore	furthermore	ADV
ejpam-6226	5	2	,	,	PUNCT
ejpam-6226	5	3	we	we	PRON
ejpam-6226	5	4	establish	establish	VERB
ejpam-6226	5	5	that	that	SCONJ
ejpam-6226	5	6	the	the	DET
ejpam-6226	5	7	homomorphic	homomorphic	ADJ
ejpam-6226	5	8	pre	pre	NOUN
ejpam-6226	5	9	-	-	NOUN
ejpam-6226	5	10	images	image	NOUN
ejpam-6226	5	11	of	of	ADP
ejpam-6226	5	12	these	these	DET
ejpam-6226	5	13	ideals	ideal	NOUN
ejpam-6226	5	14	also	also	ADV
ejpam-6226	5	15	preserve	preserve	VERB
ejpam-6226	5	16	their	their	PRON
ejpam-6226	5	17	respective	respective	ADJ
ejpam-6226	5	18	fuzzy	fuzzy	ADJ
ejpam-6226	5	19	and	and	CCONJ
ejpam-6226	5	20	neutrosophic	neutrosophic	ADJ
ejpam-6226	5	21	implicative	implicative	ADJ
ejpam-6226	5	22	structures	structure	NOUN
ejpam-6226	5	23	.	.	PUNCT
ejpam-6226	6	1	the	the	DET
ejpam-6226	6	2	results	result	NOUN
ejpam-6226	6	3	contribute	contribute	VERB
ejpam-6226	6	4	to	to	ADP
ejpam-6226	6	5	a	a	DET
ejpam-6226	6	6	deeper	deep	ADJ
ejpam-6226	6	7	understanding	understanding	NOUN
ejpam-6226	6	8	of	of	ADP
ejpam-6226	6	9	ideal	ideal	ADJ
ejpam-6226	6	10	theory	theory	NOUN
ejpam-6226	6	11	in	in	ADP
ejpam-6226	6	12	ink	ink	NOUN
ejpam-6226	6	13	-	-	PUNCT
ejpam-6226	6	14	algebras	algebras	NOUN
ejpam-6226	6	15	under	under	ADP
ejpam-6226	6	16	uncertainty	uncertainty	NOUN
ejpam-6226	6	17	and	and	CCONJ
ejpam-6226	6	18	open	open	ADJ
ejpam-6226	6	19	pathways	pathway	NOUN
ejpam-6226	6	20	for	for	ADP
ejpam-6226	6	21	applications	application	NOUN
ejpam-6226	6	22	in	in	ADP
ejpam-6226	6	23	fuzzy	fuzzy	ADJ
ejpam-6226	6	24	logic	logic	NOUN
ejpam-6226	6	25	and	and	CCONJ
ejpam-6226	6	26	neutrosophic	neutrosophic	ADJ
ejpam-6226	6	27	systems	system	NOUN
ejpam-6226	6	28	.	.	PUNCT
ejpam-6226	7	1	2020	2020	NUM
ejpam-6226	7	2	mathematics	mathematic	NOUN
ejpam-6226	7	3	subject	subject	NOUN
ejpam-6226	7	4	classifications	classification	NOUN
ejpam-6226	7	5	:	:	PUNCT
ejpam-6226	7	6	03g25	03g25	NUM
ejpam-6226	7	7	,	,	PUNCT
ejpam-6226	7	8	03e72	03e72	AUX
ejpam-6226	7	9	key	key	ADJ
ejpam-6226	7	10	words	word	NOUN
ejpam-6226	7	11	and	and	CCONJ
ejpam-6226	7	12	phrases	phrase	NOUN
ejpam-6226	7	13	:	:	PUNCT
ejpam-6226	7	14	ink	ink	NOUN
ejpam-6226	7	15	-	-	PUNCT
ejpam-6226	7	16	algebra	algebra	NOUN
ejpam-6226	7	17	,	,	PUNCT
ejpam-6226	7	18	fuzzy	fuzzy	ADJ
ejpam-6226	7	19	set	set	NOUN
ejpam-6226	7	20	,	,	PUNCT
ejpam-6226	7	21	neutrosophic	neutrosophic	ADJ
ejpam-6226	7	22	set	set	NOUN
ejpam-6226	7	23	,	,	PUNCT
ejpam-6226	7	24	implicative	implicative	ADJ
ejpam-6226	7	25	ink	ink	NOUN
ejpam-6226	7	26	-	-	PUNCT
ejpam-6226	7	27	ideal	ideal	ADJ
ejpam-6226	7	28	,	,	PUNCT
ejpam-6226	7	29	positive	positive	ADJ
ejpam-6226	7	30	implicative	implicative	ADJ
ejpam-6226	7	31	ink	ink	NOUN
ejpam-6226	7	32	-	-	PUNCT
ejpam-6226	7	33	ideal	ideal	ADJ
ejpam-6226	7	34	,	,	PUNCT
ejpam-6226	7	35	fuzzy	fuzzy	ADJ
ejpam-6226	7	36	implicative	implicative	ADJ
ejpam-6226	7	37	ink	ink	NOUN
ejpam-6226	7	38	-	-	PUNCT
ejpam-6226	7	39	ideal	ideal	ADJ
ejpam-6226	7	40	,	,	PUNCT
ejpam-6226	7	41	fuzzy	fuzzy	ADJ
ejpam-6226	7	42	positive	positive	ADJ
ejpam-6226	7	43	implicative	implicative	ADJ
ejpam-6226	7	44	ink	ink	NOUN
ejpam-6226	7	45	-	-	PUNCT
ejpam-6226	7	46	ideal	ideal	NOUN
ejpam-6226	7	47	,	,	PUNCT
ejpam-6226	7	48	neutrosophic	neutrosophic	ADJ
ejpam-6226	7	49	implicative	implicative	ADJ
ejpam-6226	7	50	ink	ink	NOUN
ejpam-6226	7	51	-	-	PUNCT
ejpam-6226	7	52	ideal	ideal	NOUN
ejpam-6226	7	53	,	,	PUNCT
ejpam-6226	7	54	neutrosophic	neutrosophic	ADJ
ejpam-6226	7	55	positive	positive	ADJ
ejpam-6226	7	56	implicative	implicative	ADJ
ejpam-6226	7	57	ink	ink	NOUN
ejpam-6226	7	58	-	-	PUNCT
ejpam-6226	7	59	ideal	ideal	NOUN
ejpam-6226	7	60	1	1	NUM
ejpam-6226	7	61	.	.	PUNCT
ejpam-6226	8	1	introduction	introduction	NOUN
ejpam-6226	8	2	iséki	iséki	PUNCT
ejpam-6226	8	3	and	and	CCONJ
ejpam-6226	8	4	tanaka	tanaka	PROPN
ejpam-6226	9	1	[	[	X
ejpam-6226	9	2	1	1	NUM
ejpam-6226	9	3	,	,	PUNCT
ejpam-6226	9	4	2	2	NUM
ejpam-6226	9	5	]	]	PUNCT
ejpam-6226	9	6	have	have	AUX
ejpam-6226	9	7	worked	work	VERB
ejpam-6226	9	8	on	on	ADP
ejpam-6226	9	9	the	the	DET
ejpam-6226	9	10	thought	thought	NOUN
ejpam-6226	9	11	of	of	ADP
ejpam-6226	9	12	bck	bck	PROPN
ejpam-6226	9	13	and	and	CCONJ
ejpam-6226	9	14	bci	bci	NOUN
ejpam-6226	9	15	-	-	PUNCT
ejpam-6226	9	16	algebras	algebras	PROPN
ejpam-6226	9	17	to	to	PART
ejpam-6226	9	18	pick	pick	VERB
ejpam-6226	9	19	up	up	ADP
ejpam-6226	9	20	their	their	PRON
ejpam-6226	9	21	characteristics	characteristic	NOUN
ejpam-6226	9	22	and	and	CCONJ
ejpam-6226	9	23	applications	application	NOUN
ejpam-6226	9	24	.	.	PUNCT
ejpam-6226	10	1	there	there	PRON
ejpam-6226	10	2	exists	exist	VERB
ejpam-6226	10	3	an	an	DET
ejpam-6226	10	4	immense	immense	ADJ
ejpam-6226	10	5	area	area	NOUN
ejpam-6226	10	6	of	of	ADP
ejpam-6226	10	7	empirical	empirical	ADJ
ejpam-6226	10	8	applications	application	NOUN
ejpam-6226	10	9	in	in	ADP
ejpam-6226	10	10	fuzzy	fuzzy	ADJ
ejpam-6226	10	11	sets	set	NOUN
ejpam-6226	10	12	and	and	CCONJ
ejpam-6226	10	13	their	their	PRON
ejpam-6226	10	14	generalizations	generalization	NOUN
ejpam-6226	10	15	.	.	PUNCT
ejpam-6226	11	1	the	the	DET
ejpam-6226	11	2	literature	literature	NOUN
ejpam-6226	11	3	works	work	VERB
ejpam-6226	11	4	on	on	ADP
ejpam-6226	11	5	fuzzy	fuzzy	ADJ
ejpam-6226	11	6	∗corresponding	∗corresponding	NOUN
ejpam-6226	11	7	author	author	NOUN
ejpam-6226	11	8	.	.	PUNCT
ejpam-6226	12	1	doi	doi	NOUN
ejpam-6226	12	2	:	:	PUNCT
ejpam-6226	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6226	https://doi.org/10.29020/nybg.ejpam.v18i3.6226	NUM
ejpam-6226	12	4	email	email	NOUN
ejpam-6226	12	5	addresses	address	NOUN
ejpam-6226	12	6	:	:	PUNCT
ejpam-6226	12	7	mouninaidu0521@gmail.com	mouninaidu0521@gmail.com	X
ejpam-6226	12	8	(	(	PUNCT
ejpam-6226	12	9	r.	r.	NOUN
ejpam-6226	12	10	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	12	11	)	)	PUNCT
ejpam-6226	12	12	,	,	PUNCT
ejpam-6226	12	13	eswarlal@kluniversity.in	eswarlal@kluniversity.in	PROPN
ejpam-6226	12	14	(	(	PUNCT
ejpam-6226	12	15	e.	e.	PROPN
ejpam-6226	12	16	tamma	tamma	PROPN
ejpam-6226	12	17	)	)	PUNCT
ejpam-6226	12	18	,	,	PUNCT
ejpam-6226	12	19	u.v.kalyani@gmail.com	u.v.kalyani@gmail.com	X
ejpam-6226	12	20	(	(	PUNCT
ejpam-6226	12	21	v.	v.	ADP
ejpam-6226	12	22	kalyani	kalyani	PROPN
ejpam-6226	12	23	uppuluri	uppuluri	PROPN
ejpam-6226	12	24	)	)	PUNCT
ejpam-6226	12	25	,	,	PUNCT
ejpam-6226	12	26	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6226	12	27	(	(	PUNCT
ejpam-6226	12	28	a.	a.	NOUN
ejpam-6226	12	29	iampan	iampan	PROPN
ejpam-6226	12	30	)	)	PUNCT
ejpam-6226	12	31	,	,	PUNCT
ejpam-6226	12	32	tsr	tsr	PROPN
ejpam-6226	12	33	2505@kluniversity.in	2505@kluniversity.in	NUM
ejpam-6226	12	34	(	(	PUNCT
ejpam-6226	12	35	t.	t.	PROPN
ejpam-6226	12	36	srinivasa	srinivasa	PROPN
ejpam-6226	12	37	rao	rao	PROPN
ejpam-6226	12	38	)	)	PUNCT
ejpam-6226	12	39	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6226	13	1	1	1	NUM
ejpam-6226	13	2	copyright	copyright	NOUN
ejpam-6226	13	3	:	:	PUNCT
ejpam-6226	13	4	©	©	PROPN
ejpam-6226	13	5	2025	2025	NUM
ejpam-6226	13	6	the	the	DET
ejpam-6226	13	7	author(s	author(s	NOUN
ejpam-6226	13	8	)	)	PUNCT
ejpam-6226	13	9	.	.	PUNCT
ejpam-6226	14	1	(	(	PUNCT
ejpam-6226	14	2	cc	cc	NOUN
ejpam-6226	14	3	by	by	ADP
ejpam-6226	14	4	-	-	PUNCT
ejpam-6226	14	5	nc	nc	PROPN
ejpam-6226	14	6	4.0	4.0	NUM
ejpam-6226	14	7	)	)	PUNCT
ejpam-6226	14	8	r.	r.	NOUN
ejpam-6226	14	9	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	14	10	et	et	PROPN
ejpam-6226	14	11	al	al	PROPN
ejpam-6226	14	12	.	.	PUNCT
ejpam-6226	14	13	/	/	SYM
ejpam-6226	14	14	eur	eur	PROPN
ejpam-6226	14	15	.	.	PUNCT
ejpam-6226	15	1	j.	j.	PROPN
ejpam-6226	15	2	pure	pure	PROPN
ejpam-6226	15	3	appl	appl	PROPN
ejpam-6226	15	4	.	.	PROPN
ejpam-6226	15	5	math	math	PROPN
ejpam-6226	15	6	,	,	PUNCT
ejpam-6226	15	7	18	18	NUM
ejpam-6226	15	8	(	(	PUNCT
ejpam-6226	15	9	3	3	NUM
ejpam-6226	15	10	)	)	PUNCT
ejpam-6226	15	11	(	(	PUNCT
ejpam-6226	15	12	2025	2025	NUM
ejpam-6226	15	13	)	)	PUNCT
ejpam-6226	15	14	,	,	PUNCT
ejpam-6226	15	15	6226	6226	NUM
ejpam-6226	15	16	2	2	NUM
ejpam-6226	15	17	of	of	ADP
ejpam-6226	15	18	19	19	NUM
ejpam-6226	15	19	subalgebras	subalgebra	NOUN
ejpam-6226	15	20	and	and	CCONJ
ejpam-6226	15	21	fuzzy	fuzzy	ADJ
ejpam-6226	15	22	k	k	NOUN
ejpam-6226	15	23	-	-	NOUN
ejpam-6226	15	24	ideals	ideal	NOUN
ejpam-6226	15	25	in	in	ADP
ejpam-6226	15	26	ink	ink	NOUN
ejpam-6226	15	27	-	-	PUNCT
ejpam-6226	15	28	algebras	algebra	NOUN
ejpam-6226	15	29	,	,	PUNCT
ejpam-6226	15	30	fuzzy	fuzzy	ADJ
ejpam-6226	15	31	p	p	NOUN
ejpam-6226	15	32	-	-	PUNCT
ejpam-6226	15	33	ideal	ideal	NOUN
ejpam-6226	15	34	in	in	ADP
ejpam-6226	15	35	ink	ink	NOUN
ejpam-6226	15	36	-	-	PUNCT
ejpam-6226	15	37	algebras	algebra	NOUN
ejpam-6226	15	38	,	,	PUNCT
ejpam-6226	15	39	and	and	CCONJ
ejpam-6226	15	40	fuzzy	fuzzy	ADJ
ejpam-6226	15	41	translation	translation	NOUN
ejpam-6226	15	42	of	of	ADP
ejpam-6226	15	43	ink	ink	NOUN
ejpam-6226	15	44	-	-	PUNCT
ejpam-6226	15	45	ideals	ideal	NOUN
ejpam-6226	15	46	of	of	ADP
ejpam-6226	15	47	ink	ink	NOUN
ejpam-6226	15	48	-	-	PUNCT
ejpam-6226	15	49	algebras	algebras	PROPN
ejpam-6226	15	50	.	.	PUNCT
ejpam-6226	16	1	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	16	2	et	et	PROPN
ejpam-6226	16	3	al	al	PROPN
ejpam-6226	16	4	.	.	PUNCT
ejpam-6226	17	1	[	[	X
ejpam-6226	17	2	3	3	NUM
ejpam-6226	17	3	,	,	PUNCT
ejpam-6226	17	4	4	4	NUM
ejpam-6226	17	5	]	]	PUNCT
ejpam-6226	17	6	proposed	propose	VERB
ejpam-6226	17	7	intuitionistic	intuitionistic	ADJ
ejpam-6226	17	8	fuzzy	fuzzy	ADJ
ejpam-6226	17	9	ink	ink	NOUN
ejpam-6226	17	10	-	-	PUNCT
ejpam-6226	17	11	ideals	ideal	NOUN
ejpam-6226	17	12	of	of	ADP
ejpam-6226	17	13	ink	ink	NOUN
ejpam-6226	17	14	-	-	PUNCT
ejpam-6226	17	15	algebras	algebra	NOUN
ejpam-6226	17	16	,	,	PUNCT
ejpam-6226	17	17	direct	direct	ADJ
ejpam-6226	17	18	product	product	NOUN
ejpam-6226	17	19	of	of	ADP
ejpam-6226	17	20	intuitionistic	intuitionistic	ADJ
ejpam-6226	17	21	fuzzy	fuzzy	ADJ
ejpam-6226	17	22	k	k	NOUN
ejpam-6226	17	23	-	-	NOUN
ejpam-6226	17	24	ideals	ideal	NOUN
ejpam-6226	17	25	of	of	ADP
ejpam-6226	17	26	ink	ink	NOUN
ejpam-6226	17	27	-	-	PUNCT
ejpam-6226	17	28	algebras	algebras	PROPN
ejpam-6226	17	29	,	,	PUNCT
ejpam-6226	17	30	intuitionistic	intuitionistic	ADJ
ejpam-6226	17	31	fuzzy	fuzzy	ADJ
ejpam-6226	17	32	translation	translation	NOUN
ejpam-6226	17	33	on	on	ADP
ejpam-6226	17	34	ink	ink	NOUN
ejpam-6226	17	35	-	-	PUNCT
ejpam-6226	17	36	algebras	algebra	NOUN
ejpam-6226	17	37	,	,	PUNCT
ejpam-6226	17	38	and	and	CCONJ
ejpam-6226	17	39	they	they	PRON
ejpam-6226	17	40	have	have	AUX
ejpam-6226	17	41	discussed	discuss	VERB
ejpam-6226	17	42	neutrosophic	neutrosophic	ADJ
ejpam-6226	17	43	h	h	NOUN
ejpam-6226	17	44	-	-	PUNCT
ejpam-6226	17	45	ideals	ideal	NOUN
ejpam-6226	17	46	in	in	ADP
ejpam-6226	17	47	ink	ink	NOUN
ejpam-6226	17	48	-	-	PUNCT
ejpam-6226	17	49	algebras	algebras	NOUN
ejpam-6226	17	50	.	.	PUNCT
ejpam-6226	18	1	homomorphism	homomorphism	NOUN
ejpam-6226	18	2	and	and	CCONJ
ejpam-6226	18	3	anti	anti	NOUN
ejpam-6226	18	4	-	-	NOUN
ejpam-6226	18	5	homomorphism	homomorphism	NOUN
ejpam-6226	18	6	of	of	ADP
ejpam-6226	18	7	neutrosophic	neutrosophic	ADJ
ejpam-6226	18	8	ink	ink	NOUN
ejpam-6226	18	9	-	-	PUNCT
ejpam-6226	18	10	algebras	algebra	NOUN
ejpam-6226	18	11	have	have	AUX
ejpam-6226	18	12	been	be	AUX
ejpam-6226	18	13	done	do	VERB
ejpam-6226	18	14	by	by	ADP
ejpam-6226	18	15	mounikalakshmi	mounikalakshmi	NOUN
ejpam-6226	18	16	et	et	PROPN
ejpam-6226	18	17	al	al	PROPN
ejpam-6226	18	18	.	.	PUNCT
ejpam-6226	19	1	[	[	X
ejpam-6226	19	2	5	5	NUM
ejpam-6226	19	3	,	,	PUNCT
ejpam-6226	19	4	6	6	NUM
ejpam-6226	19	5	]	]	PUNCT
ejpam-6226	19	6	.	.	PUNCT
ejpam-6226	20	1	moreover	moreover	ADV
ejpam-6226	20	2	,	,	PUNCT
ejpam-6226	20	3	the	the	DET
ejpam-6226	20	4	work	work	NOUN
ejpam-6226	20	5	of	of	ADP
ejpam-6226	20	6	ink	ink	NOUN
ejpam-6226	20	7	-	-	PUNCT
ejpam-6226	20	8	algebras	algebras	PROPN
ejpam-6226	20	9	has	have	AUX
ejpam-6226	20	10	been	be	AUX
ejpam-6226	20	11	explored	explore	VERB
ejpam-6226	20	12	in	in	ADP
ejpam-6226	20	13	different	different	ADJ
ejpam-6226	20	14	aspects	aspect	NOUN
ejpam-6226	20	15	of	of	ADP
ejpam-6226	20	16	fuzzy	fuzzy	ADJ
ejpam-6226	20	17	sets	set	NOUN
ejpam-6226	20	18	,	,	PUNCT
ejpam-6226	20	19	intuitionistic	intuitionistic	ADJ
ejpam-6226	20	20	fuzzy	fuzzy	ADJ
ejpam-6226	20	21	sets	set	NOUN
ejpam-6226	20	22	,	,	PUNCT
ejpam-6226	20	23	and	and	CCONJ
ejpam-6226	20	24	neutrosophic	neutrosophic	ADJ
ejpam-6226	20	25	sets	set	NOUN
ejpam-6226	20	26	.	.	PUNCT
ejpam-6226	21	1	recent	recent	ADJ
ejpam-6226	21	2	developments	development	NOUN
ejpam-6226	21	3	in	in	ADP
ejpam-6226	21	4	the	the	DET
ejpam-6226	21	5	study	study	NOUN
ejpam-6226	21	6	of	of	ADP
ejpam-6226	21	7	ink	ink	NOUN
ejpam-6226	21	8	-	-	PUNCT
ejpam-6226	21	9	algebras	algebra	NOUN
ejpam-6226	21	10	have	have	AUX
ejpam-6226	21	11	increasingly	increasingly	ADV
ejpam-6226	21	12	embraced	embrace	VERB
ejpam-6226	21	13	the	the	DET
ejpam-6226	21	14	framework	framework	NOUN
ejpam-6226	21	15	of	of	ADP
ejpam-6226	21	16	neutrosophic	neutrosophic	ADJ
ejpam-6226	21	17	logic	logic	NOUN
ejpam-6226	21	18	to	to	PART
ejpam-6226	21	19	handle	handle	VERB
ejpam-6226	21	20	indeterminacy	indeterminacy	NOUN
ejpam-6226	21	21	and	and	CCONJ
ejpam-6226	21	22	ambiguity	ambiguity	NOUN
ejpam-6226	21	23	in	in	ADP
ejpam-6226	21	24	algebraic	algebraic	ADJ
ejpam-6226	21	25	reasoning	reasoning	NOUN
ejpam-6226	21	26	.	.	PUNCT
ejpam-6226	22	1	notably	notably	ADV
ejpam-6226	22	2	,	,	PUNCT
ejpam-6226	22	3	al	al	PROPN
ejpam-6226	22	4	-	-	PROPN
ejpam-6226	22	5	masarwah	masarwah	NOUN
ejpam-6226	22	6	et	et	PROPN
ejpam-6226	22	7	al	al	PROPN
ejpam-6226	22	8	.	.	PUNCT
ejpam-6226	23	1	[	[	X
ejpam-6226	23	2	7	7	X
ejpam-6226	23	3	]	]	PUNCT
ejpam-6226	23	4	introduced	introduce	VERB
ejpam-6226	23	5	the	the	DET
ejpam-6226	23	6	concept	concept	NOUN
ejpam-6226	23	7	of	of	ADP
ejpam-6226	23	8	fermatean	fermatean	PROPN
ejpam-6226	23	9	neutrosophic	neutrosophic	ADJ
ejpam-6226	23	10	ink	ink	NOUN
ejpam-6226	23	11	-	-	PUNCT
ejpam-6226	23	12	algebras	algebras	PROPN
ejpam-6226	23	13	,	,	PUNCT
ejpam-6226	23	14	enriching	enrich	VERB
ejpam-6226	23	15	the	the	DET
ejpam-6226	23	16	traditional	traditional	ADJ
ejpam-6226	23	17	neutrosophic	neutrosophic	ADJ
ejpam-6226	23	18	structure	structure	NOUN
ejpam-6226	23	19	by	by	ADP
ejpam-6226	23	20	incorporating	incorporate	VERB
ejpam-6226	23	21	higher	high	ADJ
ejpam-6226	23	22	degrees	degree	NOUN
ejpam-6226	23	23	of	of	ADP
ejpam-6226	23	24	membership	membership	NOUN
ejpam-6226	23	25	and	and	CCONJ
ejpam-6226	23	26	indeterminacy	indeterminacy	NOUN
ejpam-6226	23	27	for	for	ADP
ejpam-6226	23	28	enhanced	enhance	VERB
ejpam-6226	23	29	expressive	expressive	ADJ
ejpam-6226	23	30	power	power	NOUN
ejpam-6226	23	31	.	.	PUNCT
ejpam-6226	24	1	complementing	complement	VERB
ejpam-6226	24	2	this	this	PRON
ejpam-6226	24	3	,	,	PUNCT
ejpam-6226	24	4	al	al	PROPN
ejpam-6226	24	5	-	-	PUNCT
ejpam-6226	24	6	omeri	omeri	NOUN
ejpam-6226	24	7	et	et	PROPN
ejpam-6226	24	8	al	al	PROPN
ejpam-6226	24	9	.	.	PUNCT
ejpam-6226	25	1	[	[	X
ejpam-6226	25	2	8	8	NUM
ejpam-6226	25	3	]	]	SYM
ejpam-6226	25	4	examined	examine	VERB
ejpam-6226	25	5	translation	translation	NOUN
ejpam-6226	25	6	mechanisms	mechanism	NOUN
ejpam-6226	25	7	within	within	ADP
ejpam-6226	25	8	neutrosophic	neutrosophic	ADJ
ejpam-6226	25	9	ink	ink	NOUN
ejpam-6226	25	10	-	-	PUNCT
ejpam-6226	25	11	algebras	algebras	X
ejpam-6226	25	12	,	,	PUNCT
ejpam-6226	25	13	providing	provide	VERB
ejpam-6226	25	14	insights	insight	NOUN
ejpam-6226	25	15	into	into	ADP
ejpam-6226	25	16	structural	structural	ADJ
ejpam-6226	25	17	transformations	transformation	NOUN
ejpam-6226	25	18	and	and	CCONJ
ejpam-6226	25	19	their	their	PRON
ejpam-6226	25	20	algebraic	algebraic	ADJ
ejpam-6226	25	21	consequences	consequence	NOUN
ejpam-6226	25	22	.	.	PUNCT
ejpam-6226	26	1	further	further	ADJ
ejpam-6226	26	2	foundational	foundational	ADJ
ejpam-6226	26	3	work	work	NOUN
ejpam-6226	26	4	by	by	ADP
ejpam-6226	26	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	26	6	et	et	PROPN
ejpam-6226	26	7	al	al	PROPN
ejpam-6226	26	8	.	.	PUNCT
ejpam-6226	27	1	[	[	X
ejpam-6226	27	2	9	9	NUM
ejpam-6226	27	3	]	]	PUNCT
ejpam-6226	27	4	investigated	investigate	VERB
ejpam-6226	27	5	the	the	DET
ejpam-6226	27	6	direct	direct	ADJ
ejpam-6226	27	7	product	product	NOUN
ejpam-6226	27	8	of	of	ADP
ejpam-6226	27	9	neutrosophic	neutrosophic	ADJ
ejpam-6226	27	10	ink	ink	NOUN
ejpam-6226	27	11	-	-	PUNCT
ejpam-6226	27	12	algebras	algebras	X
ejpam-6226	27	13	,	,	PUNCT
ejpam-6226	27	14	establishing	establish	VERB
ejpam-6226	27	15	critical	critical	ADJ
ejpam-6226	27	16	results	result	NOUN
ejpam-6226	27	17	on	on	ADP
ejpam-6226	27	18	ideal	ideal	ADJ
ejpam-6226	27	19	preservation	preservation	NOUN
ejpam-6226	27	20	and	and	CCONJ
ejpam-6226	27	21	operational	operational	ADJ
ejpam-6226	27	22	behavior	behavior	NOUN
ejpam-6226	27	23	in	in	ADP
ejpam-6226	27	24	product	product	NOUN
ejpam-6226	27	25	structures	structure	NOUN
ejpam-6226	27	26	.	.	PUNCT
ejpam-6226	28	1	collectively	collectively	ADV
ejpam-6226	28	2	,	,	PUNCT
ejpam-6226	28	3	these	these	DET
ejpam-6226	28	4	contributions	contribution	NOUN
ejpam-6226	28	5	have	have	AUX
ejpam-6226	28	6	expanded	expand	VERB
ejpam-6226	28	7	the	the	DET
ejpam-6226	28	8	theoretical	theoretical	ADJ
ejpam-6226	28	9	landscape	landscape	NOUN
ejpam-6226	28	10	of	of	ADP
ejpam-6226	28	11	ink	ink	NOUN
ejpam-6226	28	12	-	-	PUNCT
ejpam-6226	28	13	algebras	algebra	NOUN
ejpam-6226	28	14	,	,	PUNCT
ejpam-6226	28	15	offering	offer	VERB
ejpam-6226	28	16	versatile	versatile	ADJ
ejpam-6226	28	17	tools	tool	NOUN
ejpam-6226	28	18	for	for	ADP
ejpam-6226	28	19	modeling	model	VERB
ejpam-6226	28	20	logical	logical	ADJ
ejpam-6226	28	21	uncertainty	uncertainty	NOUN
ejpam-6226	28	22	in	in	ADP
ejpam-6226	28	23	abstract	abstract	ADJ
ejpam-6226	28	24	algebraic	algebraic	ADJ
ejpam-6226	28	25	systems	system	NOUN
ejpam-6226	28	26	.	.	PUNCT
ejpam-6226	29	1	zadeh	zadeh	NOUN
ejpam-6226	30	1	[	[	X
ejpam-6226	30	2	10	10	NUM
ejpam-6226	30	3	]	]	PUNCT
ejpam-6226	30	4	explored	explore	VERB
ejpam-6226	30	5	the	the	DET
ejpam-6226	30	6	idea	idea	NOUN
ejpam-6226	30	7	of	of	ADP
ejpam-6226	30	8	fuzzy	fuzzy	ADJ
ejpam-6226	30	9	sets	set	NOUN
ejpam-6226	30	10	(	(	PUNCT
ejpam-6226	30	11	fss	fss	NOUN
ejpam-6226	30	12	)	)	PUNCT
ejpam-6226	30	13	in	in	ADP
ejpam-6226	30	14	1965	1965	NUM
ejpam-6226	30	15	,	,	PUNCT
ejpam-6226	30	16	an	an	DET
ejpam-6226	30	17	extension	extension	NOUN
ejpam-6226	30	18	of	of	ADP
ejpam-6226	30	19	classical	classical	ADJ
ejpam-6226	30	20	set	set	NOUN
ejpam-6226	30	21	theory	theory	NOUN
ejpam-6226	30	22	that	that	SCONJ
ejpam-6226	30	23	deals	deal	VERB
ejpam-6226	30	24	with	with	ADP
ejpam-6226	30	25	vagueness	vagueness	NOUN
ejpam-6226	30	26	and	and	CCONJ
ejpam-6226	30	27	uncertainty	uncertainty	NOUN
ejpam-6226	30	28	in	in	ADP
ejpam-6226	30	29	the	the	DET
ejpam-6226	30	30	given	give	VERB
ejpam-6226	30	31	data	datum	NOUN
ejpam-6226	30	32	.	.	PUNCT
ejpam-6226	31	1	classical	classical	ADJ
ejpam-6226	31	2	set	set	NOUN
ejpam-6226	31	3	theory	theory	NOUN
ejpam-6226	31	4	asserts	assert	VERB
ejpam-6226	31	5	that	that	SCONJ
ejpam-6226	31	6	an	an	DET
ejpam-6226	31	7	element	element	NOUN
ejpam-6226	31	8	is	be	AUX
ejpam-6226	31	9	either	either	CCONJ
ejpam-6226	31	10	a	a	DET
ejpam-6226	31	11	member	member	NOUN
ejpam-6226	31	12	of	of	ADP
ejpam-6226	31	13	a	a	DET
ejpam-6226	31	14	set	set	NOUN
ejpam-6226	31	15	or	or	CCONJ
ejpam-6226	31	16	not	not	PART
ejpam-6226	31	17	.	.	PUNCT
ejpam-6226	32	1	fs	fs	ADP
ejpam-6226	32	2	theory	theory	NOUN
ejpam-6226	32	3	discourses	discourse	VERB
ejpam-6226	32	4	this	this	PRON
ejpam-6226	32	5	by	by	ADP
ejpam-6226	32	6	introducing	introduce	VERB
ejpam-6226	32	7	membership	membership	NOUN
ejpam-6226	32	8	values	value	NOUN
ejpam-6226	32	9	scaling	scale	VERB
ejpam-6226	32	10	from	from	ADP
ejpam-6226	32	11	0	0	NUM
ejpam-6226	32	12	to	to	ADP
ejpam-6226	32	13	1	1	NUM
ejpam-6226	32	14	,	,	PUNCT
ejpam-6226	32	15	which	which	PRON
ejpam-6226	32	16	have	have	AUX
ejpam-6226	32	17	been	be	AUX
ejpam-6226	32	18	used	use	VERB
ejpam-6226	32	19	to	to	PART
ejpam-6226	32	20	represent	represent	VERB
ejpam-6226	32	21	the	the	DET
ejpam-6226	32	22	degree	degree	NOUN
ejpam-6226	32	23	to	to	PART
ejpam-6226	32	24	which	which	PRON
ejpam-6226	32	25	an	an	DET
ejpam-6226	32	26	element	element	NOUN
ejpam-6226	32	27	is	be	AUX
ejpam-6226	32	28	affiliated	affiliate	VERB
ejpam-6226	32	29	with	with	ADP
ejpam-6226	32	30	a	a	DET
ejpam-6226	32	31	set	set	NOUN
ejpam-6226	32	32	.	.	PUNCT
ejpam-6226	33	1	fs	fs	PROPN
ejpam-6226	33	2	theory	theory	NOUN
ejpam-6226	33	3	has	have	VERB
ejpam-6226	33	4	innumerable	innumerable	ADJ
ejpam-6226	33	5	implementations	implementation	NOUN
ejpam-6226	33	6	in	in	ADP
ejpam-6226	33	7	diverse	diverse	ADJ
ejpam-6226	33	8	fields	field	NOUN
ejpam-6226	33	9	,	,	PUNCT
ejpam-6226	33	10	including	include	VERB
ejpam-6226	33	11	artificial	artificial	ADJ
ejpam-6226	33	12	intelligence	intelligence	NOUN
ejpam-6226	33	13	,	,	PUNCT
ejpam-6226	33	14	decision	decision	NOUN
ejpam-6226	33	15	-	-	PUNCT
ejpam-6226	33	16	making	making	NOUN
ejpam-6226	33	17	,	,	PUNCT
ejpam-6226	33	18	and	and	CCONJ
ejpam-6226	33	19	control	control	NOUN
ejpam-6226	33	20	systems	system	NOUN
ejpam-6226	33	21	that	that	PRON
ejpam-6226	33	22	allow	allow	VERB
ejpam-6226	33	23	both	both	DET
ejpam-6226	33	24	modeling	modeling	NOUN
ejpam-6226	33	25	and	and	CCONJ
ejpam-6226	33	26	handling	handling	NOUN
ejpam-6226	33	27	of	of	ADP
ejpam-6226	33	28	vague	vague	ADJ
ejpam-6226	33	29	and	and	CCONJ
ejpam-6226	33	30	imprecise	imprecise	ADJ
ejpam-6226	33	31	information	information	NOUN
ejpam-6226	33	32	.	.	PUNCT
ejpam-6226	34	1	moreover	moreover	ADV
ejpam-6226	34	2	,	,	PUNCT
ejpam-6226	34	3	jun	jun	PROPN
ejpam-6226	34	4	et	et	PROPN
ejpam-6226	34	5	al	al	PROPN
ejpam-6226	34	6	.	.	PUNCT
ejpam-6226	35	1	[	[	X
ejpam-6226	35	2	11	11	NUM
ejpam-6226	35	3	]	]	PUNCT
ejpam-6226	35	4	studied	study	VERB
ejpam-6226	35	5	the	the	DET
ejpam-6226	35	6	idea	idea	NOUN
ejpam-6226	35	7	of	of	ADP
ejpam-6226	35	8	fuzzy	fuzzy	ADJ
ejpam-6226	35	9	implicative	implicative	ADJ
ejpam-6226	35	10	ideals	ideal	NOUN
ejpam-6226	35	11	and	and	CCONJ
ejpam-6226	35	12	constructed	construct	VERB
ejpam-6226	35	13	a	a	DET
ejpam-6226	35	14	fuzzy	fuzzy	ADJ
ejpam-6226	35	15	characteristic	characteristic	ADJ
ejpam-6226	35	16	implicative	implicative	ADJ
ejpam-6226	35	17	ideal	ideal	NOUN
ejpam-6226	35	18	in	in	ADP
ejpam-6226	35	19	bck	bck	PROPN
ejpam-6226	35	20	-	-	PUNCT
ejpam-6226	35	21	algebras	algebras	PROPN
ejpam-6226	35	22	.	.	PUNCT
ejpam-6226	36	1	paad	paad	PROPN
ejpam-6226	37	1	[	[	X
ejpam-6226	37	2	12	12	NUM
ejpam-6226	37	3	]	]	PUNCT
ejpam-6226	37	4	introduced	introduce	VERB
ejpam-6226	37	5	the	the	DET
ejpam-6226	37	6	concept	concept	NOUN
ejpam-6226	37	7	of	of	ADP
ejpam-6226	37	8	fuzzy	fuzzy	ADJ
ejpam-6226	37	9	implicative	implicative	ADJ
ejpam-6226	37	10	ideals	ideal	NOUN
ejpam-6226	37	11	in	in	ADP
ejpam-6226	37	12	bl	bl	NOUN
ejpam-6226	37	13	-	-	PUNCT
ejpam-6226	37	14	algebras	algebras	X
ejpam-6226	37	15	,	,	PUNCT
ejpam-6226	37	16	and	and	CCONJ
ejpam-6226	37	17	they	they	PRON
ejpam-6226	37	18	state	state	VERB
ejpam-6226	37	19	several	several	ADJ
ejpam-6226	37	20	properties	property	NOUN
ejpam-6226	37	21	of	of	ADP
ejpam-6226	37	22	it	it	PRON
ejpam-6226	37	23	.	.	PUNCT
ejpam-6226	38	1	also	also	ADV
ejpam-6226	38	2	,	,	PUNCT
ejpam-6226	38	3	sowmia	sowmia	NOUN
ejpam-6226	38	4	and	and	CCONJ
ejpam-6226	38	5	jeyalakshmi	jeyalakshmi	NOUN
ejpam-6226	39	1	[	[	X
ejpam-6226	39	2	13	13	NUM
ejpam-6226	39	3	]	]	PUNCT
ejpam-6226	39	4	have	have	AUX
ejpam-6226	39	5	worked	work	VERB
ejpam-6226	39	6	on	on	ADP
ejpam-6226	39	7	the	the	DET
ejpam-6226	39	8	perception	perception	NOUN
ejpam-6226	39	9	of	of	ADP
ejpam-6226	39	10	fuzzy	fuzzy	ADJ
ejpam-6226	39	11	implicative	implicative	ADJ
ejpam-6226	39	12	ideals	ideal	NOUN
ejpam-6226	39	13	in	in	ADP
ejpam-6226	39	14	z	z	PROPN
ejpam-6226	39	15	-	-	PUNCT
ejpam-6226	39	16	algebras	algebras	X
ejpam-6226	39	17	.	.	PUNCT
ejpam-6226	40	1	eventually	eventually	ADV
ejpam-6226	40	2	,	,	PUNCT
ejpam-6226	40	3	atanassov	atanassov	VERB
ejpam-6226	41	1	[	[	X
ejpam-6226	41	2	14	14	NUM
ejpam-6226	41	3	]	]	PUNCT
ejpam-6226	41	4	proposed	propose	VERB
ejpam-6226	41	5	the	the	DET
ejpam-6226	41	6	generalization	generalization	NOUN
ejpam-6226	41	7	of	of	ADP
ejpam-6226	41	8	fss	fss	PROPN
ejpam-6226	41	9	,	,	PUNCT
ejpam-6226	41	10	which	which	PRON
ejpam-6226	41	11	is	be	AUX
ejpam-6226	41	12	an	an	DET
ejpam-6226	41	13	intuitionistic	intuitionistic	ADJ
ejpam-6226	41	14	fuzzy	fuzzy	ADJ
ejpam-6226	41	15	set	set	NOUN
ejpam-6226	41	16	(	(	PUNCT
ejpam-6226	41	17	ifs	ifs	PROPN
ejpam-6226	41	18	)	)	PUNCT
ejpam-6226	41	19	in	in	ADP
ejpam-6226	41	20	1980	1980	NUM
ejpam-6226	41	21	,	,	PUNCT
ejpam-6226	41	22	which	which	PRON
ejpam-6226	41	23	gives	give	VERB
ejpam-6226	41	24	information	information	NOUN
ejpam-6226	41	25	about	about	ADP
ejpam-6226	41	26	a	a	DET
ejpam-6226	41	27	fresh	fresh	ADJ
ejpam-6226	41	28	parameter	parameter	NOUN
ejpam-6226	41	29	known	know	VERB
ejpam-6226	41	30	as	as	ADP
ejpam-6226	41	31	nonmembership	nonmembership	NOUN
ejpam-6226	41	32	degree	degree	NOUN
ejpam-6226	41	33	,	,	PUNCT
ejpam-6226	41	34	where	where	SCONJ
ejpam-6226	41	35	fuzzy	fuzzy	ADJ
ejpam-6226	41	36	tells	tell	VERB
ejpam-6226	41	37	us	we	PRON
ejpam-6226	41	38	about	about	ADP
ejpam-6226	41	39	the	the	DET
ejpam-6226	41	40	membership	membership	NOUN
ejpam-6226	41	41	degree	degree	NOUN
ejpam-6226	41	42	but	but	CCONJ
ejpam-6226	41	43	in	in	ADP
ejpam-6226	41	44	ifs	ifs	PROPN
ejpam-6226	41	45	gives	give	VERB
ejpam-6226	41	46	information	information	NOUN
ejpam-6226	41	47	about	about	ADP
ejpam-6226	41	48	uncertainty	uncertainty	NOUN
ejpam-6226	41	49	and	and	CCONJ
ejpam-6226	41	50	vagueness	vagueness	NOUN
ejpam-6226	41	51	regarding	regard	VERB
ejpam-6226	41	52	membership	membership	NOUN
ejpam-6226	41	53	degrees	degree	NOUN
ejpam-6226	41	54	and	and	CCONJ
ejpam-6226	41	55	nonmembership	nonmembership	NOUN
ejpam-6226	41	56	degrees	degree	NOUN
ejpam-6226	41	57	.	.	PUNCT
ejpam-6226	42	1	ifss	ifss	PROPN
ejpam-6226	42	2	have	have	VERB
ejpam-6226	42	3	applications	application	NOUN
ejpam-6226	42	4	in	in	ADP
ejpam-6226	42	5	decision	decision	NOUN
ejpam-6226	42	6	-	-	PUNCT
ejpam-6226	42	7	making	making	NOUN
ejpam-6226	42	8	where	where	SCONJ
ejpam-6226	42	9	uncertainty	uncertainty	NOUN
ejpam-6226	42	10	plays	play	VERB
ejpam-6226	42	11	a	a	DET
ejpam-6226	42	12	significant	significant	ADJ
ejpam-6226	42	13	role	role	NOUN
ejpam-6226	42	14	.	.	PUNCT
ejpam-6226	43	1	various	various	ADJ
ejpam-6226	43	2	approaches	approach	NOUN
ejpam-6226	43	3	to	to	ADP
ejpam-6226	43	4	ifs	ifs	PROPN
ejpam-6226	43	5	include	include	VERB
ejpam-6226	43	6	expert	expert	NOUN
ejpam-6226	43	7	systems	system	NOUN
ejpam-6226	43	8	,	,	PUNCT
ejpam-6226	43	9	risk	risk	NOUN
ejpam-6226	43	10	assessment	assessment	NOUN
ejpam-6226	43	11	,	,	PUNCT
ejpam-6226	43	12	and	and	CCONJ
ejpam-6226	43	13	medical	medical	ADJ
ejpam-6226	43	14	diagnosis	diagnosis	NOUN
ejpam-6226	43	15	,	,	PUNCT
ejpam-6226	43	16	where	where	SCONJ
ejpam-6226	43	17	precise	precise	ADJ
ejpam-6226	43	18	decisions	decision	NOUN
ejpam-6226	43	19	are	be	AUX
ejpam-6226	43	20	difficult	difficult	ADJ
ejpam-6226	43	21	based	base	VERB
ejpam-6226	43	22	on	on	ADP
ejpam-6226	43	23	vague	vague	ADJ
ejpam-6226	43	24	or	or	CCONJ
ejpam-6226	43	25	uncertain	uncertain	ADJ
ejpam-6226	43	26	data	datum	NOUN
ejpam-6226	43	27	or	or	CCONJ
ejpam-6226	43	28	information	information	NOUN
ejpam-6226	43	29	.	.	PUNCT
ejpam-6226	44	1	satyanarayana	satyanarayana	PROPN
ejpam-6226	44	2	et	et	PROPN
ejpam-6226	44	3	al	al	PROPN
ejpam-6226	44	4	.	.	PUNCT
ejpam-6226	45	1	[	[	X
ejpam-6226	45	2	15	15	NUM
ejpam-6226	45	3	,	,	PUNCT
ejpam-6226	45	4	16	16	NUM
ejpam-6226	45	5	]	]	PUNCT
ejpam-6226	45	6	have	have	AUX
ejpam-6226	45	7	worked	work	VERB
ejpam-6226	45	8	on	on	ADP
ejpam-6226	45	9	the	the	DET
ejpam-6226	45	10	concept	concept	NOUN
ejpam-6226	45	11	of	of	ADP
ejpam-6226	45	12	intuitionistic	intuitionistic	ADJ
ejpam-6226	45	13	fuzzy	fuzzy	ADJ
ejpam-6226	45	14	implicative	implicative	ADJ
ejpam-6226	45	15	hyper	hyper	ADJ
ejpam-6226	45	16	bck	bck	NOUN
ejpam-6226	45	17	-	-	PUNCT
ejpam-6226	45	18	ideals	ideal	NOUN
ejpam-6226	45	19	of	of	ADP
ejpam-6226	45	20	hyper	hyper	ADJ
ejpam-6226	45	21	bck	bck	NOUN
ejpam-6226	45	22	-	-	PUNCT
ejpam-6226	45	23	algebras	algebra	NOUN
ejpam-6226	45	24	and	and	CCONJ
ejpam-6226	45	25	interval	interval	NOUN
ejpam-6226	45	26	-	-	PUNCT
ejpam-6226	45	27	valued	value	VERB
ejpam-6226	45	28	intuitionistic	intuitionistic	ADJ
ejpam-6226	45	29	fuzzy	fuzzy	ADJ
ejpam-6226	45	30	(	(	PUNCT
ejpam-6226	45	31	implicative	implicative	ADJ
ejpam-6226	45	32	and	and	CCONJ
ejpam-6226	45	33	commutative	commutative	ADJ
ejpam-6226	45	34	)	)	PUNCT
ejpam-6226	45	35	ideals	ideal	NOUN
ejpam-6226	45	36	of	of	ADP
ejpam-6226	45	37	bck	bck	NOUN
ejpam-6226	45	38	-	-	PUNCT
ejpam-6226	45	39	algebras	algebras	PROPN
ejpam-6226	45	40	.	.	PUNCT
ejpam-6226	46	1	also	also	ADV
ejpam-6226	46	2	,	,	PUNCT
ejpam-6226	46	3	satynarayana	satynarayana	PROPN
ejpam-6226	46	4	et	et	PROPN
ejpam-6226	46	5	al	al	PROPN
ejpam-6226	46	6	.	.	PUNCT
ejpam-6226	47	1	[	[	X
ejpam-6226	47	2	17	17	NUM
ejpam-6226	47	3	]	]	PUNCT
ejpam-6226	47	4	have	have	AUX
ejpam-6226	47	5	done	do	VERB
ejpam-6226	47	6	with	with	ADP
ejpam-6226	47	7	the	the	DET
ejpam-6226	47	8	concept	concept	NOUN
ejpam-6226	47	9	of	of	ADP
ejpam-6226	47	10	derivations	derivation	NOUN
ejpam-6226	47	11	of	of	ADP
ejpam-6226	47	12	intuitionistic	intuitionistic	ADJ
ejpam-6226	47	13	fuzzy	fuzzy	ADJ
ejpam-6226	47	14	implicative	implicative	PROPN
ejpam-6226	47	15	r.	r.	PROPN
ejpam-6226	47	16	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	47	17	et	et	PROPN
ejpam-6226	47	18	al	al	PROPN
ejpam-6226	47	19	.	.	PUNCT
ejpam-6226	47	20	/	/	SYM
ejpam-6226	47	21	eur	eur	PROPN
ejpam-6226	47	22	.	.	PUNCT
ejpam-6226	48	1	j.	j.	PROPN
ejpam-6226	48	2	pure	pure	PROPN
ejpam-6226	48	3	appl	appl	PROPN
ejpam-6226	48	4	.	.	PROPN
ejpam-6226	48	5	math	math	PROPN
ejpam-6226	48	6	,	,	PUNCT
ejpam-6226	48	7	18	18	NUM
ejpam-6226	48	8	(	(	PUNCT
ejpam-6226	48	9	3	3	NUM
ejpam-6226	48	10	)	)	PUNCT
ejpam-6226	48	11	(	(	PUNCT
ejpam-6226	48	12	2025	2025	NUM
ejpam-6226	48	13	)	)	PUNCT
ejpam-6226	48	14	,	,	PUNCT
ejpam-6226	48	15	6226	6226	NUM
ejpam-6226	48	16	3	3	NUM
ejpam-6226	48	17	of	of	ADP
ejpam-6226	48	18	19	19	NUM
ejpam-6226	48	19	ideals	ideal	NOUN
ejpam-6226	48	20	of	of	ADP
ejpam-6226	48	21	bck	bck	NOUN
ejpam-6226	48	22	-	-	PUNCT
ejpam-6226	48	23	algebras	algebras	PROPN
ejpam-6226	48	24	.	.	PUNCT
ejpam-6226	49	1	also	also	ADV
ejpam-6226	49	2	,	,	PUNCT
ejpam-6226	49	3	rasuli	rasuli	PROPN
ejpam-6226	49	4	[	[	X
ejpam-6226	49	5	18	18	NUM
ejpam-6226	49	6	]	]	PUNCT
ejpam-6226	49	7	has	have	AUX
ejpam-6226	49	8	worked	work	VERB
ejpam-6226	49	9	on	on	ADP
ejpam-6226	49	10	intuitionistic	intuitionistic	ADJ
ejpam-6226	49	11	fuzzy	fuzzy	ADJ
ejpam-6226	49	12	bci	bci	NOUN
ejpam-6226	49	13	-	-	PUNCT
ejpam-6226	49	14	algebras	algebras	X
ejpam-6226	49	15	(	(	PUNCT
ejpam-6226	49	16	implicative	implicative	ADJ
ejpam-6226	49	17	ideals	ideal	NOUN
ejpam-6226	49	18	,	,	PUNCT
ejpam-6226	49	19	closed	close	VERB
ejpam-6226	49	20	implicative	implicative	ADJ
ejpam-6226	49	21	ideals	ideal	NOUN
ejpam-6226	49	22	,	,	PUNCT
ejpam-6226	49	23	commutative	commutative	ADJ
ejpam-6226	49	24	ideals	ideal	NOUN
ejpam-6226	49	25	)	)	PUNCT
ejpam-6226	49	26	under	under	ADP
ejpam-6226	49	27	norms	norm	NOUN
ejpam-6226	49	28	.	.	PUNCT
ejpam-6226	50	1	later	later	ADV
ejpam-6226	50	2	,	,	PUNCT
ejpam-6226	50	3	the	the	DET
ejpam-6226	50	4	neutrosophic	neutrosophic	ADJ
ejpam-6226	50	5	sets	set	NOUN
ejpam-6226	50	6	(	(	PUNCT
ejpam-6226	50	7	nss	ns	NOUN
ejpam-6226	50	8	)	)	PUNCT
ejpam-6226	50	9	were	be	AUX
ejpam-6226	50	10	introduced	introduce	VERB
ejpam-6226	50	11	by	by	ADP
ejpam-6226	50	12	smarandache	smarandache	NOUN
ejpam-6226	50	13	[	[	X
ejpam-6226	50	14	19	19	NUM
ejpam-6226	50	15	]	]	PUNCT
ejpam-6226	50	16	in	in	ADP
ejpam-6226	50	17	1999	1999	NUM
ejpam-6226	50	18	,	,	PUNCT
ejpam-6226	50	19	which	which	PRON
ejpam-6226	50	20	is	be	AUX
ejpam-6226	50	21	the	the	DET
ejpam-6226	50	22	generalization	generalization	NOUN
ejpam-6226	50	23	of	of	ADP
ejpam-6226	50	24	classical	classical	ADJ
ejpam-6226	50	25	sets	set	NOUN
ejpam-6226	50	26	,	,	PUNCT
ejpam-6226	50	27	fss	fss	ADJ
ejpam-6226	50	28	,	,	PUNCT
ejpam-6226	50	29	and	and	CCONJ
ejpam-6226	50	30	ifss	ifss	NOUN
ejpam-6226	50	31	involving	involve	VERB
ejpam-6226	50	32	a	a	DET
ejpam-6226	50	33	new	new	ADJ
ejpam-6226	50	34	parameter	parameter	NOUN
ejpam-6226	50	35	called	call	VERB
ejpam-6226	50	36	indeterminacy	indeterminacy	NOUN
ejpam-6226	50	37	.	.	PUNCT
ejpam-6226	51	1	neutrosophic	neutrosophic	ADJ
ejpam-6226	51	2	sets	set	NOUN
ejpam-6226	51	3	are	be	AUX
ejpam-6226	51	4	particularly	particularly	ADV
ejpam-6226	51	5	useful	useful	ADJ
ejpam-6226	51	6	when	when	SCONJ
ejpam-6226	51	7	uncertainty	uncertainty	NOUN
ejpam-6226	51	8	exists	exist	VERB
ejpam-6226	51	9	and	and	CCONJ
ejpam-6226	51	10	the	the	DET
ejpam-6226	51	11	basic	basic	ADJ
ejpam-6226	51	12	components	component	NOUN
ejpam-6226	51	13	of	of	ADP
ejpam-6226	51	14	truth	truth	NOUN
ejpam-6226	51	15	,	,	PUNCT
ejpam-6226	51	16	falsehood	falsehood	NOUN
ejpam-6226	51	17	,	,	PUNCT
ejpam-6226	51	18	and	and	CCONJ
ejpam-6226	51	19	indeterminacy	indeterminacy	NOUN
ejpam-6226	51	20	are	be	AUX
ejpam-6226	51	21	simultaneously	simultaneously	ADV
ejpam-6226	51	22	considered	consider	VERB
ejpam-6226	51	23	.	.	PUNCT
ejpam-6226	52	1	nss	ns	NOUN
ejpam-6226	52	2	have	have	VERB
ejpam-6226	52	3	many	many	ADJ
ejpam-6226	52	4	approaches	approach	NOUN
ejpam-6226	52	5	in	in	ADP
ejpam-6226	52	6	many	many	ADJ
ejpam-6226	52	7	fields	field	NOUN
ejpam-6226	52	8	,	,	PUNCT
ejpam-6226	52	9	like	like	ADP
ejpam-6226	52	10	decision	decision	NOUN
ejpam-6226	52	11	-	-	PUNCT
ejpam-6226	52	12	making	making	NOUN
ejpam-6226	52	13	,	,	PUNCT
ejpam-6226	52	14	expert	expert	NOUN
ejpam-6226	52	15	systems	system	NOUN
ejpam-6226	52	16	,	,	PUNCT
ejpam-6226	52	17	image	image	NOUN
ejpam-6226	52	18	processing	processing	NOUN
ejpam-6226	52	19	,	,	PUNCT
ejpam-6226	52	20	and	and	CCONJ
ejpam-6226	52	21	fuzzy	fuzzy	ADJ
ejpam-6226	52	22	logic	logic	NOUN
ejpam-6226	52	23	,	,	PUNCT
ejpam-6226	52	24	thus	thus	ADV
ejpam-6226	52	25	enabling	enable	VERB
ejpam-6226	52	26	us	we	PRON
ejpam-6226	52	27	to	to	PART
ejpam-6226	52	28	do	do	VERB
ejpam-6226	52	29	effective	effective	ADJ
ejpam-6226	52	30	modeling	modeling	NOUN
ejpam-6226	52	31	and	and	CCONJ
ejpam-6226	52	32	analysis	analysis	NOUN
ejpam-6226	52	33	in	in	ADP
ejpam-6226	52	34	situations	situation	NOUN
ejpam-6226	52	35	where	where	SCONJ
ejpam-6226	52	36	the	the	DET
ejpam-6226	52	37	classical	classical	ADJ
ejpam-6226	52	38	set	set	NOUN
ejpam-6226	52	39	theory	theory	NOUN
ejpam-6226	52	40	falls	fall	VERB
ejpam-6226	52	41	short	short	ADJ
ejpam-6226	52	42	.	.	PUNCT
ejpam-6226	53	1	some	some	DET
ejpam-6226	53	2	authors	author	NOUN
ejpam-6226	53	3	,	,	PUNCT
ejpam-6226	53	4	jun	jun	PROPN
ejpam-6226	53	5	and	and	CCONJ
ejpam-6226	53	6	roh	roh	PROPN
ejpam-6226	54	1	[	[	X
ejpam-6226	54	2	20	20	NUM
ejpam-6226	54	3	]	]	PUNCT
ejpam-6226	54	4	have	have	AUX
ejpam-6226	54	5	discussed	discuss	VERB
ejpam-6226	54	6	a	a	DET
ejpam-6226	54	7	few	few	ADJ
ejpam-6226	54	8	results	result	NOUN
ejpam-6226	54	9	on	on	ADP
ejpam-6226	54	10	mbj	mbj	PROPN
ejpam-6226	54	11	-	-	PUNCT
ejpam-6226	54	12	neutrosophic	neutrosophic	ADJ
ejpam-6226	54	13	ideals	ideal	NOUN
ejpam-6226	54	14	of	of	ADP
ejpam-6226	54	15	bck	bck	PROPN
ejpam-6226	54	16	/	/	SYM
ejpam-6226	54	17	bci	bci	NOUN
ejpam-6226	54	18	-	-	PUNCT
ejpam-6226	54	19	algebras	algebras	PROPN
ejpam-6226	54	20	.	.	PUNCT
ejpam-6226	55	1	borzooei	borzooei	PROPN
ejpam-6226	55	2	et	et	PROPN
ejpam-6226	55	3	al	al	PROPN
ejpam-6226	55	4	.	.	PUNCT
ejpam-6226	56	1	[	[	X
ejpam-6226	56	2	21	21	NUM
ejpam-6226	56	3	]	]	PUNCT
ejpam-6226	56	4	have	have	AUX
ejpam-6226	56	5	worked	work	VERB
ejpam-6226	56	6	on	on	ADP
ejpam-6226	56	7	the	the	DET
ejpam-6226	56	8	concept	concept	NOUN
ejpam-6226	56	9	of	of	ADP
ejpam-6226	56	10	positive	positive	ADJ
ejpam-6226	56	11	implicative	implicative	ADJ
ejpam-6226	56	12	bmbj	bmbj	ADJ
ejpam-6226	56	13	-	-	PUNCT
ejpam-6226	56	14	neutrosophic	neutrosophic	ADJ
ejpam-6226	56	15	ideals	ideal	NOUN
ejpam-6226	56	16	in	in	ADP
ejpam-6226	56	17	bck	bck	NOUN
ejpam-6226	56	18	-	-	PUNCT
ejpam-6226	56	19	algebras	algebras	PROPN
ejpam-6226	56	20	.	.	PUNCT
ejpam-6226	57	1	bordbar	bordbar	PROPN
ejpam-6226	57	2	et	et	PROPN
ejpam-6226	57	3	al	al	PROPN
ejpam-6226	57	4	.	.	PUNCT
ejpam-6226	58	1	[	[	X
ejpam-6226	58	2	22	22	NUM
ejpam-6226	58	3	]	]	PUNCT
ejpam-6226	58	4	have	have	AUX
ejpam-6226	58	5	worked	work	VERB
ejpam-6226	58	6	on	on	ADP
ejpam-6226	58	7	the	the	DET
ejpam-6226	58	8	concept	concept	NOUN
ejpam-6226	58	9	of	of	ADP
ejpam-6226	58	10	positive	positive	ADJ
ejpam-6226	58	11	implicative	implicative	ADJ
ejpam-6226	58	12	ideals	ideal	NOUN
ejpam-6226	58	13	of	of	ADP
ejpam-6226	58	14	bck	bck	NOUN
ejpam-6226	58	15	-	-	PUNCT
ejpam-6226	58	16	algebras	algebras	PROPN
ejpam-6226	58	17	based	base	VERB
ejpam-6226	58	18	on	on	ADP
ejpam-6226	58	19	nss	nss	NOUN
ejpam-6226	58	20	and	and	CCONJ
ejpam-6226	58	21	falling	fall	VERB
ejpam-6226	58	22	shadows	shadow	NOUN
ejpam-6226	58	23	.	.	PUNCT
ejpam-6226	59	1	also	also	ADV
ejpam-6226	59	2	,	,	PUNCT
ejpam-6226	59	3	satyanarayana	satyanarayana	PROPN
ejpam-6226	59	4	and	and	CCONJ
ejpam-6226	59	5	baji	baji	PROPN
ejpam-6226	59	6	[	[	X
ejpam-6226	59	7	23	23	NUM
ejpam-6226	59	8	]	]	PUNCT
ejpam-6226	59	9	have	have	AUX
ejpam-6226	59	10	worked	work	VERB
ejpam-6226	59	11	on	on	ADP
ejpam-6226	59	12	positive	positive	ADJ
ejpam-6226	59	13	implicative	implicative	ADJ
ejpam-6226	59	14	,	,	PUNCT
ejpam-6226	59	15	implicative	implicative	ADJ
ejpam-6226	59	16	,	,	PUNCT
ejpam-6226	59	17	and	and	CCONJ
ejpam-6226	59	18	commutative	commutative	ADJ
ejpam-6226	59	19	sb	sb	PROPN
ejpam-6226	59	20	-	-	ADJ
ejpam-6226	59	21	neutrosophic	neutrosophic	ADJ
ejpam-6226	59	22	ideals	ideal	NOUN
ejpam-6226	59	23	in	in	ADP
ejpam-6226	59	24	bck	bck	PROPN
ejpam-6226	59	25	/	/	SYM
ejpam-6226	59	26	bci	bci	NOUN
ejpam-6226	59	27	-	-	PUNCT
ejpam-6226	59	28	algebras	algebras	X
ejpam-6226	59	29	.	.	PUNCT
ejpam-6226	60	1	this	this	DET
ejpam-6226	60	2	article	article	NOUN
ejpam-6226	60	3	aims	aim	VERB
ejpam-6226	60	4	to	to	PART
ejpam-6226	60	5	introduce	introduce	VERB
ejpam-6226	60	6	and	and	CCONJ
ejpam-6226	60	7	investigate	investigate	VERB
ejpam-6226	60	8	the	the	DET
ejpam-6226	60	9	notions	notion	NOUN
ejpam-6226	60	10	of	of	ADP
ejpam-6226	60	11	mink	mink	NOUN
ejpam-6226	60	12	-	-	PUNCT
ejpam-6226	60	13	is	be	AUX
ejpam-6226	60	14	and	and	CCONJ
ejpam-6226	60	15	pminkis	pminkis	ADJ
ejpam-6226	60	16	in	in	ADP
ejpam-6226	60	17	the	the	DET
ejpam-6226	60	18	framework	framework	NOUN
ejpam-6226	60	19	of	of	ADP
ejpam-6226	60	20	ink	ink	NOUN
ejpam-6226	60	21	-	-	PUNCT
ejpam-6226	60	22	algebras	algebras	PROPN
ejpam-6226	60	23	.	.	PUNCT
ejpam-6226	61	1	the	the	DET
ejpam-6226	61	2	study	study	NOUN
ejpam-6226	61	3	further	far	ADV
ejpam-6226	61	4	extends	extend	VERB
ejpam-6226	61	5	these	these	DET
ejpam-6226	61	6	notions	notion	NOUN
ejpam-6226	61	7	to	to	ADP
ejpam-6226	61	8	fuzzy	fuzzy	ADJ
ejpam-6226	61	9	and	and	CCONJ
ejpam-6226	61	10	neutrosophic	neutrosophic	ADJ
ejpam-6226	61	11	environments	environment	NOUN
ejpam-6226	61	12	,	,	PUNCT
ejpam-6226	61	13	resulting	result	VERB
ejpam-6226	61	14	in	in	ADP
ejpam-6226	61	15	the	the	DET
ejpam-6226	61	16	definitions	definition	NOUN
ejpam-6226	61	17	of	of	ADP
ejpam-6226	61	18	fmink	fmink	NOUN
ejpam-6226	61	19	-	-	PUNCT
ejpam-6226	61	20	is	be	AUX
ejpam-6226	61	21	,	,	PUNCT
ejpam-6226	61	22	fpmink	fpmink	NOUN
ejpam-6226	61	23	-	-	PUNCT
ejpam-6226	61	24	is	be	AUX
ejpam-6226	61	25	,	,	PUNCT
ejpam-6226	61	26	nmink	nmink	NOUN
ejpam-6226	61	27	-	-	PUNCT
ejpam-6226	61	28	is	be	AUX
ejpam-6226	61	29	,	,	PUNCT
ejpam-6226	61	30	and	and	CCONJ
ejpam-6226	61	31	npmink	npmink	NOUN
ejpam-6226	61	32	-	-	PUNCT
ejpam-6226	61	33	is	be	AUX
ejpam-6226	61	34	.	.	PUNCT
ejpam-6226	62	1	we	we	PRON
ejpam-6226	62	2	examine	examine	VERB
ejpam-6226	62	3	their	their	PRON
ejpam-6226	62	4	structural	structural	ADJ
ejpam-6226	62	5	properties	property	NOUN
ejpam-6226	62	6	,	,	PUNCT
ejpam-6226	62	7	including	include	VERB
ejpam-6226	62	8	closure	closure	NOUN
ejpam-6226	62	9	under	under	ADP
ejpam-6226	62	10	intersection	intersection	NOUN
ejpam-6226	62	11	and	and	CCONJ
ejpam-6226	62	12	behavior	behavior	NOUN
ejpam-6226	62	13	under	under	ADP
ejpam-6226	62	14	homomorphisms	homomorphism	NOUN
ejpam-6226	62	15	.	.	PUNCT
ejpam-6226	63	1	the	the	DET
ejpam-6226	63	2	results	result	NOUN
ejpam-6226	63	3	presented	present	VERB
ejpam-6226	63	4	herein	herein	NOUN
ejpam-6226	63	5	provide	provide	VERB
ejpam-6226	63	6	a	a	DET
ejpam-6226	63	7	comprehensive	comprehensive	ADJ
ejpam-6226	63	8	generalization	generalization	NOUN
ejpam-6226	63	9	of	of	ADP
ejpam-6226	63	10	ideal	ideal	ADJ
ejpam-6226	63	11	theory	theory	NOUN
ejpam-6226	63	12	within	within	ADP
ejpam-6226	63	13	ink	ink	NOUN
ejpam-6226	63	14	-	-	PUNCT
ejpam-6226	63	15	algebras	algebra	NOUN
ejpam-6226	63	16	and	and	CCONJ
ejpam-6226	63	17	contribute	contribute	VERB
ejpam-6226	63	18	to	to	ADP
ejpam-6226	63	19	the	the	DET
ejpam-6226	63	20	algebraic	algebraic	ADJ
ejpam-6226	63	21	modeling	modeling	NOUN
ejpam-6226	63	22	of	of	ADP
ejpam-6226	63	23	uncertainty	uncertainty	NOUN
ejpam-6226	63	24	and	and	CCONJ
ejpam-6226	63	25	indeterminacy	indeterminacy	NOUN
ejpam-6226	63	26	.	.	PUNCT
ejpam-6226	64	1	list	list	NOUN
ejpam-6226	64	2	of	of	ADP
ejpam-6226	64	3	abbreviations	abbreviation	NOUN
ejpam-6226	64	4	to	to	PART
ejpam-6226	64	5	facilitate	facilitate	VERB
ejpam-6226	64	6	the	the	DET
ejpam-6226	64	7	understanding	understanding	NOUN
ejpam-6226	64	8	of	of	ADP
ejpam-6226	64	9	frequently	frequently	ADV
ejpam-6226	64	10	used	use	VERB
ejpam-6226	64	11	terminology	terminology	NOUN
ejpam-6226	64	12	,	,	PUNCT
ejpam-6226	64	13	we	we	PRON
ejpam-6226	64	14	provide	provide	VERB
ejpam-6226	64	15	a	a	DET
ejpam-6226	64	16	list	list	NOUN
ejpam-6226	64	17	of	of	ADP
ejpam-6226	64	18	abbreviations	abbreviation	NOUN
ejpam-6226	64	19	employed	employ	VERB
ejpam-6226	64	20	throughout	throughout	ADP
ejpam-6226	64	21	the	the	DET
ejpam-6226	64	22	paper	paper	NOUN
ejpam-6226	64	23	.	.	PUNCT
ejpam-6226	65	1	abbreviation	abbreviation	NOUN
ejpam-6226	65	2	full	full	ADJ
ejpam-6226	65	3	term	term	NOUN
ejpam-6226	65	4	fs	fs	ADP
ejpam-6226	65	5	fuzzy	fuzzy	ADJ
ejpam-6226	65	6	set	set	VERB
ejpam-6226	65	7	ifs	ifs	PROPN
ejpam-6226	65	8	intuitionistic	intuitionistic	ADJ
ejpam-6226	65	9	fuzzy	fuzzy	ADJ
ejpam-6226	65	10	set	set	VERB
ejpam-6226	65	11	ns	ns	NUM
ejpam-6226	65	12	neutrosophic	neutrosophic	ADJ
ejpam-6226	65	13	set	set	VERB
ejpam-6226	65	14	mink	mink	NOUN
ejpam-6226	65	15	-	-	PUNCT
ejpam-6226	65	16	i	i	PROPN
ejpam-6226	65	17	implicative	implicative	ADJ
ejpam-6226	65	18	ink	ink	NOUN
ejpam-6226	65	19	-	-	PUNCT
ejpam-6226	65	20	ideal	ideal	NOUN
ejpam-6226	65	21	pmink	pmink	NOUN
ejpam-6226	65	22	-	-	PUNCT
ejpam-6226	65	23	i	i	PRON
ejpam-6226	65	24	positive	positive	ADJ
ejpam-6226	65	25	implicative	implicative	ADJ
ejpam-6226	65	26	ink	ink	NOUN
ejpam-6226	65	27	-	-	PUNCT
ejpam-6226	65	28	ideal	ideal	NOUN
ejpam-6226	65	29	fink	fink	NOUN
ejpam-6226	65	30	-	-	PUNCT
ejpam-6226	65	31	s	s	NOUN
ejpam-6226	65	32	fuzzy	fuzzy	ADJ
ejpam-6226	65	33	ink	ink	NOUN
ejpam-6226	65	34	-	-	PUNCT
ejpam-6226	65	35	subalgebra	subalgebra	NOUN
ejpam-6226	65	36	fink	fink	NOUN
ejpam-6226	65	37	-	-	PUNCT
ejpam-6226	65	38	i	i	PRON
ejpam-6226	65	39	fuzzy	fuzzy	ADJ
ejpam-6226	65	40	ink	ink	NOUN
ejpam-6226	65	41	-	-	PUNCT
ejpam-6226	65	42	ideal	ideal	NOUN
ejpam-6226	65	43	fmink	fmink	NOUN
ejpam-6226	65	44	-	-	PUNCT
ejpam-6226	65	45	i	i	PRON
ejpam-6226	65	46	fuzzy	fuzzy	ADJ
ejpam-6226	65	47	implicative	implicative	ADJ
ejpam-6226	65	48	ink	ink	NOUN
ejpam-6226	65	49	-	-	PUNCT
ejpam-6226	65	50	ideal	ideal	NOUN
ejpam-6226	65	51	fpmink	fpmink	NOUN
ejpam-6226	65	52	-	-	PUNCT
ejpam-6226	65	53	i	i	PRON
ejpam-6226	65	54	fuzzy	fuzzy	ADJ
ejpam-6226	65	55	positive	positive	ADJ
ejpam-6226	65	56	implicative	implicative	ADJ
ejpam-6226	65	57	ink	ink	NOUN
ejpam-6226	65	58	-	-	PUNCT
ejpam-6226	65	59	ideal	ideal	NOUN
ejpam-6226	65	60	nink	nink	NOUN
ejpam-6226	65	61	-	-	PUNCT
ejpam-6226	65	62	s	s	NOUN
ejpam-6226	65	63	neutrosophic	neutrosophic	ADJ
ejpam-6226	65	64	ink	ink	NOUN
ejpam-6226	65	65	-	-	PUNCT
ejpam-6226	65	66	subalgebra	subalgebra	NOUN
ejpam-6226	65	67	nink	nink	NOUN
ejpam-6226	65	68	-	-	PUNCT
ejpam-6226	65	69	i	i	PRON
ejpam-6226	65	70	neutrosophic	neutrosophic	ADJ
ejpam-6226	65	71	ink	ink	NOUN
ejpam-6226	65	72	-	-	PUNCT
ejpam-6226	65	73	ideal	ideal	NOUN
ejpam-6226	65	74	nmink	nmink	NOUN
ejpam-6226	65	75	-	-	PUNCT
ejpam-6226	65	76	i	i	PRON
ejpam-6226	65	77	neutrosophic	neutrosophic	ADJ
ejpam-6226	65	78	implicative	implicative	ADJ
ejpam-6226	65	79	ink	ink	NOUN
ejpam-6226	65	80	-	-	PUNCT
ejpam-6226	65	81	ideal	ideal	NOUN
ejpam-6226	65	82	npmink	npmink	NOUN
ejpam-6226	65	83	-	-	PUNCT
ejpam-6226	65	84	i	i	PRON
ejpam-6226	65	85	neutrosophic	neutrosophic	ADJ
ejpam-6226	65	86	positive	positive	ADJ
ejpam-6226	65	87	implicative	implicative	ADJ
ejpam-6226	65	88	ink	ink	NOUN
ejpam-6226	65	89	-	-	PUNCT
ejpam-6226	65	90	ideal	ideal	NOUN
ejpam-6226	65	91	table	table	NOUN
ejpam-6226	65	92	1	1	NUM
ejpam-6226	65	93	:	:	PUNCT
ejpam-6226	65	94	list	list	NOUN
ejpam-6226	65	95	of	of	ADP
ejpam-6226	65	96	abbreviations	abbreviation	NOUN
ejpam-6226	65	97	used	use	VERB
ejpam-6226	65	98	in	in	ADP
ejpam-6226	65	99	the	the	DET
ejpam-6226	65	100	paper	paper	NOUN
ejpam-6226	65	101	r.	r.	PROPN
ejpam-6226	65	102	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	65	103	et	et	PROPN
ejpam-6226	65	104	al	al	PROPN
ejpam-6226	65	105	.	.	PUNCT
ejpam-6226	65	106	/	/	SYM
ejpam-6226	65	107	eur	eur	PROPN
ejpam-6226	65	108	.	.	PUNCT
ejpam-6226	66	1	j.	j.	PROPN
ejpam-6226	66	2	pure	pure	PROPN
ejpam-6226	66	3	appl	appl	PROPN
ejpam-6226	66	4	.	.	PROPN
ejpam-6226	66	5	math	math	PROPN
ejpam-6226	66	6	,	,	PUNCT
ejpam-6226	66	7	18	18	NUM
ejpam-6226	66	8	(	(	PUNCT
ejpam-6226	66	9	3	3	NUM
ejpam-6226	66	10	)	)	PUNCT
ejpam-6226	66	11	(	(	PUNCT
ejpam-6226	66	12	2025	2025	NUM
ejpam-6226	66	13	)	)	PUNCT
ejpam-6226	66	14	,	,	PUNCT
ejpam-6226	66	15	6226	6226	NUM
ejpam-6226	66	16	4	4	NUM
ejpam-6226	66	17	of	of	ADP
ejpam-6226	66	18	19	19	NUM
ejpam-6226	66	19	2	2	NUM
ejpam-6226	66	20	.	.	PUNCT
ejpam-6226	66	21	preliminaries	preliminary	NOUN
ejpam-6226	66	22	in	in	ADP
ejpam-6226	66	23	this	this	DET
ejpam-6226	66	24	section	section	NOUN
ejpam-6226	67	1	,	,	PUNCT
ejpam-6226	67	2	we	we	PRON
ejpam-6226	67	3	present	present	VERB
ejpam-6226	67	4	some	some	DET
ejpam-6226	67	5	fundamental	fundamental	ADJ
ejpam-6226	67	6	definitions	definition	NOUN
ejpam-6226	67	7	and	and	CCONJ
ejpam-6226	67	8	properties	property	NOUN
ejpam-6226	67	9	that	that	PRON
ejpam-6226	67	10	are	be	AUX
ejpam-6226	67	11	essential	essential	ADJ
ejpam-6226	67	12	for	for	ADP
ejpam-6226	67	13	developing	develop	VERB
ejpam-6226	67	14	the	the	DET
ejpam-6226	67	15	main	main	ADJ
ejpam-6226	67	16	results	result	NOUN
ejpam-6226	67	17	of	of	ADP
ejpam-6226	67	18	this	this	DET
ejpam-6226	67	19	paper	paper	NOUN
ejpam-6226	67	20	.	.	PUNCT
ejpam-6226	68	1	these	these	PRON
ejpam-6226	68	2	include	include	VERB
ejpam-6226	68	3	the	the	DET
ejpam-6226	68	4	basic	basic	ADJ
ejpam-6226	68	5	structure	structure	NOUN
ejpam-6226	68	6	and	and	CCONJ
ejpam-6226	68	7	axioms	axiom	NOUN
ejpam-6226	68	8	of	of	ADP
ejpam-6226	68	9	ink	ink	NOUN
ejpam-6226	68	10	-	-	PUNCT
ejpam-6226	68	11	algebras	algebras	PROPN
ejpam-6226	68	12	,	,	PUNCT
ejpam-6226	68	13	the	the	DET
ejpam-6226	68	14	concepts	concept	NOUN
ejpam-6226	68	15	of	of	ADP
ejpam-6226	68	16	ink	ink	NOUN
ejpam-6226	68	17	-	-	PUNCT
ejpam-6226	68	18	subalgebras	subalgebras	PROPN
ejpam-6226	68	19	and	and	CCONJ
ejpam-6226	68	20	ink	ink	NOUN
ejpam-6226	68	21	-	-	PUNCT
ejpam-6226	68	22	ideals	ideal	NOUN
ejpam-6226	68	23	,	,	PUNCT
ejpam-6226	68	24	as	as	ADV
ejpam-6226	68	25	well	well	ADV
ejpam-6226	68	26	as	as	ADP
ejpam-6226	68	27	their	their	PRON
ejpam-6226	68	28	fuzzy	fuzzy	ADJ
ejpam-6226	68	29	and	and	CCONJ
ejpam-6226	68	30	neutrosophic	neutrosophic	ADJ
ejpam-6226	68	31	counterparts	counterpart	NOUN
ejpam-6226	68	32	.	.	PUNCT
ejpam-6226	69	1	the	the	DET
ejpam-6226	69	2	definitions	definition	NOUN
ejpam-6226	69	3	and	and	CCONJ
ejpam-6226	69	4	notations	notation	NOUN
ejpam-6226	69	5	introduced	introduce	VERB
ejpam-6226	69	6	herein	herein	NOUN
ejpam-6226	69	7	will	will	AUX
ejpam-6226	69	8	form	form	VERB
ejpam-6226	69	9	the	the	DET
ejpam-6226	69	10	groundwork	groundwork	NOUN
ejpam-6226	69	11	for	for	ADP
ejpam-6226	69	12	the	the	DET
ejpam-6226	69	13	subsequent	subsequent	ADJ
ejpam-6226	69	14	sections	section	NOUN
ejpam-6226	69	15	,	,	PUNCT
ejpam-6226	69	16	where	where	SCONJ
ejpam-6226	69	17	we	we	PRON
ejpam-6226	69	18	extend	extend	VERB
ejpam-6226	69	19	the	the	DET
ejpam-6226	69	20	notions	notion	NOUN
ejpam-6226	69	21	of	of	ADP
ejpam-6226	69	22	implicative	implicative	ADJ
ejpam-6226	69	23	ink	ink	NOUN
ejpam-6226	69	24	-	-	PUNCT
ejpam-6226	69	25	ideals	ideal	NOUN
ejpam-6226	69	26	(	(	PUNCT
ejpam-6226	69	27	mink	mink	NOUN
ejpam-6226	69	28	-	-	PUNCT
ejpam-6226	69	29	is	be	AUX
ejpam-6226	69	30	)	)	PUNCT
ejpam-6226	69	31	and	and	CCONJ
ejpam-6226	69	32	positive	positive	ADJ
ejpam-6226	69	33	implicative	implicative	ADJ
ejpam-6226	69	34	ink	ink	NOUN
ejpam-6226	69	35	-	-	PUNCT
ejpam-6226	69	36	ideals	ideal	NOUN
ejpam-6226	69	37	(	(	PUNCT
ejpam-6226	69	38	pmink	pmink	NOUN
ejpam-6226	69	39	-	-	PUNCT
ejpam-6226	69	40	is	be	AUX
ejpam-6226	69	41	)	)	PUNCT
ejpam-6226	69	42	within	within	ADP
ejpam-6226	69	43	fuzzy	fuzzy	ADJ
ejpam-6226	69	44	and	and	CCONJ
ejpam-6226	69	45	neutrosophic	neutrosophic	ADJ
ejpam-6226	69	46	frameworks	framework	NOUN
ejpam-6226	69	47	.	.	PUNCT
ejpam-6226	70	1	definition	definition	NOUN
ejpam-6226	70	2	1	1	NUM
ejpam-6226	70	3	.	.	PUNCT
ejpam-6226	71	1	[	[	X
ejpam-6226	71	2	24	24	NUM
ejpam-6226	71	3	]	]	PUNCT
ejpam-6226	71	4	an	an	DET
ejpam-6226	71	5	algebra	algebra	NOUN
ejpam-6226	71	6	(	(	PUNCT
ejpam-6226	71	7	i	i	PROPN
ejpam-6226	71	8	,	,	PUNCT
ejpam-6226	71	9	•	•	PROPN
ejpam-6226	71	10	,	,	PUNCT
ejpam-6226	71	11	0	0	NUM
ejpam-6226	71	12	)	)	PUNCT
ejpam-6226	71	13	is	be	AUX
ejpam-6226	71	14	termed	term	VERB
ejpam-6226	71	15	to	to	PART
ejpam-6226	71	16	be	be	AUX
ejpam-6226	71	17	an	an	DET
ejpam-6226	71	18	ink	ink	NOUN
ejpam-6226	71	19	-	-	PUNCT
ejpam-6226	71	20	algebra	algebra	NOUN
ejpam-6226	71	21	where	where	SCONJ
ejpam-6226	71	22	•	•	NOUN
ejpam-6226	71	23	is	be	AUX
ejpam-6226	71	24	a	a	DET
ejpam-6226	71	25	binary	binary	NOUN
ejpam-6226	71	26	and	and	CCONJ
ejpam-6226	72	1	the	the	DET
ejpam-6226	72	2	0	0	NUM
ejpam-6226	72	3	is	be	AUX
ejpam-6226	72	4	a	a	DET
ejpam-6226	72	5	constant	constant	NOUN
ejpam-6226	72	6	of	of	ADP
ejpam-6226	72	7	i	i	PRON
ejpam-6226	72	8	if	if	SCONJ
ejpam-6226	72	9	it	it	PRON
ejpam-6226	72	10	gratifies	gratify	VERB
ejpam-6226	72	11	the	the	DET
ejpam-6226	72	12	following	following	ADJ
ejpam-6226	72	13	conditions	condition	NOUN
ejpam-6226	72	14	:	:	PUNCT
ejpam-6226	72	15	ink-1	ink-1	NUM
ejpam-6226	72	16	:	:	PUNCT
ejpam-6226	72	17	(	(	PUNCT
ejpam-6226	72	18	(	(	PUNCT
ejpam-6226	72	19	ϵ	ϵ	PART
ejpam-6226	72	20	•	•	NUM
ejpam-6226	72	21	ξ	ξ	NOUN
ejpam-6226	72	22	)	)	PUNCT
ejpam-6226	72	23	•	•	NOUN
ejpam-6226	72	24	(	(	PUNCT
ejpam-6226	72	25	ϵ	ϵ	NOUN
ejpam-6226	72	26	•	•	NUM
ejpam-6226	72	27	ς	ς	PROPN
ejpam-6226	72	28	)	)	PUNCT
ejpam-6226	72	29	)	)	PUNCT
ejpam-6226	73	1	•	•	X
ejpam-6226	73	2	(	(	PUNCT
ejpam-6226	73	3	ς	ς	PROPN
ejpam-6226	73	4	•	•	NUM
ejpam-6226	73	5	ξ	ξ	NOUN
ejpam-6226	73	6	)	)	PUNCT
ejpam-6226	73	7	=	=	SYM
ejpam-6226	73	8	0	0	NUM
ejpam-6226	73	9	ink-2	ink-2	NOUN
ejpam-6226	73	10	:	:	PUNCT
ejpam-6226	73	11	(	(	PUNCT
ejpam-6226	73	12	(	(	PUNCT
ejpam-6226	73	13	ϵ	ϵ	PART
ejpam-6226	73	14	•	•	NUM
ejpam-6226	73	15	ς	ς	PROPN
ejpam-6226	73	16	)	)	PUNCT
ejpam-6226	73	17	•	•	NOUN
ejpam-6226	73	18	(	(	PUNCT
ejpam-6226	73	19	ξ	ξ	PROPN
ejpam-6226	73	20	•	•	NUM
ejpam-6226	73	21	ς	ς	NOUN
ejpam-6226	73	22	)	)	PUNCT
ejpam-6226	73	23	)	)	PUNCT
ejpam-6226	74	1	•	•	X
ejpam-6226	74	2	(	(	PUNCT
ejpam-6226	74	3	ϵ	ϵ	NOUN
ejpam-6226	74	4	•	•	NUM
ejpam-6226	74	5	ξ	ξ	NOUN
ejpam-6226	74	6	)	)	PUNCT
ejpam-6226	74	7	=	=	SYM
ejpam-6226	74	8	0	0	NUM
ejpam-6226	74	9	ink-3	ink-3	NOUN
ejpam-6226	74	10	:	:	PUNCT
ejpam-6226	74	11	ϵ	ϵ	X
ejpam-6226	74	12	•	•	NOUN
ejpam-6226	74	13	0	0	NUM
ejpam-6226	74	14	=	=	SYM
ejpam-6226	75	1	ϵ	ϵ	PRON
ejpam-6226	75	2	ink-4	ink-4	VERB
ejpam-6226	75	3	:	:	PUNCT
ejpam-6226	75	4	ϵ	ϵ	X
ejpam-6226	75	5	•	•	SYM
ejpam-6226	75	6	ξ	ξ	X
ejpam-6226	75	7	=	=	SYM
ejpam-6226	75	8	0	0	NUM
ejpam-6226	75	9	,	,	PUNCT
ejpam-6226	75	10	ξ	ξ	PROPN
ejpam-6226	75	11	•	•	NOUN
ejpam-6226	75	12	ϵ	ϵ	X
ejpam-6226	75	13	=	=	SYM
ejpam-6226	75	14	0	0	NUM
ejpam-6226	75	15	⇒	⇒	NOUN
ejpam-6226	75	16	ϵ	ϵ	X
ejpam-6226	75	17	=	=	SYM
ejpam-6226	75	18	ξ,∀ϵ	ξ,∀ϵ	PROPN
ejpam-6226	75	19	,	,	PUNCT
ejpam-6226	75	20	ξ	ξ	PROPN
ejpam-6226	75	21	,	,	PUNCT
ejpam-6226	75	22	ς	ς	PROPN
ejpam-6226	75	23	∈	∈	PROPN
ejpam-6226	75	24	i.	i.	NOUN
ejpam-6226	75	25	definition	definition	NOUN
ejpam-6226	75	26	2	2	NUM
ejpam-6226	75	27	.	.	PUNCT
ejpam-6226	76	1	[	[	X
ejpam-6226	76	2	24	24	NUM
ejpam-6226	76	3	]	]	PUNCT
ejpam-6226	76	4	let	let	VERB
ejpam-6226	76	5	s	s	PRON
ejpam-6226	76	6	be	be	AUX
ejpam-6226	76	7	a	a	DET
ejpam-6226	76	8	non	non	ADJ
ejpam-6226	76	9	-	-	ADJ
ejpam-6226	76	10	empty	empty	ADJ
ejpam-6226	76	11	subset	subset	NOUN
ejpam-6226	76	12	of	of	ADP
ejpam-6226	76	13	an	an	DET
ejpam-6226	76	14	ink	ink	NOUN
ejpam-6226	76	15	-	-	PUNCT
ejpam-6226	76	16	algebra	algebra	NOUN
ejpam-6226	76	17	i.	i.	NOUN
ejpam-6226	76	18	then	then	ADV
ejpam-6226	76	19	s	s	VERB
ejpam-6226	76	20	is	be	AUX
ejpam-6226	76	21	termed	term	VERB
ejpam-6226	76	22	to	to	PART
ejpam-6226	76	23	be	be	AUX
ejpam-6226	76	24	an	an	DET
ejpam-6226	76	25	ink	ink	NOUN
ejpam-6226	76	26	-	-	PUNCT
ejpam-6226	76	27	subalgebra	subalgebra	NOUN
ejpam-6226	76	28	of	of	ADP
ejpam-6226	76	29	i	i	PRON
ejpam-6226	76	30	if	if	SCONJ
ejpam-6226	76	31	ϵ	ϵ	PROPN
ejpam-6226	76	32	•	•	NUM
ejpam-6226	76	33	ξ	ξ	X
ejpam-6226	76	34	∈	∈	PROPN
ejpam-6226	76	35	s,∀ϵ	s,∀ϵ	NOUN
ejpam-6226	76	36	,	,	PUNCT
ejpam-6226	76	37	ξ	ξ	PROPN
ejpam-6226	76	38	∈	∈	PROPN
ejpam-6226	76	39	s.	s.	PROPN
ejpam-6226	76	40	definition	definition	NOUN
ejpam-6226	76	41	3	3	NUM
ejpam-6226	76	42	.	.	PUNCT
ejpam-6226	77	1	[	[	X
ejpam-6226	77	2	24	24	NUM
ejpam-6226	77	3	]	]	PUNCT
ejpam-6226	77	4	let	let	VERB
ejpam-6226	77	5	s	s	PRON
ejpam-6226	77	6	be	be	AUX
ejpam-6226	77	7	a	a	DET
ejpam-6226	77	8	non	non	ADJ
ejpam-6226	77	9	-	-	ADJ
ejpam-6226	77	10	empty	empty	ADJ
ejpam-6226	77	11	subset	subset	NOUN
ejpam-6226	77	12	of	of	ADP
ejpam-6226	77	13	an	an	DET
ejpam-6226	77	14	ink	ink	NOUN
ejpam-6226	77	15	-	-	PUNCT
ejpam-6226	77	16	algebra	algebra	NOUN
ejpam-6226	77	17	i.	i.	NOUN
ejpam-6226	77	18	then	then	ADV
ejpam-6226	77	19	s	s	VERB
ejpam-6226	77	20	is	be	AUX
ejpam-6226	77	21	entitled	entitle	VERB
ejpam-6226	77	22	as	as	ADP
ejpam-6226	77	23	ink	ink	NOUN
ejpam-6226	77	24	-	-	PUNCT
ejpam-6226	77	25	ideal	ideal	NOUN
ejpam-6226	77	26	of	of	ADP
ejpam-6226	77	27	i	i	PRON
ejpam-6226	77	28	if	if	SCONJ
ejpam-6226	77	29	(	(	PUNCT
ejpam-6226	77	30	b1	b1	NOUN
ejpam-6226	77	31	)	)	PUNCT
ejpam-6226	77	32	0	0	PUNCT
ejpam-6226	78	1	∈	∈	NOUN
ejpam-6226	78	2	s	s	PART
ejpam-6226	78	3	(	(	PUNCT
ejpam-6226	78	4	b2	b2	NOUN
ejpam-6226	78	5	)	)	PUNCT
ejpam-6226	78	6	(	(	PUNCT
ejpam-6226	78	7	ς	ς	PROPN
ejpam-6226	78	8	•	•	NUM
ejpam-6226	78	9	ϵ	ϵ	NOUN
ejpam-6226	78	10	)	)	PUNCT
ejpam-6226	78	11	•	•	NOUN
ejpam-6226	78	12	(	(	PUNCT
ejpam-6226	78	13	ς	ς	PROPN
ejpam-6226	78	14	•	•	NUM
ejpam-6226	78	15	ξ	ξ	NOUN
ejpam-6226	78	16	)	)	PUNCT
ejpam-6226	78	17	∈	∈	PROPN
ejpam-6226	78	18	s	s	PROPN
ejpam-6226	78	19	,	,	PUNCT
ejpam-6226	78	20	ξ	ξ	PROPN
ejpam-6226	78	21	∈	∈	PROPN
ejpam-6226	78	22	s	s	PART
ejpam-6226	78	23	⇒	⇒	NOUN
ejpam-6226	78	24	ϵ	ϵ	X
ejpam-6226	78	25	∈	∈	PROPN
ejpam-6226	79	1	s,∀ϵ	s,∀ϵ	PROPN
ejpam-6226	79	2	,	,	PUNCT
ejpam-6226	79	3	ξ	ξ	PROPN
ejpam-6226	79	4	,	,	PUNCT
ejpam-6226	79	5	ς	ς	PROPN
ejpam-6226	79	6	∈	∈	PROPN
ejpam-6226	79	7	i.	i.	NOUN
ejpam-6226	79	8	definition	definition	NOUN
ejpam-6226	79	9	4	4	NUM
ejpam-6226	79	10	.	.	PUNCT
ejpam-6226	80	1	[	[	X
ejpam-6226	80	2	24	24	NUM
ejpam-6226	80	3	]	]	PUNCT
ejpam-6226	80	4	let	let	VERB
ejpam-6226	80	5	i	i	PRON
ejpam-6226	80	6	be	be	AUX
ejpam-6226	80	7	an	an	DET
ejpam-6226	80	8	ink	ink	NOUN
ejpam-6226	80	9	-	-	PUNCT
ejpam-6226	80	10	algebra	algebra	NOUN
ejpam-6226	80	11	with	with	ADP
ejpam-6226	80	12	binary	binary	ADJ
ejpam-6226	80	13	operation	operation	NOUN
ejpam-6226	80	14	•	•	NOUN
ejpam-6226	80	15	and	and	CCONJ
ejpam-6226	80	16	constant	constant	ADJ
ejpam-6226	80	17	element	element	NOUN
ejpam-6226	80	18	0	0	NUM
ejpam-6226	80	19	.	.	PUNCT
ejpam-6226	81	1	for	for	ADP
ejpam-6226	81	2	any	any	DET
ejpam-6226	81	3	ϵ	ϵ	NOUN
ejpam-6226	81	4	,	,	PUNCT
ejpam-6226	81	5	ξ	ξ	PROPN
ejpam-6226	81	6	∈	∈	PROPN
ejpam-6226	81	7	i	i	PRON
ejpam-6226	81	8	,	,	PUNCT
ejpam-6226	81	9	we	we	PRON
ejpam-6226	81	10	define	define	VERB
ejpam-6226	81	11	the	the	DET
ejpam-6226	81	12	partial	partial	ADJ
ejpam-6226	81	13	order	order	NOUN
ejpam-6226	81	14	relation	relation	NOUN
ejpam-6226	81	15	≤	≤	NOUN
ejpam-6226	81	16	as	as	SCONJ
ejpam-6226	81	17	follows	follow	VERB
ejpam-6226	81	18	:	:	PUNCT
ejpam-6226	81	19	ϵ	ϵ	X
ejpam-6226	81	20	≤	≤	PROPN
ejpam-6226	81	21	ξ	ξ	PUNCT
ejpam-6226	81	22	⇔	⇔	X
ejpam-6226	81	23	ϵ	ϵ	PROPN
ejpam-6226	81	24	•	•	NUM
ejpam-6226	81	25	ξ	ξ	X
ejpam-6226	81	26	=	=	SYM
ejpam-6226	81	27	0	0	X
ejpam-6226	81	28	.	.	PUNCT
ejpam-6226	81	29	theorem	theorem	NOUN
ejpam-6226	81	30	1	1	NUM
ejpam-6226	81	31	.	.	PUNCT
ejpam-6226	82	1	every	every	DET
ejpam-6226	82	2	ink	ink	NOUN
ejpam-6226	82	3	-	-	PUNCT
ejpam-6226	82	4	ideal	ideal	NOUN
ejpam-6226	82	5	s	s	NOUN
ejpam-6226	82	6	of	of	ADP
ejpam-6226	82	7	an	an	DET
ejpam-6226	82	8	ink	ink	NOUN
ejpam-6226	82	9	-	-	PUNCT
ejpam-6226	82	10	algebra	algebra	NOUN
ejpam-6226	82	11	i	i	PRON
ejpam-6226	82	12	has	have	VERB
ejpam-6226	82	13	the	the	DET
ejpam-6226	82	14	following	follow	VERB
ejpam-6226	82	15	assertion	assertion	NOUN
ejpam-6226	82	16	:	:	PUNCT
ejpam-6226	82	17	ϵ	ϵ	X
ejpam-6226	82	18	≤	≤	NOUN
ejpam-6226	82	19	ξ	ξ	PRON
ejpam-6226	82	20	⇒	⇒	NOUN
ejpam-6226	83	1	ϵ	ϵ	X
ejpam-6226	83	2	∈	∈	PROPN
ejpam-6226	83	3	s,∀ϵ	s,∀ϵ	PROPN
ejpam-6226	84	1	∈	∈	PROPN
ejpam-6226	85	1	i	i	PRON
ejpam-6226	85	2	,	,	PUNCT
ejpam-6226	85	3	ξ	ξ	PROPN
ejpam-6226	85	4	∈	∈	PROPN
ejpam-6226	85	5	s.	s.	PROPN
ejpam-6226	85	6	proof	proof	PROPN
ejpam-6226	85	7	.	.	PUNCT
ejpam-6226	86	1	it	it	PRON
ejpam-6226	86	2	is	be	AUX
ejpam-6226	86	3	obtained	obtain	VERB
ejpam-6226	86	4	immediately	immediately	ADV
ejpam-6226	86	5	from	from	ADP
ejpam-6226	86	6	definition	definition	NOUN
ejpam-6226	86	7	3	3	NUM
ejpam-6226	86	8	by	by	ADP
ejpam-6226	86	9	replacing	replace	VERB
ejpam-6226	86	10	ς	ς	PROPN
ejpam-6226	86	11	with	with	ADP
ejpam-6226	86	12	0	0	NUM
ejpam-6226	86	13	.	.	PUNCT
ejpam-6226	87	1	definition	definition	NOUN
ejpam-6226	87	2	5	5	NUM
ejpam-6226	87	3	.	.	PUNCT
ejpam-6226	88	1	[	[	X
ejpam-6226	88	2	25	25	NUM
ejpam-6226	88	3	]	]	PUNCT
ejpam-6226	88	4	an	an	DET
ejpam-6226	88	5	fs	fs	NOUN
ejpam-6226	88	6	g	g	NOUN
ejpam-6226	88	7	in	in	ADP
ejpam-6226	88	8	an	an	DET
ejpam-6226	88	9	ink	ink	NOUN
ejpam-6226	88	10	-	-	PUNCT
ejpam-6226	88	11	algebra	algebra	NOUN
ejpam-6226	88	12	i	i	PRON
ejpam-6226	88	13	is	be	AUX
ejpam-6226	88	14	entitled	entitle	VERB
ejpam-6226	88	15	as	as	ADP
ejpam-6226	88	16	a	a	DET
ejpam-6226	88	17	fuzzy	fuzzy	ADJ
ejpam-6226	88	18	ink	ink	NOUN
ejpam-6226	88	19	-	-	PUNCT
ejpam-6226	88	20	subalgebra	subalgebra	NOUN
ejpam-6226	88	21	(	(	PUNCT
ejpam-6226	88	22	fink	fink	NOUN
ejpam-6226	88	23	-	-	PUNCT
ejpam-6226	88	24	s	s	NOUN
ejpam-6226	88	25	)	)	PUNCT
ejpam-6226	88	26	of	of	ADP
ejpam-6226	88	27	i	i	PRON
ejpam-6226	88	28	if	if	SCONJ
ejpam-6226	88	29	g(ϵ	g(ϵ	PROPN
ejpam-6226	88	30	•	•	NUM
ejpam-6226	88	31	ξ	ξ	NOUN
ejpam-6226	88	32	)	)	PUNCT
ejpam-6226	88	33	≥	≥	NOUN
ejpam-6226	88	34	min{g(ϵ	min{g(ϵ	PROPN
ejpam-6226	88	35	)	)	PUNCT
ejpam-6226	88	36	,	,	PUNCT
ejpam-6226	88	37	g(ξ)},∀ϵ	g(ξ)},∀ϵ	PROPN
ejpam-6226	88	38	,	,	PUNCT
ejpam-6226	88	39	ξ	ξ	PROPN
ejpam-6226	88	40	∈	∈	PROPN
ejpam-6226	88	41	i.	i.	NOUN
ejpam-6226	88	42	definition	definition	NOUN
ejpam-6226	88	43	6	6	NUM
ejpam-6226	88	44	.	.	PUNCT
ejpam-6226	89	1	[	[	X
ejpam-6226	89	2	9	9	NUM
ejpam-6226	89	3	]	]	PUNCT
ejpam-6226	89	4	let	let	VERB
ejpam-6226	89	5	g	g	NOUN
ejpam-6226	89	6	and	and	CCONJ
ejpam-6226	89	7	h	h	NOUN
ejpam-6226	89	8	be	be	AUX
ejpam-6226	89	9	fss	fss	ADJ
ejpam-6226	89	10	of	of	ADP
ejpam-6226	89	11	an	an	DET
ejpam-6226	89	12	ink	ink	NOUN
ejpam-6226	89	13	-	-	PUNCT
ejpam-6226	89	14	algebra	algebra	NOUN
ejpam-6226	89	15	(	(	PUNCT
ejpam-6226	89	16	i	i	PROPN
ejpam-6226	89	17	,	,	PUNCT
ejpam-6226	89	18	•	•	PROPN
ejpam-6226	89	19	,	,	PUNCT
ejpam-6226	89	20	0	0	NUM
ejpam-6226	89	21	)	)	PUNCT
ejpam-6226	89	22	.	.	PUNCT
ejpam-6226	90	1	then	then	ADV
ejpam-6226	90	2	the	the	DET
ejpam-6226	90	3	direct	direct	ADJ
ejpam-6226	90	4	product	product	NOUN
ejpam-6226	90	5	of	of	ADP
ejpam-6226	90	6	g	g	PROPN
ejpam-6226	90	7	×	×	PROPN
ejpam-6226	90	8	h	h	NOUN
ejpam-6226	90	9	:	:	PUNCT
ejpam-6226	90	10	i	i	PRON
ejpam-6226	90	11	×	×	VERB
ejpam-6226	90	12	i	i	INTJ
ejpam-6226	90	13	→	→	PUNCT
ejpam-6226	91	1	[	[	X
ejpam-6226	91	2	0	0	NUM
ejpam-6226	91	3	,	,	PUNCT
ejpam-6226	91	4	1	1	NUM
ejpam-6226	91	5	]	]	PUNCT
ejpam-6226	91	6	is	be	AUX
ejpam-6226	91	7	well	well	ADV
ejpam-6226	91	8	entitled	entitle	VERB
ejpam-6226	91	9	as	as	ADP
ejpam-6226	91	10	(	(	PUNCT
ejpam-6226	91	11	g	g	PROPN
ejpam-6226	91	12	×	×	NOUN
ejpam-6226	91	13	h)(ϵ	h)(ϵ	ADP
ejpam-6226	91	14	,	,	PUNCT
ejpam-6226	91	15	ξ	ξ	NOUN
ejpam-6226	91	16	)	)	PUNCT
ejpam-6226	91	17	=	=	SYM
ejpam-6226	91	18	min{g(ϵ	min{g(ϵ	PROPN
ejpam-6226	91	19	)	)	PUNCT
ejpam-6226	91	20	,	,	PUNCT
ejpam-6226	91	21	h(ξ	h(ξ	PROPN
ejpam-6226	91	22	)	)	PUNCT
ejpam-6226	91	23	}	}	PUNCT
ejpam-6226	91	24	,	,	PUNCT
ejpam-6226	91	25	∀ϵ	∀ϵ	PROPN
ejpam-6226	91	26	,	,	PUNCT
ejpam-6226	91	27	ξ	ξ	PROPN
ejpam-6226	91	28	∈	∈	PROPN
ejpam-6226	91	29	i.	i.	NOUN
ejpam-6226	91	30	definition	definition	NOUN
ejpam-6226	91	31	7	7	NUM
ejpam-6226	91	32	.	.	PUNCT
ejpam-6226	92	1	[	[	X
ejpam-6226	92	2	25	25	NUM
ejpam-6226	92	3	]	]	PUNCT
ejpam-6226	92	4	let	let	VERB
ejpam-6226	92	5	an	an	DET
ejpam-6226	92	6	fs	fs	ADP
ejpam-6226	92	7	g	g	NOUN
ejpam-6226	92	8	in	in	ADP
ejpam-6226	92	9	an	an	DET
ejpam-6226	92	10	ink	ink	NOUN
ejpam-6226	92	11	-	-	PUNCT
ejpam-6226	92	12	algebra	algebra	NOUN
ejpam-6226	92	13	i	i	PRON
ejpam-6226	92	14	is	be	AUX
ejpam-6226	92	15	known	know	VERB
ejpam-6226	92	16	as	as	ADP
ejpam-6226	92	17	a	a	DET
ejpam-6226	92	18	fuzzy	fuzzy	ADJ
ejpam-6226	92	19	ink	ink	NOUN
ejpam-6226	92	20	-	-	PUNCT
ejpam-6226	92	21	ideal	ideal	NOUN
ejpam-6226	92	22	(	(	PUNCT
ejpam-6226	92	23	fink	fink	NOUN
ejpam-6226	92	24	-	-	PUNCT
ejpam-6226	92	25	i	i	PROPN
ejpam-6226	92	26	)	)	PUNCT
ejpam-6226	92	27	of	of	ADP
ejpam-6226	92	28	i	i	PRON
ejpam-6226	92	29	if	if	SCONJ
ejpam-6226	92	30	it	it	PRON
ejpam-6226	92	31	gratifies	gratify	VERB
ejpam-6226	92	32	(	(	PUNCT
ejpam-6226	92	33	c1	c1	NOUN
ejpam-6226	92	34	)	)	PUNCT
ejpam-6226	92	35	g(0	g(0	PROPN
ejpam-6226	92	36	)	)	PUNCT
ejpam-6226	92	37	≥	≥	NOUN
ejpam-6226	92	38	g(ϵ	g(ϵ	PROPN
ejpam-6226	92	39	)	)	PUNCT
ejpam-6226	92	40	(	(	PUNCT
ejpam-6226	92	41	c2	c2	PROPN
ejpam-6226	92	42	)	)	PUNCT
ejpam-6226	92	43	g(ϵ	g(ϵ	PROPN
ejpam-6226	92	44	)	)	PUNCT
ejpam-6226	92	45	≥	≥	NOUN
ejpam-6226	92	46	min{g(ϵ	min{g(ϵ	VERB
ejpam-6226	92	47	•	•	NUM
ejpam-6226	92	48	ξ	ξ	NOUN
ejpam-6226	92	49	)	)	PUNCT
ejpam-6226	92	50	,	,	PUNCT
ejpam-6226	92	51	g(ξ	g(ξ	PROPN
ejpam-6226	92	52	)	)	PUNCT
ejpam-6226	92	53	}	}	PUNCT
ejpam-6226	92	54	,	,	PUNCT
ejpam-6226	92	55	∀ϵ	∀ϵ	PROPN
ejpam-6226	92	56	,	,	PUNCT
ejpam-6226	92	57	ξ	ξ	PROPN
ejpam-6226	92	58	∈	∈	PROPN
ejpam-6226	92	59	i.	i.	PROPN
ejpam-6226	92	60	r.	r.	PROPN
ejpam-6226	92	61	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	93	1	et	et	PROPN
ejpam-6226	93	2	al	al	PROPN
ejpam-6226	93	3	.	.	PUNCT
ejpam-6226	93	4	/	/	SYM
ejpam-6226	93	5	eur	eur	PROPN
ejpam-6226	93	6	.	.	PUNCT
ejpam-6226	94	1	j.	j.	PROPN
ejpam-6226	94	2	pure	pure	PROPN
ejpam-6226	94	3	appl	appl	PROPN
ejpam-6226	94	4	.	.	PROPN
ejpam-6226	94	5	math	math	PROPN
ejpam-6226	94	6	,	,	PUNCT
ejpam-6226	94	7	18	18	NUM
ejpam-6226	94	8	(	(	PUNCT
ejpam-6226	94	9	3	3	NUM
ejpam-6226	94	10	)	)	PUNCT
ejpam-6226	94	11	(	(	PUNCT
ejpam-6226	94	12	2025	2025	NUM
ejpam-6226	94	13	)	)	PUNCT
ejpam-6226	94	14	,	,	PUNCT
ejpam-6226	94	15	6226	6226	NUM
ejpam-6226	94	16	5	5	NUM
ejpam-6226	94	17	of	of	ADP
ejpam-6226	94	18	19	19	NUM
ejpam-6226	94	19	definition	definition	NOUN
ejpam-6226	94	20	8	8	NUM
ejpam-6226	94	21	.	.	PUNCT
ejpam-6226	95	1	[	[	X
ejpam-6226	95	2	26	26	NUM
ejpam-6226	95	3	]	]	PUNCT
ejpam-6226	95	4	an	an	DET
ejpam-6226	95	5	ns	ns	NOUN
ejpam-6226	95	6	g	g	NOUN
ejpam-6226	95	7	=	=	PUNCT
ejpam-6226	95	8	(	(	PUNCT
ejpam-6226	95	9	gt	gt	INTJ
ejpam-6226	95	10	,	,	PUNCT
ejpam-6226	95	11	gi	gi	INTJ
ejpam-6226	95	12	,	,	PUNCT
ejpam-6226	95	13	gf	gf	NOUN
ejpam-6226	95	14	)	)	PUNCT
ejpam-6226	95	15	in	in	ADP
ejpam-6226	95	16	an	an	DET
ejpam-6226	95	17	ink	ink	NOUN
ejpam-6226	95	18	-	-	PUNCT
ejpam-6226	95	19	algebra	algebra	NOUN
ejpam-6226	95	20	i	i	PRON
ejpam-6226	95	21	is	be	AUX
ejpam-6226	95	22	called	call	VERB
ejpam-6226	95	23	a	a	DET
ejpam-6226	95	24	neutrosophic	neutrosophic	ADJ
ejpam-6226	95	25	ink	ink	NOUN
ejpam-6226	95	26	-	-	PUNCT
ejpam-6226	95	27	subalgebra	subalgebra	NOUN
ejpam-6226	95	28	(	(	PUNCT
ejpam-6226	95	29	nink	nink	VERB
ejpam-6226	95	30	-	-	PUNCT
ejpam-6226	95	31	s	s	NOUN
ejpam-6226	95	32	)	)	PUNCT
ejpam-6226	95	33	of	of	ADP
ejpam-6226	95	34	i	i	PRON
ejpam-6226	95	35	if	if	SCONJ
ejpam-6226	95	36	it	it	PRON
ejpam-6226	95	37	gratifies	gratify	VERB
ejpam-6226	95	38	the	the	DET
ejpam-6226	95	39	following	follow	VERB
ejpam-6226	95	40	condition	condition	NOUN
ejpam-6226	95	41	:	:	PUNCT
ejpam-6226	95	42	(	(	PUNCT
ejpam-6226	95	43	d1	d1	NOUN
ejpam-6226	95	44	)	)	PUNCT
ejpam-6226	95	45	gt	gt	PROPN
ejpam-6226	96	1	(	(	PUNCT
ejpam-6226	96	2	ϵ	ϵ	NOUN
ejpam-6226	96	3	•	•	NUM
ejpam-6226	96	4	ξ	ξ	NOUN
ejpam-6226	96	5	)	)	PUNCT
ejpam-6226	96	6	≥	≥	NOUN
ejpam-6226	96	7	min{gt	min{gt	X
ejpam-6226	96	8	(	(	PUNCT
ejpam-6226	96	9	ϵ	ϵ	X
ejpam-6226	96	10	)	)	PUNCT
ejpam-6226	96	11	,	,	PUNCT
ejpam-6226	96	12	gt	gt	PROPN
ejpam-6226	96	13	(	(	PUNCT
ejpam-6226	96	14	ξ	ξ	NOUN
ejpam-6226	96	15	)	)	PUNCT
ejpam-6226	96	16	}	}	PUNCT
ejpam-6226	96	17	(	(	PUNCT
ejpam-6226	96	18	d2	d2	PROPN
ejpam-6226	96	19	)	)	PUNCT
ejpam-6226	96	20	gi(ϵ	gi(ϵ	VERB
ejpam-6226	96	21	•	•	NUM
ejpam-6226	96	22	ξ	ξ	NOUN
ejpam-6226	96	23	)	)	PUNCT
ejpam-6226	96	24	≤	≤	NUM
ejpam-6226	96	25	max{gi(ϵ	max{gi(ϵ	NOUN
ejpam-6226	96	26	)	)	PUNCT
ejpam-6226	96	27	,	,	PUNCT
ejpam-6226	96	28	gi(ξ	gi(ξ	X
ejpam-6226	96	29	)	)	PUNCT
ejpam-6226	96	30	}	}	PUNCT
ejpam-6226	96	31	(	(	PUNCT
ejpam-6226	96	32	d3	d3	PROPN
ejpam-6226	96	33	)	)	PUNCT
ejpam-6226	96	34	gf	gf	NOUN
ejpam-6226	96	35	(	(	PUNCT
ejpam-6226	96	36	ϵ	ϵ	NOUN
ejpam-6226	96	37	•	•	NUM
ejpam-6226	96	38	ξ	ξ	NOUN
ejpam-6226	96	39	)	)	PUNCT
ejpam-6226	96	40	≤	≤	NUM
ejpam-6226	96	41	max{gf	max{gf	PUNCT
ejpam-6226	96	42	(	(	PUNCT
ejpam-6226	96	43	ϵ	ϵ	NOUN
ejpam-6226	96	44	)	)	PUNCT
ejpam-6226	96	45	,	,	PUNCT
ejpam-6226	96	46	gf	gf	X
ejpam-6226	96	47	(	(	PUNCT
ejpam-6226	96	48	ξ	ξ	NOUN
ejpam-6226	96	49	)	)	PUNCT
ejpam-6226	96	50	}	}	PUNCT
ejpam-6226	96	51	,	,	PUNCT
ejpam-6226	96	52	∀ϵ	∀ϵ	PROPN
ejpam-6226	96	53	,	,	PUNCT
ejpam-6226	96	54	ξ	ξ	PROPN
ejpam-6226	96	55	,	,	PUNCT
ejpam-6226	96	56	ς	ς	PROPN
ejpam-6226	96	57	∈	∈	PROPN
ejpam-6226	96	58	i.	i.	NOUN
ejpam-6226	96	59	definition	definition	NOUN
ejpam-6226	96	60	9	9	NUM
ejpam-6226	96	61	.	.	PUNCT
ejpam-6226	97	1	[	[	X
ejpam-6226	97	2	26	26	NUM
ejpam-6226	97	3	]	]	PUNCT
ejpam-6226	97	4	an	an	DET
ejpam-6226	97	5	ns	ns	NOUN
ejpam-6226	97	6	g	g	NOUN
ejpam-6226	97	7	=	=	PUNCT
ejpam-6226	97	8	(	(	PUNCT
ejpam-6226	97	9	gt	gt	INTJ
ejpam-6226	97	10	,	,	PUNCT
ejpam-6226	97	11	gi	gi	INTJ
ejpam-6226	97	12	,	,	PUNCT
ejpam-6226	97	13	gf	gf	NOUN
ejpam-6226	97	14	)	)	PUNCT
ejpam-6226	97	15	in	in	ADP
ejpam-6226	97	16	an	an	DET
ejpam-6226	97	17	ink	ink	NOUN
ejpam-6226	97	18	-	-	PUNCT
ejpam-6226	97	19	algebra	algebra	NOUN
ejpam-6226	97	20	i	i	PRON
ejpam-6226	97	21	is	be	AUX
ejpam-6226	97	22	termed	term	VERB
ejpam-6226	97	23	as	as	ADP
ejpam-6226	97	24	a	a	DET
ejpam-6226	97	25	neutrosophic	neutrosophic	ADJ
ejpam-6226	97	26	ink	ink	NOUN
ejpam-6226	97	27	-	-	PUNCT
ejpam-6226	97	28	ideal	ideal	NOUN
ejpam-6226	97	29	(	(	PUNCT
ejpam-6226	97	30	nink	nink	NOUN
ejpam-6226	97	31	-	-	PUNCT
ejpam-6226	97	32	i	i	NOUN
ejpam-6226	97	33	)	)	PUNCT
ejpam-6226	97	34	of	of	ADP
ejpam-6226	97	35	i	i	PRON
ejpam-6226	97	36	if	if	SCONJ
ejpam-6226	97	37	it	it	PRON
ejpam-6226	97	38	gratifies	gratify	VERB
ejpam-6226	97	39	the	the	DET
ejpam-6226	97	40	following	follow	VERB
ejpam-6226	97	41	condition	condition	NOUN
ejpam-6226	97	42	:	:	PUNCT
ejpam-6226	97	43	(	(	PUNCT
ejpam-6226	97	44	d4	d4	PROPN
ejpam-6226	97	45	)	)	PUNCT
ejpam-6226	97	46	gt	gt	PROPN
ejpam-6226	97	47	(	(	PUNCT
ejpam-6226	97	48	0	0	NUM
ejpam-6226	97	49	)	)	PUNCT
ejpam-6226	97	50	≥	≥	NOUN
ejpam-6226	97	51	gt	gt	INTJ
ejpam-6226	97	52	(	(	PUNCT
ejpam-6226	97	53	ϵ	ϵ	NOUN
ejpam-6226	97	54	)	)	PUNCT
ejpam-6226	97	55	,	,	PUNCT
ejpam-6226	97	56	gi(0	gi(0	PROPN
ejpam-6226	97	57	)	)	PUNCT
ejpam-6226	97	58	≤	≤	NOUN
ejpam-6226	97	59	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	97	60	)	)	PUNCT
ejpam-6226	97	61	,	,	PUNCT
ejpam-6226	97	62	gf	gf	X
ejpam-6226	97	63	(	(	PUNCT
ejpam-6226	97	64	0	0	NUM
ejpam-6226	97	65	)	)	PUNCT
ejpam-6226	97	66	≤	≤	NOUN
ejpam-6226	97	67	gf	gf	X
ejpam-6226	97	68	(	(	PUNCT
ejpam-6226	97	69	ϵ	ϵ	NOUN
ejpam-6226	97	70	)	)	PUNCT
ejpam-6226	97	71	(	(	PUNCT
ejpam-6226	97	72	d5	d5	NOUN
ejpam-6226	97	73	)	)	PUNCT
ejpam-6226	97	74	gt	gt	PROPN
ejpam-6226	97	75	(	(	PUNCT
ejpam-6226	97	76	ϵ	ϵ	X
ejpam-6226	97	77	)	)	PUNCT
ejpam-6226	97	78	≥	≥	NOUN
ejpam-6226	97	79	min{gt	min{gt	X
ejpam-6226	97	80	(	(	PUNCT
ejpam-6226	97	81	ϵ	ϵ	PART
ejpam-6226	97	82	•	•	NUM
ejpam-6226	97	83	ξ	ξ	NOUN
ejpam-6226	97	84	)	)	PUNCT
ejpam-6226	97	85	,	,	PUNCT
ejpam-6226	97	86	gt	gt	PROPN
ejpam-6226	97	87	(	(	PUNCT
ejpam-6226	97	88	ξ	ξ	NOUN
ejpam-6226	97	89	)	)	PUNCT
ejpam-6226	97	90	}	}	PUNCT
ejpam-6226	97	91	(	(	PUNCT
ejpam-6226	97	92	d6	d6	NOUN
ejpam-6226	97	93	)	)	PUNCT
ejpam-6226	97	94	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	97	95	)	)	PUNCT
ejpam-6226	97	96	≤	≤	NUM
ejpam-6226	97	97	max{gi(ϵ	max{gi(ϵ	NOUN
ejpam-6226	97	98	•	•	NUM
ejpam-6226	97	99	ξ	ξ	NOUN
ejpam-6226	97	100	)	)	PUNCT
ejpam-6226	97	101	,	,	PUNCT
ejpam-6226	97	102	gi(ξ	gi(ξ	X
ejpam-6226	97	103	)	)	PUNCT
ejpam-6226	97	104	}	}	PUNCT
ejpam-6226	97	105	(	(	PUNCT
ejpam-6226	97	106	d7	d7	PROPN
ejpam-6226	97	107	)	)	PUNCT
ejpam-6226	97	108	gf	gf	NOUN
ejpam-6226	97	109	(	(	PUNCT
ejpam-6226	97	110	ϵ	ϵ	NOUN
ejpam-6226	97	111	)	)	PUNCT
ejpam-6226	97	112	≤	≤	NOUN
ejpam-6226	97	113	max{gf	max{gf	PUNCT
ejpam-6226	97	114	(	(	PUNCT
ejpam-6226	97	115	ϵ	ϵ	PROPN
ejpam-6226	97	116	•	•	NUM
ejpam-6226	97	117	ξ	ξ	NOUN
ejpam-6226	97	118	)	)	PUNCT
ejpam-6226	97	119	,	,	PUNCT
ejpam-6226	97	120	gf	gf	X
ejpam-6226	97	121	(	(	PUNCT
ejpam-6226	97	122	ξ	ξ	NOUN
ejpam-6226	97	123	)	)	PUNCT
ejpam-6226	97	124	}	}	PUNCT
ejpam-6226	97	125	,	,	PUNCT
ejpam-6226	97	126	∀ϵ	∀ϵ	PROPN
ejpam-6226	97	127	,	,	PUNCT
ejpam-6226	97	128	ξ	ξ	PROPN
ejpam-6226	97	129	∈	∈	PROPN
ejpam-6226	97	130	i.	i.	NOUN
ejpam-6226	97	131	theorem	theorem	VERB
ejpam-6226	97	132	2	2	NUM
ejpam-6226	97	133	.	.	PUNCT
ejpam-6226	98	1	an	an	DET
ejpam-6226	98	2	ns	ns	ADJ
ejpam-6226	98	3	g	g	NOUN
ejpam-6226	98	4	=	=	PUNCT
ejpam-6226	98	5	(	(	PUNCT
ejpam-6226	98	6	gt	gt	INTJ
ejpam-6226	98	7	,	,	PUNCT
ejpam-6226	98	8	gi	gi	INTJ
ejpam-6226	98	9	,	,	PUNCT
ejpam-6226	98	10	gf	gf	NOUN
ejpam-6226	98	11	)	)	PUNCT
ejpam-6226	98	12	in	in	ADP
ejpam-6226	98	13	an	an	DET
ejpam-6226	98	14	ink	ink	NOUN
ejpam-6226	98	15	-	-	PUNCT
ejpam-6226	98	16	algebra	algebra	NOUN
ejpam-6226	98	17	i	i	PRON
ejpam-6226	98	18	is	be	AUX
ejpam-6226	98	19	termed	term	VERB
ejpam-6226	98	20	as	as	ADP
ejpam-6226	98	21	an	an	DET
ejpam-6226	98	22	nink	nink	NOUN
ejpam-6226	98	23	-	-	PUNCT
ejpam-6226	98	24	i	i	PRON
ejpam-6226	98	25	of	of	ADP
ejpam-6226	98	26	i	i	PRON
ejpam-6226	98	27	if	if	SCONJ
ejpam-6226	98	28	and	and	CCONJ
ejpam-6226	98	29	only	only	ADV
ejpam-6226	98	30	if	if	SCONJ
ejpam-6226	98	31	it	it	PRON
ejpam-6226	98	32	gratifies	gratify	VERB
ejpam-6226	98	33	the	the	DET
ejpam-6226	98	34	following	follow	VERB
ejpam-6226	98	35	conditions	condition	NOUN
ejpam-6226	98	36	(	(	PUNCT
ejpam-6226	98	37	d4	d4	PROPN
ejpam-6226	98	38	)	)	PUNCT
ejpam-6226	98	39	and	and	CCONJ
ejpam-6226	98	40	(	(	PUNCT
ejpam-6226	98	41	d8	d8	PROPN
ejpam-6226	98	42	)	)	PUNCT
ejpam-6226	98	43	gt	gt	PROPN
ejpam-6226	98	44	(	(	PUNCT
ejpam-6226	98	45	ϵ	ϵ	X
ejpam-6226	98	46	)	)	PUNCT
ejpam-6226	98	47	≥	≥	NOUN
ejpam-6226	98	48	min{gt	min{gt	X
ejpam-6226	98	49	(	(	PUNCT
ejpam-6226	98	50	(	(	PUNCT
ejpam-6226	98	51	ς	ς	PROPN
ejpam-6226	98	52	•	•	NUM
ejpam-6226	98	53	ϵ	ϵ	NOUN
ejpam-6226	98	54	)	)	PUNCT
ejpam-6226	98	55	•	•	NOUN
ejpam-6226	98	56	(	(	PUNCT
ejpam-6226	98	57	ς	ς	PROPN
ejpam-6226	98	58	•	•	NUM
ejpam-6226	98	59	ξ	ξ	NOUN
ejpam-6226	98	60	)	)	PUNCT
ejpam-6226	98	61	)	)	PUNCT
ejpam-6226	98	62	,	,	PUNCT
ejpam-6226	98	63	gt	gt	PROPN
ejpam-6226	98	64	(	(	PUNCT
ejpam-6226	98	65	ξ	ξ	NOUN
ejpam-6226	98	66	)	)	PUNCT
ejpam-6226	98	67	}	}	PUNCT
ejpam-6226	98	68	(	(	PUNCT
ejpam-6226	98	69	d9	d9	PROPN
ejpam-6226	98	70	)	)	PUNCT
ejpam-6226	98	71	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	98	72	)	)	PUNCT
ejpam-6226	98	73	≤	≤	NUM
ejpam-6226	98	74	max{gi((ς	max{gi((ς	NOUN
ejpam-6226	98	75	•	•	NOUN
ejpam-6226	98	76	ϵ	ϵ	NOUN
ejpam-6226	98	77	)	)	PUNCT
ejpam-6226	98	78	•	•	NOUN
ejpam-6226	98	79	(	(	PUNCT
ejpam-6226	98	80	ς	ς	PROPN
ejpam-6226	98	81	•	•	NUM
ejpam-6226	98	82	ξ	ξ	NOUN
ejpam-6226	98	83	)	)	PUNCT
ejpam-6226	98	84	)	)	PUNCT
ejpam-6226	98	85	,	,	PUNCT
ejpam-6226	98	86	gi(ξ	gi(ξ	X
ejpam-6226	98	87	)	)	PUNCT
ejpam-6226	98	88	}	}	PUNCT
ejpam-6226	98	89	(	(	PUNCT
ejpam-6226	98	90	d10	d10	PROPN
ejpam-6226	98	91	)	)	PUNCT
ejpam-6226	98	92	gf	gf	NOUN
ejpam-6226	98	93	(	(	PUNCT
ejpam-6226	98	94	ϵ	ϵ	NOUN
ejpam-6226	98	95	)	)	PUNCT
ejpam-6226	98	96	≤	≤	NOUN
ejpam-6226	98	97	max{gf	max{gf	PUNCT
ejpam-6226	98	98	(	(	PUNCT
ejpam-6226	98	99	(	(	PUNCT
ejpam-6226	98	100	ς	ς	PROPN
ejpam-6226	98	101	•	•	NUM
ejpam-6226	98	102	ϵ	ϵ	NOUN
ejpam-6226	98	103	)	)	PUNCT
ejpam-6226	98	104	•	•	NOUN
ejpam-6226	98	105	(	(	PUNCT
ejpam-6226	98	106	ς	ς	PROPN
ejpam-6226	98	107	•	•	NUM
ejpam-6226	98	108	ξ	ξ	NOUN
ejpam-6226	98	109	)	)	PUNCT
ejpam-6226	98	110	)	)	PUNCT
ejpam-6226	98	111	,	,	PUNCT
ejpam-6226	98	112	gf	gf	X
ejpam-6226	98	113	(	(	PUNCT
ejpam-6226	98	114	ξ)},∀ϵ	ξ)},∀ϵ	PROPN
ejpam-6226	98	115	,	,	PUNCT
ejpam-6226	98	116	ξ	ξ	PROPN
ejpam-6226	98	117	,	,	PUNCT
ejpam-6226	98	118	ς	ς	PROPN
ejpam-6226	98	119	∈	∈	PROPN
ejpam-6226	98	120	i.	i.	NOUN
ejpam-6226	98	121	proof	proof	NOUN
ejpam-6226	98	122	.	.	PUNCT
ejpam-6226	99	1	suppose	suppose	VERB
ejpam-6226	99	2	g	g	PROPN
ejpam-6226	99	3	satisfies	satisfie	NOUN
ejpam-6226	99	4	(	(	PUNCT
ejpam-6226	99	5	d4	d4	PROPN
ejpam-6226	99	6	)	)	PUNCT
ejpam-6226	99	7	,	,	PUNCT
ejpam-6226	99	8	(	(	PUNCT
ejpam-6226	99	9	d8	d8	PROPN
ejpam-6226	99	10	)	)	PUNCT
ejpam-6226	99	11	,	,	PUNCT
ejpam-6226	99	12	(	(	PUNCT
ejpam-6226	99	13	d9	d9	PROPN
ejpam-6226	99	14	)	)	PUNCT
ejpam-6226	99	15	,	,	PUNCT
ejpam-6226	99	16	and	and	CCONJ
ejpam-6226	99	17	(	(	PUNCT
ejpam-6226	99	18	d10	d10	PROPN
ejpam-6226	99	19	)	)	PUNCT
ejpam-6226	99	20	.	.	PUNCT
ejpam-6226	100	1	we	we	PRON
ejpam-6226	100	2	prove	prove	VERB
ejpam-6226	100	3	that	that	SCONJ
ejpam-6226	100	4	g	g	PROPN
ejpam-6226	100	5	is	be	AUX
ejpam-6226	100	6	an	an	DET
ejpam-6226	100	7	nink	nink	NOUN
ejpam-6226	100	8	-	-	PUNCT
ejpam-6226	100	9	i	i	NOUN
ejpam-6226	100	10	,	,	PUNCT
ejpam-6226	100	11	i.e.	i.e.	X
ejpam-6226	100	12	,	,	PUNCT
ejpam-6226	100	13	it	it	PRON
ejpam-6226	100	14	also	also	ADV
ejpam-6226	100	15	satisfies	satisfy	VERB
ejpam-6226	100	16	(	(	PUNCT
ejpam-6226	100	17	d5	d5	NOUN
ejpam-6226	100	18	)	)	PUNCT
ejpam-6226	100	19	,	,	PUNCT
ejpam-6226	100	20	(	(	PUNCT
ejpam-6226	100	21	d6	d6	NOUN
ejpam-6226	100	22	)	)	PUNCT
ejpam-6226	100	23	,	,	PUNCT
ejpam-6226	100	24	and	and	CCONJ
ejpam-6226	100	25	(	(	PUNCT
ejpam-6226	100	26	d7	d7	PROPN
ejpam-6226	100	27	)	)	PUNCT
ejpam-6226	100	28	.	.	PUNCT
ejpam-6226	101	1	let	let	VERB
ejpam-6226	101	2	ϵ	ϵ	X
ejpam-6226	101	3	,	,	PUNCT
ejpam-6226	101	4	ξ	ξ	PROPN
ejpam-6226	101	5	∈	∈	PROPN
ejpam-6226	101	6	i	i	PRON
ejpam-6226	101	7	,	,	PUNCT
ejpam-6226	101	8	and	and	CCONJ
ejpam-6226	101	9	choose	choose	VERB
ejpam-6226	101	10	ς	ς	PROPN
ejpam-6226	101	11	=	=	SYM
ejpam-6226	101	12	0	0	PROPN
ejpam-6226	101	13	,	,	PUNCT
ejpam-6226	101	14	the	the	DET
ejpam-6226	101	15	constant	constant	ADJ
ejpam-6226	101	16	of	of	ADP
ejpam-6226	101	17	the	the	DET
ejpam-6226	101	18	ink	ink	NOUN
ejpam-6226	101	19	-	-	PUNCT
ejpam-6226	101	20	algebra	algebra	NOUN
ejpam-6226	101	21	.	.	PUNCT
ejpam-6226	102	1	from	from	ADP
ejpam-6226	102	2	axiom	axiom	NOUN
ejpam-6226	102	3	(	(	PUNCT
ejpam-6226	102	4	ink-3	ink-3	NOUN
ejpam-6226	102	5	)	)	PUNCT
ejpam-6226	102	6	,	,	PUNCT
ejpam-6226	102	7	we	we	PRON
ejpam-6226	102	8	know	know	VERB
ejpam-6226	102	9	0	0	NUM
ejpam-6226	102	10	•	•	NOUN
ejpam-6226	103	1	ϵ	ϵ	X
ejpam-6226	103	2	=	=	SYM
ejpam-6226	103	3	ϵ	ϵ	NOUN
ejpam-6226	103	4	,	,	PUNCT
ejpam-6226	103	5	0	0	NUM
ejpam-6226	103	6	•	•	NUM
ejpam-6226	103	7	ξ	ξ	X
ejpam-6226	103	8	=	=	SYM
ejpam-6226	103	9	ξ	ξ	PROPN
ejpam-6226	103	10	⇒	⇒	NOUN
ejpam-6226	103	11	(	(	PUNCT
ejpam-6226	103	12	0	0	NUM
ejpam-6226	103	13	•	•	NUM
ejpam-6226	103	14	ϵ	ϵ	NOUN
ejpam-6226	103	15	)	)	PUNCT
ejpam-6226	103	16	•	•	NOUN
ejpam-6226	103	17	(	(	PUNCT
ejpam-6226	103	18	0	0	NUM
ejpam-6226	103	19	•	•	NUM
ejpam-6226	103	20	ξ	ξ	NOUN
ejpam-6226	103	21	)	)	PUNCT
ejpam-6226	103	22	=	=	SYM
ejpam-6226	104	1	ϵ	ϵ	PROPN
ejpam-6226	104	2	•	•	NUM
ejpam-6226	104	3	ξ	ξ	X
ejpam-6226	104	4	.	.	PUNCT
ejpam-6226	104	5	now	now	ADV
ejpam-6226	104	6	substitute	substitute	VERB
ejpam-6226	104	7	into	into	ADP
ejpam-6226	104	8	(	(	PUNCT
ejpam-6226	104	9	d8)-(d10	d8)-(d10	X
ejpam-6226	104	10	):	):	PUNCT
ejpam-6226	104	11	from	from	ADP
ejpam-6226	104	12	(	(	PUNCT
ejpam-6226	104	13	d8	d8	PROPN
ejpam-6226	104	14	)	)	PUNCT
ejpam-6226	104	15	,	,	PUNCT
ejpam-6226	104	16	we	we	PRON
ejpam-6226	104	17	have	have	VERB
ejpam-6226	104	18	gt	gt	PROPN
ejpam-6226	104	19	(	(	PUNCT
ejpam-6226	104	20	ϵ	ϵ	NOUN
ejpam-6226	104	21	)	)	PUNCT
ejpam-6226	104	22	≥	≥	NOUN
ejpam-6226	104	23	min{gt	min{gt	X
ejpam-6226	104	24	(	(	PUNCT
ejpam-6226	104	25	(	(	PUNCT
ejpam-6226	104	26	0	0	NUM
ejpam-6226	104	27	•	•	NUM
ejpam-6226	104	28	ϵ	ϵ	NOUN
ejpam-6226	104	29	)	)	PUNCT
ejpam-6226	104	30	•	•	NOUN
ejpam-6226	104	31	(	(	PUNCT
ejpam-6226	104	32	0	0	NUM
ejpam-6226	104	33	•	•	NUM
ejpam-6226	104	34	ξ	ξ	NOUN
ejpam-6226	104	35	)	)	PUNCT
ejpam-6226	104	36	)	)	PUNCT
ejpam-6226	104	37	,	,	PUNCT
ejpam-6226	104	38	gt	gt	PROPN
ejpam-6226	104	39	(	(	PUNCT
ejpam-6226	104	40	ξ	ξ	NOUN
ejpam-6226	104	41	)	)	PUNCT
ejpam-6226	104	42	}	}	PUNCT
ejpam-6226	104	43	=	=	SYM
ejpam-6226	104	44	min{gt	min{gt	NOUN
ejpam-6226	104	45	(	(	PUNCT
ejpam-6226	104	46	ϵ	ϵ	PART
ejpam-6226	104	47	•	•	NUM
ejpam-6226	104	48	ξ	ξ	NOUN
ejpam-6226	104	49	)	)	PUNCT
ejpam-6226	104	50	,	,	PUNCT
ejpam-6226	104	51	gt	gt	PROPN
ejpam-6226	104	52	(	(	PUNCT
ejpam-6226	104	53	ξ	ξ	NOUN
ejpam-6226	104	54	)	)	PUNCT
ejpam-6226	104	55	}	}	PUNCT
ejpam-6226	104	56	which	which	PRON
ejpam-6226	104	57	is	be	AUX
ejpam-6226	104	58	exactly	exactly	ADV
ejpam-6226	104	59	(	(	PUNCT
ejpam-6226	104	60	d5	d5	NOUN
ejpam-6226	104	61	)	)	PUNCT
ejpam-6226	104	62	.	.	PUNCT
ejpam-6226	105	1	from	from	ADP
ejpam-6226	105	2	(	(	PUNCT
ejpam-6226	105	3	d9	d9	PROPN
ejpam-6226	105	4	)	)	PUNCT
ejpam-6226	105	5	,	,	PUNCT
ejpam-6226	105	6	we	we	PRON
ejpam-6226	105	7	have	have	AUX
ejpam-6226	105	8	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	105	9	)	)	PUNCT
ejpam-6226	105	10	≤	≤	NOUN
ejpam-6226	105	11	max{gi((0	max{gi((0	NUM
ejpam-6226	105	12	•	•	NOUN
ejpam-6226	105	13	ϵ	ϵ	NOUN
ejpam-6226	105	14	)	)	PUNCT
ejpam-6226	105	15	•	•	NOUN
ejpam-6226	105	16	(	(	PUNCT
ejpam-6226	105	17	0	0	NUM
ejpam-6226	105	18	•	•	NUM
ejpam-6226	105	19	ξ	ξ	NOUN
ejpam-6226	105	20	)	)	PUNCT
ejpam-6226	105	21	)	)	PUNCT
ejpam-6226	105	22	,	,	PUNCT
ejpam-6226	105	23	gi(ξ	gi(ξ	X
ejpam-6226	105	24	)	)	PUNCT
ejpam-6226	105	25	}	}	PUNCT
ejpam-6226	105	26	=	=	PUNCT
ejpam-6226	105	27	max{gi(ϵ	max{gi(ϵ	NUM
ejpam-6226	105	28	•	•	NUM
ejpam-6226	105	29	ξ	ξ	NOUN
ejpam-6226	105	30	)	)	PUNCT
ejpam-6226	105	31	,	,	PUNCT
ejpam-6226	105	32	gi(ξ	gi(ξ	X
ejpam-6226	105	33	)	)	PUNCT
ejpam-6226	105	34	}	}	PUNCT
ejpam-6226	105	35	which	which	PRON
ejpam-6226	105	36	is	be	AUX
ejpam-6226	105	37	(	(	PUNCT
ejpam-6226	105	38	d6	d6	NOUN
ejpam-6226	105	39	)	)	PUNCT
ejpam-6226	105	40	.	.	PUNCT
ejpam-6226	106	1	from	from	ADP
ejpam-6226	106	2	(	(	PUNCT
ejpam-6226	106	3	d10	d10	PROPN
ejpam-6226	106	4	)	)	PUNCT
ejpam-6226	106	5	,	,	PUNCT
ejpam-6226	106	6	we	we	PRON
ejpam-6226	106	7	have	have	VERB
ejpam-6226	106	8	gf	gf	VERB
ejpam-6226	106	9	(	(	PUNCT
ejpam-6226	106	10	ϵ	ϵ	NOUN
ejpam-6226	106	11	)	)	PUNCT
ejpam-6226	106	12	≤	≤	NOUN
ejpam-6226	106	13	max{gf	max{gf	PUNCT
ejpam-6226	106	14	(	(	PUNCT
ejpam-6226	106	15	(	(	PUNCT
ejpam-6226	106	16	0	0	NUM
ejpam-6226	106	17	•	•	NUM
ejpam-6226	106	18	ϵ	ϵ	NOUN
ejpam-6226	106	19	)	)	PUNCT
ejpam-6226	106	20	•	•	NOUN
ejpam-6226	106	21	(	(	PUNCT
ejpam-6226	106	22	0	0	NUM
ejpam-6226	106	23	•	•	NUM
ejpam-6226	106	24	ξ	ξ	NOUN
ejpam-6226	106	25	)	)	PUNCT
ejpam-6226	106	26	)	)	PUNCT
ejpam-6226	106	27	,	,	PUNCT
ejpam-6226	106	28	gf	gf	X
ejpam-6226	106	29	(	(	PUNCT
ejpam-6226	106	30	ξ	ξ	NOUN
ejpam-6226	106	31	)	)	PUNCT
ejpam-6226	106	32	}	}	PUNCT
ejpam-6226	106	33	=	=	SYM
ejpam-6226	106	34	max{gf	max{gf	X
ejpam-6226	107	1	(	(	PUNCT
ejpam-6226	107	2	ϵ	ϵ	PROPN
ejpam-6226	107	3	•	•	NUM
ejpam-6226	107	4	ξ	ξ	NOUN
ejpam-6226	107	5	)	)	PUNCT
ejpam-6226	107	6	,	,	PUNCT
ejpam-6226	107	7	gf	gf	X
ejpam-6226	107	8	(	(	PUNCT
ejpam-6226	107	9	ξ	ξ	NOUN
ejpam-6226	107	10	)	)	PUNCT
ejpam-6226	107	11	}	}	PUNCT
ejpam-6226	107	12	which	which	PRON
ejpam-6226	107	13	is	be	AUX
ejpam-6226	107	14	(	(	PUNCT
ejpam-6226	107	15	d7	d7	PROPN
ejpam-6226	107	16	)	)	PUNCT
ejpam-6226	107	17	.	.	PUNCT
ejpam-6226	108	1	therefore	therefore	ADV
ejpam-6226	108	2	,	,	PUNCT
ejpam-6226	108	3	g	g	PROPN
ejpam-6226	108	4	is	be	AUX
ejpam-6226	108	5	an	an	DET
ejpam-6226	108	6	nink	nink	NOUN
ejpam-6226	108	7	-	-	PUNCT
ejpam-6226	108	8	i	i	PRON
ejpam-6226	108	9	of	of	ADP
ejpam-6226	108	10	i.	i.	NOUN
ejpam-6226	108	11	conversely	conversely	ADV
ejpam-6226	108	12	,	,	PUNCT
ejpam-6226	108	13	suppose	suppose	VERB
ejpam-6226	108	14	g	g	PROPN
ejpam-6226	108	15	is	be	AUX
ejpam-6226	108	16	an	an	DET
ejpam-6226	108	17	nink	nink	NOUN
ejpam-6226	108	18	-	-	PUNCT
ejpam-6226	108	19	i	i	PRON
ejpam-6226	108	20	of	of	ADP
ejpam-6226	108	21	i	i	PRON
ejpam-6226	108	22	,	,	PUNCT
ejpam-6226	108	23	i.e.	i.e.	X
ejpam-6226	108	24	,	,	PUNCT
ejpam-6226	108	25	it	it	PRON
ejpam-6226	108	26	satisfies	satisfy	VERB
ejpam-6226	108	27	(	(	PUNCT
ejpam-6226	108	28	d4)-(d7	d4)-(d7	PROPN
ejpam-6226	108	29	)	)	PUNCT
ejpam-6226	108	30	.	.	PUNCT
ejpam-6226	109	1	we	we	PRON
ejpam-6226	109	2	prove	prove	VERB
ejpam-6226	109	3	that	that	SCONJ
ejpam-6226	109	4	it	it	PRON
ejpam-6226	109	5	satisfies	satisfy	VERB
ejpam-6226	109	6	(	(	PUNCT
ejpam-6226	109	7	d8)-(d10	d8)-(d10	X
ejpam-6226	109	8	)	)	PUNCT
ejpam-6226	109	9	.	.	PUNCT
ejpam-6226	110	1	let	let	VERB
ejpam-6226	110	2	ϵ	ϵ	PRON
ejpam-6226	110	3	,	,	PUNCT
ejpam-6226	110	4	ξ	ξ	PROPN
ejpam-6226	110	5	,	,	PUNCT
ejpam-6226	110	6	ς	ς	PROPN
ejpam-6226	110	7	∈	∈	PROPN
ejpam-6226	110	8	i.	i.	NOUN
ejpam-6226	110	9	using	use	VERB
ejpam-6226	110	10	(	(	PUNCT
ejpam-6226	110	11	d5	d5	NOUN
ejpam-6226	110	12	)	)	PUNCT
ejpam-6226	110	13	,	,	PUNCT
ejpam-6226	110	14	we	we	PRON
ejpam-6226	110	15	have	have	VERB
ejpam-6226	110	16	gt	gt	PROPN
ejpam-6226	110	17	(	(	PUNCT
ejpam-6226	110	18	ϵ	ϵ	NOUN
ejpam-6226	110	19	)	)	PUNCT
ejpam-6226	110	20	≥	≥	NOUN
ejpam-6226	110	21	min{gt	min{gt	X
ejpam-6226	110	22	(	(	PUNCT
ejpam-6226	110	23	ϵ	ϵ	PART
ejpam-6226	110	24	•	•	NUM
ejpam-6226	110	25	ξ	ξ	NOUN
ejpam-6226	110	26	)	)	PUNCT
ejpam-6226	110	27	,	,	PUNCT
ejpam-6226	110	28	gt	gt	PROPN
ejpam-6226	110	29	(	(	PUNCT
ejpam-6226	110	30	ξ	ξ	NOUN
ejpam-6226	110	31	)	)	PUNCT
ejpam-6226	110	32	}	}	PUNCT
ejpam-6226	110	33	r.	r.	VERB
ejpam-6226	110	34	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	110	35	et	et	PROPN
ejpam-6226	110	36	al	al	PROPN
ejpam-6226	110	37	.	.	PUNCT
ejpam-6226	110	38	/	/	SYM
ejpam-6226	110	39	eur	eur	PROPN
ejpam-6226	110	40	.	.	PUNCT
ejpam-6226	111	1	j.	j.	PROPN
ejpam-6226	111	2	pure	pure	PROPN
ejpam-6226	111	3	appl	appl	PROPN
ejpam-6226	111	4	.	.	PROPN
ejpam-6226	111	5	math	math	PROPN
ejpam-6226	111	6	,	,	PUNCT
ejpam-6226	111	7	18	18	NUM
ejpam-6226	111	8	(	(	PUNCT
ejpam-6226	111	9	3	3	NUM
ejpam-6226	111	10	)	)	PUNCT
ejpam-6226	111	11	(	(	PUNCT
ejpam-6226	111	12	2025	2025	NUM
ejpam-6226	111	13	)	)	PUNCT
ejpam-6226	111	14	,	,	PUNCT
ejpam-6226	111	15	6226	6226	NUM
ejpam-6226	111	16	6	6	NUM
ejpam-6226	111	17	of	of	ADP
ejpam-6226	111	18	19	19	NUM
ejpam-6226	111	19	which	which	PRON
ejpam-6226	111	20	holds	hold	VERB
ejpam-6226	111	21	for	for	ADP
ejpam-6226	111	22	all	all	DET
ejpam-6226	111	23	elements	element	NOUN
ejpam-6226	111	24	in	in	ADP
ejpam-6226	111	25	i	i	PRON
ejpam-6226	111	26	,	,	PUNCT
ejpam-6226	111	27	and	and	CCONJ
ejpam-6226	111	28	in	in	ADP
ejpam-6226	111	29	particular	particular	ADJ
ejpam-6226	111	30	,	,	PUNCT
ejpam-6226	111	31	for	for	ADP
ejpam-6226	111	32	(	(	PUNCT
ejpam-6226	111	33	ς	ς	PROPN
ejpam-6226	111	34	•	•	NUM
ejpam-6226	111	35	ϵ	ϵ	NOUN
ejpam-6226	111	36	)	)	PUNCT
ejpam-6226	111	37	•	•	NOUN
ejpam-6226	111	38	(	(	PUNCT
ejpam-6226	111	39	ς	ς	PROPN
ejpam-6226	111	40	•	•	NUM
ejpam-6226	111	41	ξ	ξ	NOUN
ejpam-6226	111	42	)	)	PUNCT
ejpam-6226	111	43	and	and	CCONJ
ejpam-6226	111	44	ξ	ξ	X
ejpam-6226	111	45	.	.	PUNCT
ejpam-6226	112	1	therefore	therefore	ADV
ejpam-6226	112	2	,	,	PUNCT
ejpam-6226	112	3	gt	gt	PROPN
ejpam-6226	112	4	(	(	PUNCT
ejpam-6226	112	5	ϵ	ϵ	X
ejpam-6226	112	6	)	)	PUNCT
ejpam-6226	112	7	≥	≥	NOUN
ejpam-6226	112	8	min{gt	min{gt	X
ejpam-6226	112	9	(	(	PUNCT
ejpam-6226	112	10	(	(	PUNCT
ejpam-6226	112	11	ς	ς	PROPN
ejpam-6226	112	12	•	•	NUM
ejpam-6226	112	13	ϵ	ϵ	NOUN
ejpam-6226	112	14	)	)	PUNCT
ejpam-6226	112	15	•	•	NOUN
ejpam-6226	112	16	(	(	PUNCT
ejpam-6226	112	17	ς	ς	PROPN
ejpam-6226	112	18	•	•	NUM
ejpam-6226	112	19	ξ	ξ	NOUN
ejpam-6226	112	20	)	)	PUNCT
ejpam-6226	112	21	)	)	PUNCT
ejpam-6226	112	22	,	,	PUNCT
ejpam-6226	112	23	gt	gt	PROPN
ejpam-6226	112	24	(	(	PUNCT
ejpam-6226	112	25	ξ	ξ	NOUN
ejpam-6226	112	26	)	)	PUNCT
ejpam-6226	112	27	}	}	PUNCT
ejpam-6226	112	28	.	.	PUNCT
ejpam-6226	113	1	similarly	similarly	ADV
ejpam-6226	113	2	,	,	PUNCT
ejpam-6226	113	3	from	from	ADP
ejpam-6226	113	4	(	(	PUNCT
ejpam-6226	113	5	d6	d6	NOUN
ejpam-6226	113	6	)	)	PUNCT
ejpam-6226	113	7	and	and	CCONJ
ejpam-6226	113	8	(	(	PUNCT
ejpam-6226	113	9	d7	d7	PROPN
ejpam-6226	113	10	)	)	PUNCT
ejpam-6226	113	11	,	,	PUNCT
ejpam-6226	113	12	we	we	PRON
ejpam-6226	113	13	have	have	AUX
ejpam-6226	113	14	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	113	15	)	)	PUNCT
ejpam-6226	113	16	≤	≤	NUM
ejpam-6226	113	17	max{gi((ς	max{gi((ς	NOUN
ejpam-6226	113	18	•	•	NOUN
ejpam-6226	113	19	ϵ	ϵ	NOUN
ejpam-6226	113	20	)	)	PUNCT
ejpam-6226	113	21	•	•	NOUN
ejpam-6226	113	22	(	(	PUNCT
ejpam-6226	113	23	ς	ς	PROPN
ejpam-6226	113	24	•	•	NUM
ejpam-6226	113	25	ξ	ξ	NOUN
ejpam-6226	113	26	)	)	PUNCT
ejpam-6226	113	27	)	)	PUNCT
ejpam-6226	113	28	,	,	PUNCT
ejpam-6226	113	29	gi(ξ	gi(ξ	NOUN
ejpam-6226	113	30	)	)	PUNCT
ejpam-6226	113	31	}	}	PUNCT
ejpam-6226	113	32	,	,	PUNCT
ejpam-6226	113	33	gf	gf	X
ejpam-6226	113	34	(	(	PUNCT
ejpam-6226	113	35	ϵ	ϵ	NOUN
ejpam-6226	113	36	)	)	PUNCT
ejpam-6226	113	37	≤	≤	NOUN
ejpam-6226	113	38	max{gf	max{gf	PUNCT
ejpam-6226	113	39	(	(	PUNCT
ejpam-6226	113	40	(	(	PUNCT
ejpam-6226	113	41	ς	ς	PROPN
ejpam-6226	113	42	•	•	NUM
ejpam-6226	113	43	ϵ	ϵ	NOUN
ejpam-6226	113	44	)	)	PUNCT
ejpam-6226	113	45	•	•	NOUN
ejpam-6226	113	46	(	(	PUNCT
ejpam-6226	113	47	ς	ς	PROPN
ejpam-6226	113	48	•	•	NUM
ejpam-6226	113	49	ξ	ξ	NOUN
ejpam-6226	113	50	)	)	PUNCT
ejpam-6226	113	51	)	)	PUNCT
ejpam-6226	113	52	,	,	PUNCT
ejpam-6226	113	53	gf	gf	X
ejpam-6226	113	54	(	(	PUNCT
ejpam-6226	113	55	ξ	ξ	NOUN
ejpam-6226	113	56	)	)	PUNCT
ejpam-6226	113	57	}	}	PUNCT
ejpam-6226	113	58	.	.	PUNCT
ejpam-6226	114	1	thus	thus	ADV
ejpam-6226	114	2	,	,	PUNCT
ejpam-6226	114	3	g	g	PROPN
ejpam-6226	114	4	satisfies	satisfie	NOUN
ejpam-6226	114	5	(	(	PUNCT
ejpam-6226	114	6	d8	d8	PROPN
ejpam-6226	114	7	)	)	PUNCT
ejpam-6226	114	8	,	,	PUNCT
ejpam-6226	114	9	(	(	PUNCT
ejpam-6226	114	10	d9	d9	PROPN
ejpam-6226	114	11	)	)	PUNCT
ejpam-6226	114	12	,	,	PUNCT
ejpam-6226	114	13	and	and	CCONJ
ejpam-6226	114	14	(	(	PUNCT
ejpam-6226	114	15	d10	d10	PROPN
ejpam-6226	114	16	)	)	PUNCT
ejpam-6226	114	17	as	as	SCONJ
ejpam-6226	114	18	required	require	VERB
ejpam-6226	114	19	.	.	PUNCT
ejpam-6226	115	1	definition	definition	NOUN
ejpam-6226	115	2	10	10	NUM
ejpam-6226	115	3	.	.	PUNCT
ejpam-6226	116	1	[	[	X
ejpam-6226	116	2	26	26	NUM
ejpam-6226	116	3	]	]	PUNCT
ejpam-6226	116	4	let	let	VERB
ejpam-6226	116	5	g	g	NOUN
ejpam-6226	116	6	=	=	SYM
ejpam-6226	116	7	(	(	PUNCT
ejpam-6226	116	8	gt	gt	INTJ
ejpam-6226	116	9	,	,	PUNCT
ejpam-6226	116	10	gi	gi	INTJ
ejpam-6226	116	11	,	,	PUNCT
ejpam-6226	116	12	gf	gf	PROPN
ejpam-6226	116	13	)	)	PUNCT
ejpam-6226	116	14	and	and	CCONJ
ejpam-6226	116	15	h	h	NOUN
ejpam-6226	116	16	=	=	SYM
ejpam-6226	116	17	(	(	PUNCT
ejpam-6226	116	18	ht	ht	INTJ
ejpam-6226	116	19	,	,	PUNCT
ejpam-6226	116	20	hi	hi	INTJ
ejpam-6226	116	21	,	,	PUNCT
ejpam-6226	116	22	hf	hf	INTJ
ejpam-6226	116	23	)	)	PUNCT
ejpam-6226	116	24	be	be	AUX
ejpam-6226	116	25	two	two	NUM
ejpam-6226	116	26	nss	ns	NOUN
ejpam-6226	116	27	in	in	ADP
ejpam-6226	116	28	an	an	DET
ejpam-6226	116	29	inkalgebra	inkalgebra	NOUN
ejpam-6226	116	30	i.	i.	NOUN
ejpam-6226	116	31	then	then	ADV
ejpam-6226	116	32	,	,	PUNCT
ejpam-6226	116	33	the	the	DET
ejpam-6226	116	34	union	union	NOUN
ejpam-6226	116	35	and	and	CCONJ
ejpam-6226	116	36	the	the	DET
ejpam-6226	116	37	intersection	intersection	NOUN
ejpam-6226	116	38	are	be	AUX
ejpam-6226	116	39	defined	define	VERB
ejpam-6226	116	40	as	as	SCONJ
ejpam-6226	116	41	follows	follow	VERB
ejpam-6226	116	42	:	:	PUNCT
ejpam-6226	116	43	(	(	PUNCT
ejpam-6226	116	44	i	i	NOUN
ejpam-6226	116	45	)	)	PUNCT
ejpam-6226	116	46	(	(	PUNCT
ejpam-6226	116	47	g∪h)(ϵ	g∪h)(ϵ	NOUN
ejpam-6226	116	48	)	)	PUNCT
ejpam-6226	117	1	=	=	PUNCT
ejpam-6226	117	2	{	{	PUNCT
ejpam-6226	117	3	<	<	X
ejpam-6226	117	4	ϵ,max{gt	ϵ,max{gt	X
ejpam-6226	117	5	(	(	PUNCT
ejpam-6226	117	6	ϵ	ϵ	NOUN
ejpam-6226	117	7	)	)	PUNCT
ejpam-6226	117	8	,	,	PUNCT
ejpam-6226	117	9	ht	ht	PROPN
ejpam-6226	117	10	(	(	PUNCT
ejpam-6226	117	11	ϵ)},min{gi(ϵ	ϵ)},min{gi(ϵ	NOUN
ejpam-6226	117	12	)	)	PUNCT
ejpam-6226	117	13	,	,	PUNCT
ejpam-6226	117	14	hi(ϵ)},min{gf	hi(ϵ)},min{gf	PROPN
ejpam-6226	117	15	(	(	PUNCT
ejpam-6226	117	16	ϵ	ϵ	NOUN
ejpam-6226	117	17	)	)	PUNCT
ejpam-6226	117	18	,	,	PUNCT
ejpam-6226	117	19	hf	hf	X
ejpam-6226	117	20	(	(	PUNCT
ejpam-6226	117	21	ϵ	ϵ	NOUN
ejpam-6226	117	22	)	)	PUNCT
ejpam-6226	117	23	}	}	PUNCT
ejpam-6226	117	24	>	>	PUNCT
ejpam-6226	118	1	|	|	NOUN
ejpam-6226	118	2	ϵ	ϵ	X
ejpam-6226	118	3	∈	∈	PROPN
ejpam-6226	119	1	i	i	PRON
ejpam-6226	119	2	}	}	PUNCT
ejpam-6226	119	3	(	(	PUNCT
ejpam-6226	119	4	ii	ii	NOUN
ejpam-6226	119	5	)	)	PUNCT
ejpam-6226	119	6	(	(	PUNCT
ejpam-6226	119	7	g	g	PROPN
ejpam-6226	119	8	∩	∩	NOUN
ejpam-6226	119	9	h)(ϵ	h)(ϵ	PRON
ejpam-6226	119	10	)	)	PUNCT
ejpam-6226	119	11	=	=	PRON
ejpam-6226	119	12	{	{	PUNCT
ejpam-6226	119	13	<	<	X
ejpam-6226	119	14	ϵ,min{gt	ϵ,min{gt	INTJ
ejpam-6226	119	15	(	(	PUNCT
ejpam-6226	119	16	ϵ	ϵ	NOUN
ejpam-6226	119	17	)	)	PUNCT
ejpam-6226	119	18	,	,	PUNCT
ejpam-6226	119	19	ht	ht	PROPN
ejpam-6226	119	20	(	(	PUNCT
ejpam-6226	119	21	ϵ)},max{gi(ϵ	ϵ)},max{gi(ϵ	PROPN
ejpam-6226	119	22	)	)	PUNCT
ejpam-6226	119	23	,	,	PUNCT
ejpam-6226	119	24	hi(ϵ)},max{gf	hi(ϵ)},max{gf	X
ejpam-6226	119	25	(	(	PUNCT
ejpam-6226	119	26	ϵ	ϵ	NOUN
ejpam-6226	119	27	)	)	PUNCT
ejpam-6226	119	28	,	,	PUNCT
ejpam-6226	119	29	hf	hf	X
ejpam-6226	119	30	(	(	PUNCT
ejpam-6226	119	31	ϵ	ϵ	NOUN
ejpam-6226	119	32	)	)	PUNCT
ejpam-6226	119	33	}	}	PUNCT
ejpam-6226	119	34	>	>	PUNCT
ejpam-6226	120	1	|	|	NOUN
ejpam-6226	120	2	ϵ	ϵ	X
ejpam-6226	120	3	∈	∈	PROPN
ejpam-6226	121	1	i	i	X
ejpam-6226	121	2	}	}	PUNCT
ejpam-6226	121	3	.	.	PUNCT
ejpam-6226	122	1	3	3	X
ejpam-6226	122	2	.	.	X
ejpam-6226	122	3	main	main	ADJ
ejpam-6226	122	4	results	result	NOUN
ejpam-6226	122	5	in	in	ADP
ejpam-6226	122	6	this	this	DET
ejpam-6226	122	7	section	section	NOUN
ejpam-6226	122	8	,	,	PUNCT
ejpam-6226	122	9	we	we	PRON
ejpam-6226	122	10	develop	develop	VERB
ejpam-6226	122	11	and	and	CCONJ
ejpam-6226	122	12	analyze	analyze	VERB
ejpam-6226	122	13	various	various	ADJ
ejpam-6226	122	14	classes	class	NOUN
ejpam-6226	122	15	of	of	ADP
ejpam-6226	122	16	fink	fink	PROPN
ejpam-6226	122	17	-	-	PUNCT
ejpam-6226	122	18	is	be	AUX
ejpam-6226	122	19	in	in	ADP
ejpam-6226	122	20	the	the	DET
ejpam-6226	122	21	context	context	NOUN
ejpam-6226	122	22	of	of	ADP
ejpam-6226	122	23	ink	ink	NOUN
ejpam-6226	122	24	-	-	PUNCT
ejpam-6226	122	25	algebras	algebras	PROPN
ejpam-6226	122	26	.	.	PUNCT
ejpam-6226	123	1	the	the	DET
ejpam-6226	123	2	discussion	discussion	NOUN
ejpam-6226	123	3	is	be	AUX
ejpam-6226	123	4	organized	organize	VERB
ejpam-6226	123	5	into	into	ADP
ejpam-6226	123	6	three	three	NUM
ejpam-6226	123	7	key	key	ADJ
ejpam-6226	123	8	subsections	subsection	NOUN
ejpam-6226	123	9	.	.	PUNCT
ejpam-6226	124	1	first	first	ADV
ejpam-6226	124	2	,	,	PUNCT
ejpam-6226	124	3	in	in	ADP
ejpam-6226	124	4	subsection	subsection	NOUN
ejpam-6226	124	5	3.1	3.1	NUM
ejpam-6226	124	6	,	,	PUNCT
ejpam-6226	124	7	we	we	PRON
ejpam-6226	124	8	introduce	introduce	VERB
ejpam-6226	124	9	the	the	DET
ejpam-6226	124	10	concepts	concept	NOUN
ejpam-6226	124	11	of	of	ADP
ejpam-6226	124	12	fuzzy	fuzzy	ADJ
ejpam-6226	124	13	implicative	implicative	ADJ
ejpam-6226	124	14	ink	ink	NOUN
ejpam-6226	124	15	-	-	PUNCT
ejpam-6226	124	16	ideals	ideal	NOUN
ejpam-6226	124	17	(	(	PUNCT
ejpam-6226	124	18	fmink	fmink	NOUN
ejpam-6226	124	19	-	-	PUNCT
ejpam-6226	124	20	i	i	NOUN
ejpam-6226	124	21	)	)	PUNCT
ejpam-6226	124	22	and	and	CCONJ
ejpam-6226	124	23	fuzzy	fuzzy	ADJ
ejpam-6226	124	24	positive	positive	ADJ
ejpam-6226	124	25	implicative	implicative	ADJ
ejpam-6226	124	26	ink	ink	NOUN
ejpam-6226	124	27	-	-	PUNCT
ejpam-6226	124	28	ideals	ideal	NOUN
ejpam-6226	124	29	(	(	PUNCT
ejpam-6226	124	30	fpmink	fpmink	NOUN
ejpam-6226	124	31	-	-	PUNCT
ejpam-6226	124	32	i	i	NOUN
ejpam-6226	124	33	)	)	PUNCT
ejpam-6226	124	34	and	and	CCONJ
ejpam-6226	124	35	explore	explore	VERB
ejpam-6226	124	36	their	their	PRON
ejpam-6226	124	37	defining	define	VERB
ejpam-6226	124	38	properties	property	NOUN
ejpam-6226	124	39	with	with	ADP
ejpam-6226	124	40	supporting	support	VERB
ejpam-6226	124	41	examples	example	NOUN
ejpam-6226	124	42	.	.	PUNCT
ejpam-6226	125	1	subsection	subsection	NOUN
ejpam-6226	125	2	3.2	3.2	NUM
ejpam-6226	125	3	investigates	investigate	VERB
ejpam-6226	125	4	the	the	DET
ejpam-6226	125	5	structural	structural	ADJ
ejpam-6226	125	6	behavior	behavior	NOUN
ejpam-6226	125	7	of	of	ADP
ejpam-6226	125	8	these	these	DET
ejpam-6226	125	9	fink	fink	NOUN
ejpam-6226	125	10	-	-	PUNCT
ejpam-6226	125	11	is	be	AUX
ejpam-6226	125	12	under	under	ADP
ejpam-6226	125	13	intersection	intersection	NOUN
ejpam-6226	125	14	and	and	CCONJ
ejpam-6226	125	15	union	union	NOUN
ejpam-6226	125	16	operations	operation	NOUN
ejpam-6226	125	17	,	,	PUNCT
ejpam-6226	125	18	showing	show	VERB
ejpam-6226	125	19	that	that	SCONJ
ejpam-6226	125	20	intersection	intersection	NOUN
ejpam-6226	125	21	preserves	preserve	VERB
ejpam-6226	125	22	the	the	DET
ejpam-6226	125	23	implicative	implicative	ADJ
ejpam-6226	125	24	properties	property	NOUN
ejpam-6226	125	25	,	,	PUNCT
ejpam-6226	125	26	whereas	whereas	SCONJ
ejpam-6226	125	27	union	union	NOUN
ejpam-6226	125	28	may	may	AUX
ejpam-6226	125	29	not	not	PART
ejpam-6226	125	30	.	.	PUNCT
ejpam-6226	126	1	finally	finally	ADV
ejpam-6226	126	2	,	,	PUNCT
ejpam-6226	126	3	subsection	subsection	NOUN
ejpam-6226	126	4	3.3	3.3	NUM
ejpam-6226	126	5	addresses	address	NOUN
ejpam-6226	126	6	the	the	DET
ejpam-6226	126	7	behavior	behavior	NOUN
ejpam-6226	126	8	of	of	ADP
ejpam-6226	126	9	fuzzy	fuzzy	ADJ
ejpam-6226	126	10	implicative	implicative	ADJ
ejpam-6226	126	11	and	and	CCONJ
ejpam-6226	126	12	positive	positive	ADJ
ejpam-6226	126	13	implicative	implicative	ADJ
ejpam-6226	126	14	ink	ink	NOUN
ejpam-6226	126	15	-	-	PUNCT
ejpam-6226	126	16	ideals	ideal	NOUN
ejpam-6226	126	17	under	under	ADP
ejpam-6226	126	18	homomorphic	homomorphic	ADJ
ejpam-6226	126	19	pre	pre	NOUN
ejpam-6226	126	20	-	-	NOUN
ejpam-6226	126	21	images	image	NOUN
ejpam-6226	126	22	,	,	PUNCT
ejpam-6226	126	23	proving	prove	VERB
ejpam-6226	126	24	that	that	SCONJ
ejpam-6226	126	25	these	these	DET
ejpam-6226	126	26	properties	property	NOUN
ejpam-6226	126	27	are	be	AUX
ejpam-6226	126	28	preserved	preserve	VERB
ejpam-6226	126	29	under	under	ADP
ejpam-6226	126	30	ink	ink	NOUN
ejpam-6226	126	31	-	-	PUNCT
ejpam-6226	126	32	algebra	algebra	NOUN
ejpam-6226	126	33	homomorphisms	homomorphism	NOUN
ejpam-6226	126	34	.	.	PUNCT
ejpam-6226	127	1	these	these	DET
ejpam-6226	127	2	results	result	NOUN
ejpam-6226	127	3	establish	establish	VERB
ejpam-6226	127	4	a	a	DET
ejpam-6226	127	5	robust	robust	ADJ
ejpam-6226	127	6	algebraic	algebraic	ADJ
ejpam-6226	127	7	foundation	foundation	NOUN
ejpam-6226	127	8	for	for	ADP
ejpam-6226	127	9	the	the	DET
ejpam-6226	127	10	study	study	NOUN
ejpam-6226	127	11	of	of	ADP
ejpam-6226	127	12	fuzzy	fuzzy	ADJ
ejpam-6226	127	13	logical	logical	ADJ
ejpam-6226	127	14	structures	structure	NOUN
ejpam-6226	127	15	in	in	ADP
ejpam-6226	127	16	ink	ink	NOUN
ejpam-6226	127	17	-	-	PUNCT
ejpam-6226	127	18	algebras	algebra	NOUN
ejpam-6226	127	19	and	and	CCONJ
ejpam-6226	127	20	contribute	contribute	VERB
ejpam-6226	127	21	to	to	ADP
ejpam-6226	127	22	their	their	PRON
ejpam-6226	127	23	potential	potential	ADJ
ejpam-6226	127	24	applications	application	NOUN
ejpam-6226	127	25	in	in	ADP
ejpam-6226	127	26	uncertainty	uncertainty	NOUN
ejpam-6226	127	27	modeling	model	VERB
ejpam-6226	127	28	and	and	CCONJ
ejpam-6226	127	29	reasoning	reasoning	NOUN
ejpam-6226	127	30	.	.	PUNCT
ejpam-6226	128	1	3.1	3.1	NUM
ejpam-6226	128	2	.	.	PUNCT
ejpam-6226	128	3	fuzzy	fuzzy	ADJ
ejpam-6226	128	4	implicative	implicative	ADJ
ejpam-6226	128	5	and	and	CCONJ
ejpam-6226	128	6	positive	positive	ADJ
ejpam-6226	128	7	implicative	implicative	ADJ
ejpam-6226	128	8	ink	ink	NOUN
ejpam-6226	128	9	-	-	PUNCT
ejpam-6226	128	10	ideals	ideal	NOUN
ejpam-6226	128	11	of	of	ADP
ejpam-6226	128	12	ink	ink	NOUN
ejpam-6226	128	13	-	-	PUNCT
ejpam-6226	128	14	algebras	algebras	NOUN
ejpam-6226	128	15	building	building	NOUN
ejpam-6226	128	16	upon	upon	SCONJ
ejpam-6226	128	17	the	the	DET
ejpam-6226	128	18	foundational	foundational	ADJ
ejpam-6226	128	19	notions	notion	NOUN
ejpam-6226	128	20	of	of	ADP
ejpam-6226	128	21	fink	fink	PROPN
ejpam-6226	128	22	-	-	PUNCT
ejpam-6226	128	23	is	be	AUX
ejpam-6226	128	24	introduced	introduce	VERB
ejpam-6226	128	25	in	in	ADP
ejpam-6226	128	26	the	the	DET
ejpam-6226	128	27	previous	previous	ADJ
ejpam-6226	128	28	section	section	NOUN
ejpam-6226	128	29	,	,	PUNCT
ejpam-6226	128	30	we	we	PRON
ejpam-6226	128	31	now	now	ADV
ejpam-6226	128	32	define	define	VERB
ejpam-6226	128	33	and	and	CCONJ
ejpam-6226	128	34	explore	explore	VERB
ejpam-6226	128	35	two	two	NUM
ejpam-6226	128	36	novel	novel	ADJ
ejpam-6226	128	37	types	type	NOUN
ejpam-6226	128	38	of	of	ADP
ejpam-6226	128	39	fink	fink	NOUN
ejpam-6226	128	40	-	-	PUNCT
ejpam-6226	128	41	is	be	AUX
ejpam-6226	128	42	:	:	PUNCT
ejpam-6226	128	43	fmink	fmink	ADJ
ejpam-6226	128	44	-	-	PUNCT
ejpam-6226	128	45	is	be	AUX
ejpam-6226	128	46	and	and	CCONJ
ejpam-6226	128	47	fpmink	fpmink	NOUN
ejpam-6226	128	48	-	-	PUNCT
ejpam-6226	128	49	is	be	AUX
ejpam-6226	128	50	in	in	ADP
ejpam-6226	128	51	the	the	DET
ejpam-6226	128	52	setting	setting	NOUN
ejpam-6226	128	53	of	of	ADP
ejpam-6226	128	54	ink	ink	NOUN
ejpam-6226	128	55	-	-	PUNCT
ejpam-6226	128	56	algebras	algebras	PROPN
ejpam-6226	128	57	.	.	PUNCT
ejpam-6226	129	1	these	these	DET
ejpam-6226	129	2	concepts	concept	NOUN
ejpam-6226	129	3	are	be	AUX
ejpam-6226	129	4	natural	natural	ADJ
ejpam-6226	129	5	extensions	extension	NOUN
ejpam-6226	129	6	of	of	ADP
ejpam-6226	129	7	classical	classical	ADJ
ejpam-6226	129	8	implicative	implicative	ADJ
ejpam-6226	129	9	structures	structure	NOUN
ejpam-6226	129	10	and	and	CCONJ
ejpam-6226	129	11	aim	aim	VERB
ejpam-6226	129	12	to	to	PART
ejpam-6226	129	13	incorporate	incorporate	VERB
ejpam-6226	129	14	reasoning	reasoning	NOUN
ejpam-6226	129	15	under	under	ADP
ejpam-6226	129	16	uncertainty	uncertainty	NOUN
ejpam-6226	129	17	within	within	ADP
ejpam-6226	129	18	algebraic	algebraic	ADJ
ejpam-6226	129	19	systems	system	NOUN
ejpam-6226	129	20	.	.	PUNCT
ejpam-6226	130	1	we	we	PRON
ejpam-6226	130	2	provide	provide	VERB
ejpam-6226	130	3	precise	precise	ADJ
ejpam-6226	130	4	definitions	definition	NOUN
ejpam-6226	130	5	,	,	PUNCT
ejpam-6226	130	6	discuss	discuss	VERB
ejpam-6226	130	7	their	their	PRON
ejpam-6226	130	8	algebraic	algebraic	ADJ
ejpam-6226	130	9	properties	property	NOUN
ejpam-6226	130	10	,	,	PUNCT
ejpam-6226	130	11	and	and	CCONJ
ejpam-6226	130	12	illustrate	illustrate	VERB
ejpam-6226	130	13	them	they	PRON
ejpam-6226	130	14	through	through	ADP
ejpam-6226	130	15	relevant	relevant	ADJ
ejpam-6226	130	16	examples	example	NOUN
ejpam-6226	130	17	.	.	PUNCT
ejpam-6226	131	1	the	the	DET
ejpam-6226	131	2	aim	aim	NOUN
ejpam-6226	131	3	is	be	AUX
ejpam-6226	131	4	to	to	PART
ejpam-6226	131	5	deepen	deepen	VERB
ejpam-6226	131	6	the	the	DET
ejpam-6226	131	7	understanding	understanding	NOUN
ejpam-6226	131	8	of	of	ADP
ejpam-6226	131	9	logical	logical	ADJ
ejpam-6226	131	10	implications	implication	NOUN
ejpam-6226	131	11	in	in	ADP
ejpam-6226	131	12	fuzzy	fuzzy	ADJ
ejpam-6226	131	13	settings	setting	NOUN
ejpam-6226	131	14	and	and	CCONJ
ejpam-6226	131	15	establish	establish	VERB
ejpam-6226	131	16	the	the	DET
ejpam-6226	131	17	groundwork	groundwork	NOUN
ejpam-6226	131	18	for	for	ADP
ejpam-6226	131	19	further	further	ADJ
ejpam-6226	131	20	results	result	NOUN
ejpam-6226	131	21	concerning	concern	VERB
ejpam-6226	131	22	intersection	intersection	NOUN
ejpam-6226	131	23	properties	property	NOUN
ejpam-6226	131	24	and	and	CCONJ
ejpam-6226	131	25	homomorphic	homomorphic	ADJ
ejpam-6226	131	26	behavior	behavior	NOUN
ejpam-6226	131	27	of	of	ADP
ejpam-6226	131	28	these	these	DET
ejpam-6226	131	29	ideals	ideal	NOUN
ejpam-6226	131	30	.	.	PUNCT
ejpam-6226	132	1	definition	definition	NOUN
ejpam-6226	132	2	11	11	NUM
ejpam-6226	132	3	.	.	PUNCT
ejpam-6226	133	1	an	an	DET
ejpam-6226	133	2	ink	ink	NOUN
ejpam-6226	133	3	-	-	PUNCT
ejpam-6226	133	4	algebra	algebra	NOUN
ejpam-6226	133	5	i	i	PRON
ejpam-6226	133	6	is	be	AUX
ejpam-6226	133	7	called	call	VERB
ejpam-6226	133	8	an	an	DET
ejpam-6226	133	9	implicative	implicative	ADJ
ejpam-6226	133	10	ink	ink	NOUN
ejpam-6226	133	11	-	-	PUNCT
ejpam-6226	133	12	algebra	algebra	NOUN
ejpam-6226	133	13	if	if	SCONJ
ejpam-6226	133	14	it	it	PRON
ejpam-6226	133	15	satisfies	satisfy	VERB
ejpam-6226	133	16	the	the	DET
ejpam-6226	133	17	following	follow	VERB
ejpam-6226	133	18	condition	condition	NOUN
ejpam-6226	133	19	:	:	PUNCT
ejpam-6226	133	20	(	(	PUNCT
ejpam-6226	133	21	a1	a1	NOUN
ejpam-6226	133	22	)	)	PUNCT
ejpam-6226	133	23	ϵ	ϵ	NOUN
ejpam-6226	133	24	•	•	NOUN
ejpam-6226	133	25	(	(	PUNCT
ejpam-6226	133	26	ξ	ξ	PROPN
ejpam-6226	133	27	•	•	NUM
ejpam-6226	133	28	ϵ	ϵ	NOUN
ejpam-6226	133	29	)	)	PUNCT
ejpam-6226	133	30	=	=	SYM
ejpam-6226	133	31	ϵ,∀ϵ	ϵ,∀ϵ	PROPN
ejpam-6226	133	32	,	,	PUNCT
ejpam-6226	133	33	ξ	ξ	PROPN
ejpam-6226	133	34	∈	∈	PROPN
ejpam-6226	133	35	i.	i.	PROPN
ejpam-6226	133	36	r.	r.	PROPN
ejpam-6226	133	37	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	133	38	et	et	PROPN
ejpam-6226	133	39	al	al	PROPN
ejpam-6226	133	40	.	.	PUNCT
ejpam-6226	133	41	/	/	SYM
ejpam-6226	133	42	eur	eur	PROPN
ejpam-6226	133	43	.	.	PUNCT
ejpam-6226	134	1	j.	j.	PROPN
ejpam-6226	134	2	pure	pure	PROPN
ejpam-6226	134	3	appl	appl	PROPN
ejpam-6226	134	4	.	.	PROPN
ejpam-6226	134	5	math	math	PROPN
ejpam-6226	134	6	,	,	PUNCT
ejpam-6226	134	7	18	18	NUM
ejpam-6226	134	8	(	(	PUNCT
ejpam-6226	134	9	3	3	NUM
ejpam-6226	134	10	)	)	PUNCT
ejpam-6226	134	11	(	(	PUNCT
ejpam-6226	134	12	2025	2025	NUM
ejpam-6226	134	13	)	)	PUNCT
ejpam-6226	134	14	,	,	PUNCT
ejpam-6226	134	15	6226	6226	NUM
ejpam-6226	134	16	7	7	NUM
ejpam-6226	134	17	of	of	ADP
ejpam-6226	134	18	19	19	NUM
ejpam-6226	134	19	definition	definition	NOUN
ejpam-6226	134	20	12	12	NUM
ejpam-6226	134	21	.	.	PUNCT
ejpam-6226	135	1	an	an	DET
ejpam-6226	135	2	ink	ink	NOUN
ejpam-6226	135	3	-	-	PUNCT
ejpam-6226	135	4	algebra	algebra	NOUN
ejpam-6226	135	5	i	i	PRON
ejpam-6226	135	6	is	be	AUX
ejpam-6226	135	7	entitled	entitle	VERB
ejpam-6226	135	8	as	as	ADP
ejpam-6226	135	9	a	a	DET
ejpam-6226	135	10	positive	positive	ADJ
ejpam-6226	135	11	implicative	implicative	ADJ
ejpam-6226	135	12	ink	ink	NOUN
ejpam-6226	135	13	-	-	PUNCT
ejpam-6226	135	14	algebra	algebra	NOUN
ejpam-6226	135	15	if	if	SCONJ
ejpam-6226	135	16	it	it	PRON
ejpam-6226	135	17	satisfies	satisfy	VERB
ejpam-6226	135	18	the	the	DET
ejpam-6226	135	19	following	follow	VERB
ejpam-6226	135	20	condition	condition	NOUN
ejpam-6226	135	21	:	:	PUNCT
ejpam-6226	135	22	(	(	PUNCT
ejpam-6226	135	23	a2	a2	PROPN
ejpam-6226	135	24	)	)	PUNCT
ejpam-6226	135	25	(	(	PUNCT
ejpam-6226	135	26	ϵ	ϵ	PART
ejpam-6226	135	27	•	•	NUM
ejpam-6226	135	28	ς	ς	PROPN
ejpam-6226	135	29	)	)	PUNCT
ejpam-6226	135	30	•	•	NOUN
ejpam-6226	135	31	(	(	PUNCT
ejpam-6226	135	32	ξ	ξ	PROPN
ejpam-6226	135	33	•	•	NUM
ejpam-6226	135	34	ς	ς	NOUN
ejpam-6226	135	35	)	)	PUNCT
ejpam-6226	135	36	=	=	SYM
ejpam-6226	135	37	(	(	PUNCT
ejpam-6226	135	38	ϵ	ϵ	PART
ejpam-6226	135	39	•	•	NUM
ejpam-6226	135	40	ξ	ξ	NOUN
ejpam-6226	135	41	)	)	PUNCT
ejpam-6226	135	42	•	•	NUM
ejpam-6226	135	43	ς,∀ϵ	ς,∀ϵ	NUM
ejpam-6226	135	44	,	,	PUNCT
ejpam-6226	135	45	ξ	ξ	PROPN
ejpam-6226	135	46	,	,	PUNCT
ejpam-6226	135	47	ς	ς	PROPN
ejpam-6226	135	48	∈	∈	PROPN
ejpam-6226	135	49	i.	i.	NOUN
ejpam-6226	135	50	example	example	NOUN
ejpam-6226	135	51	1	1	X
ejpam-6226	135	52	.	.	X
ejpam-6226	136	1	consider	consider	VERB
ejpam-6226	136	2	an	an	DET
ejpam-6226	136	3	ink	ink	NOUN
ejpam-6226	136	4	-	-	PUNCT
ejpam-6226	136	5	algebra	algebra	NOUN
ejpam-6226	136	6	i	i	NOUN
ejpam-6226	136	7	=	=	PUNCT
ejpam-6226	136	8	{	{	PUNCT
ejpam-6226	136	9	0	0	NUM
ejpam-6226	136	10	,	,	PUNCT
ejpam-6226	136	11	ă	ă	PROPN
ejpam-6226	136	12	,	,	PUNCT
ejpam-6226	136	13	b̆	b̆	NOUN
ejpam-6226	136	14	,	,	PUNCT
ejpam-6226	136	15	c̆	c̆	NOUN
ejpam-6226	136	16	}	}	PUNCT
ejpam-6226	136	17	with	with	ADP
ejpam-6226	136	18	•	•	NOUN
ejpam-6226	136	19	as	as	ADP
ejpam-6226	136	20	the	the	DET
ejpam-6226	136	21	binary	binary	PROPN
ejpam-6226	136	22	operation	operation	NOUN
ejpam-6226	136	23	:	:	PUNCT
ejpam-6226	137	1	•	•	NOUN
ejpam-6226	137	2	0	0	NUM
ejpam-6226	137	3	ă	ă	PROPN
ejpam-6226	137	4	b̆	b̆	CCONJ
ejpam-6226	137	5	c̆	c̆	ADV
ejpam-6226	137	6	0	0	NUM
ejpam-6226	137	7	0	0	NUM
ejpam-6226	137	8	0	0	NUM
ejpam-6226	137	9	0	0	NUM
ejpam-6226	137	10	0	0	NUM
ejpam-6226	137	11	ă	ă	NOUN
ejpam-6226	137	12	ă	ă	NOUN
ejpam-6226	137	13	0	0	NUM
ejpam-6226	137	14	ă	ă	PROPN
ejpam-6226	137	15	ă	ă	PROPN
ejpam-6226	137	16	b̆	b̆	NOUN
ejpam-6226	137	17	b̆	b̆	NOUN
ejpam-6226	137	18	b̆	b̆	NOUN
ejpam-6226	137	19	0	0	NUM
ejpam-6226	137	20	b̆	b̆	NOUN
ejpam-6226	137	21	c̆	c̆	ADV
ejpam-6226	138	1	c̆	c̆	ADV
ejpam-6226	139	1	c̆	c̆	ADV
ejpam-6226	140	1	c̆	c̆	ADV
ejpam-6226	140	2	0	0	PUNCT
ejpam-6226	141	1	then	then	ADV
ejpam-6226	141	2	by	by	ADP
ejpam-6226	141	3	routine	routine	ADJ
ejpam-6226	141	4	calculations	calculation	NOUN
ejpam-6226	141	5	,	,	PUNCT
ejpam-6226	141	6	the	the	DET
ejpam-6226	141	7	ink	ink	NOUN
ejpam-6226	141	8	-	-	PUNCT
ejpam-6226	141	9	algebra	algebra	NOUN
ejpam-6226	141	10	(	(	PUNCT
ejpam-6226	141	11	i	i	PROPN
ejpam-6226	141	12	,	,	PUNCT
ejpam-6226	141	13	•	•	PROPN
ejpam-6226	141	14	,	,	PUNCT
ejpam-6226	141	15	0	0	NUM
ejpam-6226	141	16	)	)	PUNCT
ejpam-6226	141	17	is	be	AUX
ejpam-6226	141	18	an	an	DET
ejpam-6226	141	19	mink	mink	NOUN
ejpam-6226	141	20	-	-	PUNCT
ejpam-6226	141	21	i	i	PROPN
ejpam-6226	141	22	and	and	CCONJ
ejpam-6226	141	23	a	a	DET
ejpam-6226	141	24	pmink	pmink	NOUN
ejpam-6226	141	25	-	-	PUNCT
ejpam-6226	141	26	i.	i.	NOUN
ejpam-6226	141	27	definition	definition	NOUN
ejpam-6226	141	28	13	13	NUM
ejpam-6226	141	29	.	.	PUNCT
ejpam-6226	142	1	a	a	DET
ejpam-6226	142	2	subset	subset	NOUN
ejpam-6226	142	3	s	s	NOUN
ejpam-6226	142	4	of	of	ADP
ejpam-6226	142	5	an	an	DET
ejpam-6226	142	6	ink	ink	NOUN
ejpam-6226	142	7	-	-	PUNCT
ejpam-6226	142	8	algebra	algebra	NOUN
ejpam-6226	142	9	i	i	PRON
ejpam-6226	142	10	is	be	AUX
ejpam-6226	142	11	entitled	entitle	VERB
ejpam-6226	142	12	as	as	ADP
ejpam-6226	142	13	an	an	DET
ejpam-6226	142	14	implicative	implicative	ADJ
ejpam-6226	142	15	ink	ink	NOUN
ejpam-6226	142	16	-	-	PUNCT
ejpam-6226	142	17	ideal	ideal	NOUN
ejpam-6226	142	18	(	(	PUNCT
ejpam-6226	142	19	mink	mink	NOUN
ejpam-6226	142	20	-	-	PUNCT
ejpam-6226	142	21	i	i	PROPN
ejpam-6226	142	22	)	)	PUNCT
ejpam-6226	142	23	of	of	ADP
ejpam-6226	142	24	i	i	PRON
ejpam-6226	142	25	if	if	SCONJ
ejpam-6226	142	26	it	it	PRON
ejpam-6226	142	27	gratifies	gratify	VERB
ejpam-6226	142	28	(	(	PUNCT
ejpam-6226	142	29	b1	b1	NOUN
ejpam-6226	142	30	)	)	PUNCT
ejpam-6226	142	31	and	and	CCONJ
ejpam-6226	142	32	(	(	PUNCT
ejpam-6226	142	33	b3	b3	PROPN
ejpam-6226	142	34	)	)	PUNCT
ejpam-6226	142	35	(	(	PUNCT
ejpam-6226	142	36	(	(	PUNCT
ejpam-6226	142	37	ϵ	ϵ	PART
ejpam-6226	142	38	•	•	PRON
ejpam-6226	142	39	(	(	PUNCT
ejpam-6226	142	40	ξ	ξ	PROPN
ejpam-6226	142	41	•	•	NUM
ejpam-6226	142	42	ϵ	ϵ	NOUN
ejpam-6226	142	43	)	)	PUNCT
ejpam-6226	142	44	)	)	PUNCT
ejpam-6226	142	45	•	•	ADP
ejpam-6226	142	46	ς	ς	PROPN
ejpam-6226	142	47	∈	∈	PROPN
ejpam-6226	142	48	s	s	PART
ejpam-6226	142	49	,	,	PUNCT
ejpam-6226	142	50	ς	ς	PROPN
ejpam-6226	142	51	∈	∈	PROPN
ejpam-6226	142	52	s	s	PART
ejpam-6226	142	53	⇒	⇒	NOUN
ejpam-6226	142	54	ϵ	ϵ	X
ejpam-6226	142	55	∈	∈	PROPN
ejpam-6226	143	1	s,∀ϵ	s,∀ϵ	PROPN
ejpam-6226	143	2	,	,	PUNCT
ejpam-6226	143	3	ξ	ξ	PROPN
ejpam-6226	143	4	,	,	PUNCT
ejpam-6226	143	5	ς	ς	PROPN
ejpam-6226	143	6	∈	∈	PROPN
ejpam-6226	143	7	i.	i.	NOUN
ejpam-6226	143	8	proposition	proposition	NOUN
ejpam-6226	143	9	1	1	NUM
ejpam-6226	143	10	.	.	PUNCT
ejpam-6226	144	1	let	let	VERB
ejpam-6226	144	2	i1	i1	PROPN
ejpam-6226	144	3	and	and	CCONJ
ejpam-6226	144	4	i2	i2	PROPN
ejpam-6226	144	5	be	be	VERB
ejpam-6226	144	6	ink	ink	NOUN
ejpam-6226	144	7	-	-	PUNCT
ejpam-6226	144	8	ideals	ideal	NOUN
ejpam-6226	144	9	of	of	ADP
ejpam-6226	144	10	an	an	DET
ejpam-6226	144	11	ink	ink	NOUN
ejpam-6226	144	12	-	-	PUNCT
ejpam-6226	144	13	algebra	algebra	NOUN
ejpam-6226	144	14	i	i	PRON
ejpam-6226	144	15	with	with	ADP
ejpam-6226	144	16	i1	i1	PROPN
ejpam-6226	144	17	⊆	⊆	NUM
ejpam-6226	144	18	i2	i2	PROPN
ejpam-6226	144	19	.	.	PUNCT
ejpam-6226	145	1	if	if	SCONJ
ejpam-6226	145	2	i1	i1	PROPN
ejpam-6226	145	3	is	be	AUX
ejpam-6226	145	4	an	an	DET
ejpam-6226	145	5	mink	mink	NOUN
ejpam-6226	145	6	-	-	PUNCT
ejpam-6226	145	7	i	i	PROPN
ejpam-6226	145	8	,	,	PUNCT
ejpam-6226	145	9	then	then	ADV
ejpam-6226	145	10	i2	i2	PROPN
ejpam-6226	145	11	is	be	AUX
ejpam-6226	145	12	also	also	ADV
ejpam-6226	145	13	an	an	DET
ejpam-6226	145	14	mink	mink	NOUN
ejpam-6226	145	15	-	-	PUNCT
ejpam-6226	145	16	i.	i.	NOUN
ejpam-6226	145	17	definition	definition	NOUN
ejpam-6226	145	18	14	14	NUM
ejpam-6226	145	19	.	.	PUNCT
ejpam-6226	146	1	a	a	DET
ejpam-6226	146	2	subset	subset	NOUN
ejpam-6226	146	3	s	s	NOUN
ejpam-6226	146	4	of	of	ADP
ejpam-6226	146	5	an	an	DET
ejpam-6226	146	6	ink	ink	NOUN
ejpam-6226	146	7	-	-	PUNCT
ejpam-6226	146	8	algebra	algebra	NOUN
ejpam-6226	146	9	i	i	PRON
ejpam-6226	146	10	is	be	AUX
ejpam-6226	146	11	entitled	entitle	VERB
ejpam-6226	146	12	as	as	ADP
ejpam-6226	146	13	a	a	DET
ejpam-6226	146	14	positive	positive	ADJ
ejpam-6226	146	15	implicative	implicative	ADJ
ejpam-6226	146	16	inkideal	inkideal	NOUN
ejpam-6226	146	17	(	(	PUNCT
ejpam-6226	146	18	pmink	pmink	NOUN
ejpam-6226	146	19	-	-	PUNCT
ejpam-6226	146	20	i	i	NOUN
ejpam-6226	146	21	)	)	PUNCT
ejpam-6226	146	22	of	of	ADP
ejpam-6226	146	23	i	i	PRON
ejpam-6226	146	24	if	if	SCONJ
ejpam-6226	146	25	it	it	PRON
ejpam-6226	146	26	satisfies	satisfy	VERB
ejpam-6226	146	27	(	(	PUNCT
ejpam-6226	146	28	b1	b1	NOUN
ejpam-6226	146	29	)	)	PUNCT
ejpam-6226	146	30	and	and	CCONJ
ejpam-6226	146	31	(	(	PUNCT
ejpam-6226	146	32	b4	b4	NOUN
ejpam-6226	146	33	)	)	PUNCT
ejpam-6226	146	34	(	(	PUNCT
ejpam-6226	146	35	ϵ	ϵ	PART
ejpam-6226	146	36	•	•	NUM
ejpam-6226	146	37	ξ	ξ	NOUN
ejpam-6226	146	38	)	)	PUNCT
ejpam-6226	146	39	•	•	NUM
ejpam-6226	146	40	ς	ς	PROPN
ejpam-6226	146	41	∈	∈	PROPN
ejpam-6226	146	42	s	s	PROPN
ejpam-6226	146	43	,	,	PUNCT
ejpam-6226	146	44	ξ	ξ	PROPN
ejpam-6226	146	45	•	•	NOUN
ejpam-6226	146	46	ς	ς	PROPN
ejpam-6226	146	47	∈	∈	PROPN
ejpam-6226	146	48	s	s	PART
ejpam-6226	146	49	⇒	⇒	NOUN
ejpam-6226	146	50	ϵ	ϵ	X
ejpam-6226	146	51	•	•	NOUN
ejpam-6226	146	52	ς	ς	PROPN
ejpam-6226	146	53	∈	∈	PROPN
ejpam-6226	146	54	s	s	NOUN
ejpam-6226	146	55	,	,	PUNCT
ejpam-6226	146	56	∀ϵ	∀ϵ	PROPN
ejpam-6226	146	57	,	,	PUNCT
ejpam-6226	146	58	ξ	ξ	PROPN
ejpam-6226	146	59	,	,	PUNCT
ejpam-6226	146	60	ς	ς	PROPN
ejpam-6226	146	61	∈	∈	PROPN
ejpam-6226	146	62	i.	i.	NOUN
ejpam-6226	146	63	example	example	NOUN
ejpam-6226	146	64	2	2	X
ejpam-6226	146	65	.	.	X
ejpam-6226	146	66	consider	consider	VERB
ejpam-6226	146	67	a	a	DET
ejpam-6226	146	68	subset	subset	NOUN
ejpam-6226	146	69	s	s	X
ejpam-6226	146	70	=	=	X
ejpam-6226	146	71	{	{	PUNCT
ejpam-6226	146	72	0	0	PROPN
ejpam-6226	146	73	,	,	PUNCT
ejpam-6226	146	74	ă	ă	NOUN
ejpam-6226	146	75	,	,	PUNCT
ejpam-6226	146	76	b̆	b̆	NOUN
ejpam-6226	146	77	}	}	PUNCT
ejpam-6226	146	78	of	of	ADP
ejpam-6226	146	79	an	an	DET
ejpam-6226	146	80	ink	ink	NOUN
ejpam-6226	146	81	-	-	PUNCT
ejpam-6226	146	82	algebra	algebra	NOUN
ejpam-6226	146	83	i	i	PRON
ejpam-6226	146	84	defined	define	VERB
ejpam-6226	146	85	in	in	ADP
ejpam-6226	146	86	example	example	NOUN
ejpam-6226	146	87	1	1	X
ejpam-6226	146	88	.	.	PUNCT
ejpam-6226	147	1	then	then	ADV
ejpam-6226	147	2	,	,	PUNCT
ejpam-6226	147	3	the	the	DET
ejpam-6226	147	4	subset	subset	NOUN
ejpam-6226	147	5	(	(	PUNCT
ejpam-6226	147	6	s	s	NOUN
ejpam-6226	147	7	,	,	PUNCT
ejpam-6226	147	8	•	•	NOUN
ejpam-6226	147	9	,	,	PUNCT
ejpam-6226	147	10	0	0	NUM
ejpam-6226	147	11	)	)	PUNCT
ejpam-6226	147	12	is	be	AUX
ejpam-6226	147	13	an	an	DET
ejpam-6226	147	14	mink	mink	NOUN
ejpam-6226	147	15	-	-	PUNCT
ejpam-6226	147	16	i	i	PROPN
ejpam-6226	147	17	and	and	CCONJ
ejpam-6226	147	18	a	a	DET
ejpam-6226	147	19	pmink	pmink	NOUN
ejpam-6226	147	20	-	-	PUNCT
ejpam-6226	147	21	i	i	PRON
ejpam-6226	147	22	of	of	ADP
ejpam-6226	147	23	(	(	PUNCT
ejpam-6226	147	24	i	i	PROPN
ejpam-6226	147	25	,	,	PUNCT
ejpam-6226	147	26	•	•	PROPN
ejpam-6226	147	27	,	,	PUNCT
ejpam-6226	147	28	0	0	NUM
ejpam-6226	147	29	)	)	PUNCT
ejpam-6226	147	30	.	.	PUNCT
ejpam-6226	148	1	definition	definition	NOUN
ejpam-6226	148	2	15	15	NUM
ejpam-6226	148	3	.	.	PUNCT
ejpam-6226	149	1	an	an	DET
ejpam-6226	149	2	fs	fs	ADP
ejpam-6226	149	3	g	g	NOUN
ejpam-6226	149	4	in	in	ADP
ejpam-6226	149	5	an	an	DET
ejpam-6226	149	6	ink	ink	NOUN
ejpam-6226	149	7	-	-	PUNCT
ejpam-6226	149	8	algebra	algebra	NOUN
ejpam-6226	149	9	i	i	PRON
ejpam-6226	149	10	is	be	AUX
ejpam-6226	149	11	entitled	entitle	VERB
ejpam-6226	149	12	as	as	ADP
ejpam-6226	149	13	a	a	DET
ejpam-6226	149	14	fuzzy	fuzzy	ADJ
ejpam-6226	149	15	implicative	implicative	ADJ
ejpam-6226	149	16	ink	ink	NOUN
ejpam-6226	149	17	-	-	PUNCT
ejpam-6226	149	18	ideal	ideal	NOUN
ejpam-6226	149	19	(	(	PUNCT
ejpam-6226	149	20	fmink	fmink	NOUN
ejpam-6226	149	21	-	-	PUNCT
ejpam-6226	149	22	i	i	NOUN
ejpam-6226	149	23	)	)	PUNCT
ejpam-6226	149	24	of	of	ADP
ejpam-6226	149	25	i	i	PRON
ejpam-6226	149	26	if	if	SCONJ
ejpam-6226	149	27	it	it	PRON
ejpam-6226	149	28	gratifies	gratify	VERB
ejpam-6226	149	29	(	(	PUNCT
ejpam-6226	149	30	c1	c1	PROPN
ejpam-6226	149	31	)	)	PUNCT
ejpam-6226	149	32	and	and	CCONJ
ejpam-6226	149	33	(	(	PUNCT
ejpam-6226	149	34	c3	c3	PROPN
ejpam-6226	149	35	)	)	PUNCT
ejpam-6226	149	36	g(ϵ	g(ϵ	PROPN
ejpam-6226	149	37	)	)	PUNCT
ejpam-6226	149	38	≥	≥	NOUN
ejpam-6226	150	1	min{g((ϵ	min{g((ϵ	ADV
ejpam-6226	150	2	•	•	NOUN
ejpam-6226	150	3	(	(	PUNCT
ejpam-6226	150	4	ξ	ξ	NOUN
ejpam-6226	150	5	•	•	NUM
ejpam-6226	150	6	ϵ	ϵ	NOUN
ejpam-6226	150	7	)	)	PUNCT
ejpam-6226	150	8	)	)	PUNCT
ejpam-6226	150	9	•	•	ADP
ejpam-6226	150	10	ς	ς	PROPN
ejpam-6226	150	11	)	)	PUNCT
ejpam-6226	150	12	,	,	PUNCT
ejpam-6226	150	13	g(ς	g(ς	PROPN
ejpam-6226	150	14	)	)	PUNCT
ejpam-6226	150	15	}	}	PUNCT
ejpam-6226	150	16	,	,	PUNCT
ejpam-6226	150	17	∀ϵ	∀ϵ	PROPN
ejpam-6226	150	18	,	,	PUNCT
ejpam-6226	150	19	ξ	ξ	PROPN
ejpam-6226	150	20	,	,	PUNCT
ejpam-6226	150	21	ς	ς	PROPN
ejpam-6226	150	22	∈	∈	PROPN
ejpam-6226	150	23	i.	i.	NOUN
ejpam-6226	150	24	definition	definition	NOUN
ejpam-6226	150	25	16	16	NUM
ejpam-6226	150	26	.	.	PUNCT
ejpam-6226	151	1	an	an	DET
ejpam-6226	151	2	fs	fs	ADP
ejpam-6226	151	3	g	g	NOUN
ejpam-6226	151	4	in	in	ADP
ejpam-6226	151	5	an	an	DET
ejpam-6226	151	6	ink	ink	NOUN
ejpam-6226	151	7	-	-	PUNCT
ejpam-6226	151	8	algebra	algebra	NOUN
ejpam-6226	151	9	i	i	PRON
ejpam-6226	151	10	is	be	AUX
ejpam-6226	151	11	entitled	entitle	VERB
ejpam-6226	151	12	as	as	ADP
ejpam-6226	151	13	a	a	DET
ejpam-6226	151	14	fuzzy	fuzzy	ADJ
ejpam-6226	151	15	positive	positive	ADJ
ejpam-6226	151	16	implicative	implicative	ADJ
ejpam-6226	151	17	ink	ink	NOUN
ejpam-6226	151	18	-	-	PUNCT
ejpam-6226	151	19	ideal	ideal	NOUN
ejpam-6226	151	20	(	(	PUNCT
ejpam-6226	151	21	fpmink	fpmink	NOUN
ejpam-6226	151	22	-	-	PUNCT
ejpam-6226	151	23	i	i	NOUN
ejpam-6226	151	24	)	)	PUNCT
ejpam-6226	151	25	of	of	ADP
ejpam-6226	151	26	i	i	PRON
ejpam-6226	151	27	if	if	SCONJ
ejpam-6226	151	28	it	it	PRON
ejpam-6226	151	29	gratifies	gratify	VERB
ejpam-6226	151	30	(	(	PUNCT
ejpam-6226	151	31	c1	c1	PROPN
ejpam-6226	151	32	)	)	PUNCT
ejpam-6226	151	33	and	and	CCONJ
ejpam-6226	151	34	(	(	PUNCT
ejpam-6226	151	35	c4	c4	NOUN
ejpam-6226	151	36	)	)	PUNCT
ejpam-6226	151	37	g(ϵ	g(ϵ	PROPN
ejpam-6226	151	38	•	•	NUM
ejpam-6226	151	39	ς	ς	PROPN
ejpam-6226	151	40	)	)	PUNCT
ejpam-6226	151	41	≥	≥	NOUN
ejpam-6226	152	1	min{g((ϵ	min{g((ϵ	NOUN
ejpam-6226	152	2	•	•	NUM
ejpam-6226	152	3	ξ	ξ	NOUN
ejpam-6226	152	4	)	)	PUNCT
ejpam-6226	152	5	•	•	NUM
ejpam-6226	152	6	ς	ς	PROPN
ejpam-6226	152	7	)	)	PUNCT
ejpam-6226	152	8	,	,	PUNCT
ejpam-6226	152	9	g(ξ	g(ξ	PROPN
ejpam-6226	152	10	•	•	NUM
ejpam-6226	152	11	ς	ς	PROPN
ejpam-6226	152	12	)	)	PUNCT
ejpam-6226	152	13	}	}	PUNCT
ejpam-6226	152	14	,	,	PUNCT
ejpam-6226	152	15	∀ϵ	∀ϵ	PROPN
ejpam-6226	152	16	,	,	PUNCT
ejpam-6226	152	17	ξ	ξ	PROPN
ejpam-6226	152	18	,	,	PUNCT
ejpam-6226	152	19	ς	ς	PROPN
ejpam-6226	152	20	∈	∈	PROPN
ejpam-6226	152	21	i.	i.	PROPN
ejpam-6226	152	22	example	example	NOUN
ejpam-6226	152	23	3	3	X
ejpam-6226	152	24	.	.	X
ejpam-6226	152	25	consider	consider	VERB
ejpam-6226	152	26	an	an	DET
ejpam-6226	152	27	ink	ink	NOUN
ejpam-6226	152	28	-	-	PUNCT
ejpam-6226	152	29	algebra	algebra	NOUN
ejpam-6226	152	30	i	i	NOUN
ejpam-6226	152	31	=	=	PUNCT
ejpam-6226	152	32	{	{	PUNCT
ejpam-6226	152	33	0	0	NUM
ejpam-6226	152	34	,	,	PUNCT
ejpam-6226	152	35	ă	ă	NOUN
ejpam-6226	152	36	,	,	PUNCT
ejpam-6226	152	37	b̆	b̆	NOUN
ejpam-6226	152	38	}	}	PUNCT
ejpam-6226	152	39	with	with	ADP
ejpam-6226	152	40	the	the	DET
ejpam-6226	152	41	following	follow	VERB
ejpam-6226	152	42	cayley	cayley	ADJ
ejpam-6226	152	43	table	table	NOUN
ejpam-6226	152	44	:	:	PUNCT
ejpam-6226	152	45	•	•	NOUN
ejpam-6226	152	46	0	0	X
ejpam-6226	152	47	ă	ă	PROPN
ejpam-6226	152	48	b̆	b̆	NOUN
ejpam-6226	152	49	0	0	NUM
ejpam-6226	152	50	0	0	NUM
ejpam-6226	152	51	0	0	NUM
ejpam-6226	152	52	0	0	NUM
ejpam-6226	153	1	ă	ă	NOUN
ejpam-6226	153	2	ă	ă	NOUN
ejpam-6226	153	3	0	0	PUNCT
ejpam-6226	153	4	ă	ă	PROPN
ejpam-6226	153	5	b̆	b̆	NOUN
ejpam-6226	153	6	b̆	b̆	NOUN
ejpam-6226	153	7	b̆	b̆	NOUN
ejpam-6226	153	8	0	0	NUM
ejpam-6226	153	9	define	define	VERB
ejpam-6226	153	10	an	an	DET
ejpam-6226	153	11	fs	fs	NOUN
ejpam-6226	153	12	g	g	NOUN
ejpam-6226	153	13	:	:	PUNCT
ejpam-6226	153	14	i	i	PRON
ejpam-6226	153	15	→	→	PUNCT
ejpam-6226	154	1	[	[	X
ejpam-6226	154	2	0	0	NUM
ejpam-6226	154	3	,	,	PUNCT
ejpam-6226	154	4	1	1	NUM
ejpam-6226	154	5	]	]	PUNCT
ejpam-6226	154	6	by	by	ADP
ejpam-6226	154	7	0	0	NUM
ejpam-6226	154	8	ă	ă	PROPN
ejpam-6226	154	9	b̆	b̆	NOUN
ejpam-6226	154	10	g	g	PROPN
ejpam-6226	154	11	0.6	0.6	NUM
ejpam-6226	154	12	0.4	0.4	NUM
ejpam-6226	154	13	0.4	0.4	NUM
ejpam-6226	154	14	r.	r.	PROPN
ejpam-6226	154	15	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	155	1	et	et	PROPN
ejpam-6226	155	2	al	al	PROPN
ejpam-6226	155	3	.	.	PUNCT
ejpam-6226	155	4	/	/	SYM
ejpam-6226	155	5	eur	eur	PROPN
ejpam-6226	155	6	.	.	PUNCT
ejpam-6226	156	1	j.	j.	PROPN
ejpam-6226	156	2	pure	pure	PROPN
ejpam-6226	156	3	appl	appl	PROPN
ejpam-6226	156	4	.	.	PROPN
ejpam-6226	156	5	math	math	PROPN
ejpam-6226	156	6	,	,	PUNCT
ejpam-6226	156	7	18	18	NUM
ejpam-6226	156	8	(	(	PUNCT
ejpam-6226	156	9	3	3	NUM
ejpam-6226	156	10	)	)	PUNCT
ejpam-6226	156	11	(	(	PUNCT
ejpam-6226	156	12	2025	2025	NUM
ejpam-6226	156	13	)	)	PUNCT
ejpam-6226	156	14	,	,	PUNCT
ejpam-6226	156	15	6226	6226	NUM
ejpam-6226	156	16	8	8	NUM
ejpam-6226	156	17	of	of	ADP
ejpam-6226	156	18	19	19	NUM
ejpam-6226	156	19	then	then	ADV
ejpam-6226	156	20	,	,	PUNCT
ejpam-6226	156	21	g	g	PROPN
ejpam-6226	156	22	is	be	AUX
ejpam-6226	156	23	an	an	DET
ejpam-6226	156	24	fmink	fmink	NOUN
ejpam-6226	156	25	-	-	PUNCT
ejpam-6226	156	26	i	i	PRON
ejpam-6226	156	27	and	and	CCONJ
ejpam-6226	156	28	an	an	DET
ejpam-6226	156	29	fpmink	fpmink	NOUN
ejpam-6226	156	30	-	-	PUNCT
ejpam-6226	156	31	i	i	PRON
ejpam-6226	156	32	of	of	ADP
ejpam-6226	156	33	i.	i.	PROPN
ejpam-6226	156	34	theorem	theorem	PROPN
ejpam-6226	156	35	3	3	X
ejpam-6226	156	36	.	.	PUNCT
ejpam-6226	157	1	every	every	DET
ejpam-6226	157	2	fmink	fmink	NOUN
ejpam-6226	157	3	-	-	PUNCT
ejpam-6226	157	4	i	i	PRON
ejpam-6226	157	5	of	of	ADP
ejpam-6226	157	6	an	an	DET
ejpam-6226	157	7	ink	ink	NOUN
ejpam-6226	157	8	-	-	PUNCT
ejpam-6226	157	9	algebra	algebra	NOUN
ejpam-6226	157	10	i	i	PRON
ejpam-6226	157	11	is	be	AUX
ejpam-6226	157	12	an	an	DET
ejpam-6226	157	13	fink	fink	NOUN
ejpam-6226	157	14	-	-	PUNCT
ejpam-6226	157	15	i	i	PROPN
ejpam-6226	157	16	of	of	ADP
ejpam-6226	157	17	i.	i.	PROPN
ejpam-6226	157	18	proof	proof	PROPN
ejpam-6226	157	19	.	.	PUNCT
ejpam-6226	158	1	let	let	VERB
ejpam-6226	158	2	g	g	PRON
ejpam-6226	158	3	be	be	AUX
ejpam-6226	158	4	an	an	DET
ejpam-6226	158	5	fmink	fmink	NOUN
ejpam-6226	158	6	-	-	PUNCT
ejpam-6226	158	7	i	i	PRON
ejpam-6226	158	8	of	of	ADP
ejpam-6226	158	9	an	an	DET
ejpam-6226	158	10	ink	ink	NOUN
ejpam-6226	158	11	-	-	PUNCT
ejpam-6226	158	12	algebra	algebra	NOUN
ejpam-6226	158	13	i.	i.	NOUN
ejpam-6226	158	14	substituting	substitute	VERB
ejpam-6226	158	15	ξ	ξ	PROPN
ejpam-6226	158	16	=	=	SYM
ejpam-6226	158	17	0	0	NUM
ejpam-6226	158	18	in	in	ADP
ejpam-6226	158	19	(	(	PUNCT
ejpam-6226	158	20	c3	c3	PROPN
ejpam-6226	158	21	)	)	PUNCT
ejpam-6226	158	22	.	.	PUNCT
ejpam-6226	159	1	then	then	ADV
ejpam-6226	159	2	∀ϵ	∀ϵ	PROPN
ejpam-6226	159	3	,	,	PUNCT
ejpam-6226	159	4	ς	ς	PROPN
ejpam-6226	159	5	∈	∈	PROPN
ejpam-6226	159	6	i	i	PRON
ejpam-6226	159	7	,	,	PUNCT
ejpam-6226	159	8	g(ϵ	g(ϵ	PROPN
ejpam-6226	159	9	)	)	PUNCT
ejpam-6226	159	10	≥	≥	NOUN
ejpam-6226	160	1	min{g((ϵ	min{g((ϵ	ADV
ejpam-6226	160	2	•	•	NOUN
ejpam-6226	160	3	(	(	PUNCT
ejpam-6226	160	4	0	0	NUM
ejpam-6226	160	5	•	•	NUM
ejpam-6226	160	6	ϵ	ϵ	NOUN
ejpam-6226	160	7	)	)	PUNCT
ejpam-6226	160	8	)	)	PUNCT
ejpam-6226	160	9	•	•	ADP
ejpam-6226	160	10	ς	ς	PROPN
ejpam-6226	160	11	)	)	PUNCT
ejpam-6226	160	12	,	,	PUNCT
ejpam-6226	160	13	g(ς	g(ς	PROPN
ejpam-6226	160	14	)	)	PUNCT
ejpam-6226	160	15	}	}	PUNCT
ejpam-6226	161	1	=	=	PUNCT
ejpam-6226	161	2	min{g((ϵ	min{g((ϵ	NOUN
ejpam-6226	161	3	•	•	NOUN
ejpam-6226	161	4	0	0	NUM
ejpam-6226	161	5	)	)	PUNCT
ejpam-6226	161	6	•	•	NUM
ejpam-6226	161	7	ς	ς	NOUN
ejpam-6226	161	8	)	)	PUNCT
ejpam-6226	161	9	,	,	PUNCT
ejpam-6226	161	10	g(ς	g(ς	PROPN
ejpam-6226	161	11	)	)	PUNCT
ejpam-6226	161	12	}	}	PUNCT
ejpam-6226	162	1	=	=	PUNCT
ejpam-6226	162	2	min{g(ϵ	min{g(ϵ	PROPN
ejpam-6226	162	3	•	•	NUM
ejpam-6226	162	4	ς	ς	NOUN
ejpam-6226	162	5	)	)	PUNCT
ejpam-6226	162	6	,	,	PUNCT
ejpam-6226	162	7	g(ς	g(ς	PROPN
ejpam-6226	162	8	)	)	PUNCT
ejpam-6226	162	9	}	}	PUNCT
ejpam-6226	162	10	.	.	PUNCT
ejpam-6226	163	1	this	this	PRON
ejpam-6226	163	2	shows	show	VERB
ejpam-6226	163	3	that	that	SCONJ
ejpam-6226	163	4	g	g	PROPN
ejpam-6226	163	5	gratifies	gratify	VERB
ejpam-6226	163	6	(	(	PUNCT
ejpam-6226	163	7	c2	c2	PROPN
ejpam-6226	163	8	)	)	PUNCT
ejpam-6226	163	9	.	.	PUNCT
ejpam-6226	164	1	combining	combine	VERB
ejpam-6226	164	2	(	(	PUNCT
ejpam-6226	164	3	c1	c1	PROPN
ejpam-6226	164	4	)	)	PUNCT
ejpam-6226	164	5	,	,	PUNCT
ejpam-6226	164	6	g	g	PROPN
ejpam-6226	164	7	is	be	AUX
ejpam-6226	164	8	an	an	DET
ejpam-6226	164	9	fink	fink	NOUN
ejpam-6226	164	10	-	-	PUNCT
ejpam-6226	164	11	i	i	PROPN
ejpam-6226	164	12	of	of	ADP
ejpam-6226	164	13	i.	i.	PROPN
ejpam-6226	164	14	note	note	PROPN
ejpam-6226	164	15	:	:	PUNCT
ejpam-6226	164	16	every	every	DET
ejpam-6226	164	17	fmink	fmink	NOUN
ejpam-6226	164	18	-	-	PUNCT
ejpam-6226	164	19	i	i	PRON
ejpam-6226	164	20	of	of	ADP
ejpam-6226	164	21	i	i	PRON
ejpam-6226	164	22	is	be	AUX
ejpam-6226	164	23	an	an	DET
ejpam-6226	164	24	fink	fink	NOUN
ejpam-6226	164	25	-	-	PUNCT
ejpam-6226	164	26	i	i	PRON
ejpam-6226	164	27	of	of	ADP
ejpam-6226	164	28	i	i	PRON
ejpam-6226	164	29	,	,	PUNCT
ejpam-6226	164	30	but	but	CCONJ
ejpam-6226	164	31	the	the	DET
ejpam-6226	164	32	converse	converse	NOUN
ejpam-6226	164	33	is	be	AUX
ejpam-6226	164	34	not	not	PART
ejpam-6226	164	35	true	true	ADJ
ejpam-6226	164	36	.	.	PUNCT
ejpam-6226	165	1	example	example	NOUN
ejpam-6226	165	2	4	4	NUM
ejpam-6226	165	3	.	.	X
ejpam-6226	166	1	consider	consider	VERB
ejpam-6226	166	2	an	an	DET
ejpam-6226	166	3	ink	ink	NOUN
ejpam-6226	166	4	-	-	PUNCT
ejpam-6226	166	5	algebra	algebra	NOUN
ejpam-6226	166	6	i	i	NOUN
ejpam-6226	166	7	=	=	PUNCT
ejpam-6226	166	8	{	{	PUNCT
ejpam-6226	166	9	0	0	NUM
ejpam-6226	166	10	,	,	PUNCT
ejpam-6226	166	11	ă	ă	NOUN
ejpam-6226	166	12	,	,	PUNCT
ejpam-6226	166	13	b̆	b̆	NOUN
ejpam-6226	166	14	}	}	PUNCT
ejpam-6226	166	15	with	with	ADP
ejpam-6226	166	16	the	the	DET
ejpam-6226	166	17	following	follow	VERB
ejpam-6226	166	18	cayley	cayley	ADJ
ejpam-6226	166	19	table	table	NOUN
ejpam-6226	166	20	:	:	PUNCT
ejpam-6226	166	21	•	•	NOUN
ejpam-6226	166	22	0	0	X
ejpam-6226	166	23	ă	ă	PROPN
ejpam-6226	166	24	b̆	b̆	NOUN
ejpam-6226	166	25	0	0	NUM
ejpam-6226	166	26	0	0	NUM
ejpam-6226	167	1	b̆	b̆	NOUN
ejpam-6226	167	2	ă	ă	NOUN
ejpam-6226	167	3	ă	ă	PROPN
ejpam-6226	167	4	ă	ă	PROPN
ejpam-6226	167	5	0	0	NUM
ejpam-6226	167	6	b̆	b̆	NOUN
ejpam-6226	167	7	b̆	b̆	NOUN
ejpam-6226	167	8	b̆	b̆	PROPN
ejpam-6226	167	9	ă	ă	PROPN
ejpam-6226	167	10	0	0	NUM
ejpam-6226	167	11	define	define	VERB
ejpam-6226	167	12	an	an	DET
ejpam-6226	167	13	fs	fs	NOUN
ejpam-6226	167	14	g	g	NOUN
ejpam-6226	167	15	:	:	PUNCT
ejpam-6226	167	16	i	i	PRON
ejpam-6226	167	17	→	→	PUNCT
ejpam-6226	168	1	[	[	X
ejpam-6226	168	2	0	0	NUM
ejpam-6226	168	3	,	,	PUNCT
ejpam-6226	168	4	1	1	NUM
ejpam-6226	168	5	]	]	PUNCT
ejpam-6226	168	6	by	by	ADP
ejpam-6226	168	7	0	0	NUM
ejpam-6226	168	8	ă	ă	PROPN
ejpam-6226	168	9	b̆	b̆	NOUN
ejpam-6226	168	10	g	g	PROPN
ejpam-6226	168	11	0.5	0.5	NUM
ejpam-6226	168	12	0.3	0.3	NUM
ejpam-6226	168	13	0.3	0.3	NUM
ejpam-6226	168	14	then	then	ADV
ejpam-6226	168	15	,	,	PUNCT
ejpam-6226	168	16	the	the	DET
ejpam-6226	168	17	above	above	ADJ
ejpam-6226	168	18	table	table	NOUN
ejpam-6226	168	19	satisfies	satisfy	VERB
ejpam-6226	168	20	the	the	DET
ejpam-6226	168	21	fink	fink	PROPN
ejpam-6226	168	22	-	-	PUNCT
ejpam-6226	168	23	i	i	PRON
ejpam-6226	168	24	conditions	condition	NOUN
ejpam-6226	168	25	but	but	CCONJ
ejpam-6226	168	26	not	not	PART
ejpam-6226	168	27	fmink	fmink	ADJ
ejpam-6226	168	28	-	-	PUNCT
ejpam-6226	168	29	i	i	PRON
ejpam-6226	168	30	of	of	ADP
ejpam-6226	168	31	i.	i.	PROPN
ejpam-6226	168	32	theorem	theorem	VERB
ejpam-6226	168	33	4	4	NUM
ejpam-6226	168	34	.	.	PUNCT
ejpam-6226	169	1	if	if	SCONJ
ejpam-6226	169	2	i	i	PRON
ejpam-6226	169	3	is	be	AUX
ejpam-6226	169	4	an	an	DET
ejpam-6226	169	5	implicative	implicative	ADJ
ejpam-6226	169	6	ink	ink	NOUN
ejpam-6226	169	7	-	-	PUNCT
ejpam-6226	169	8	algebra	algebra	NOUN
ejpam-6226	169	9	,	,	PUNCT
ejpam-6226	169	10	then	then	ADV
ejpam-6226	169	11	every	every	DET
ejpam-6226	169	12	fink	fink	NOUN
ejpam-6226	169	13	-	-	PUNCT
ejpam-6226	169	14	i	i	PRON
ejpam-6226	169	15	of	of	ADP
ejpam-6226	169	16	i	i	PRON
ejpam-6226	169	17	is	be	AUX
ejpam-6226	169	18	an	an	DET
ejpam-6226	169	19	fmink	fmink	NOUN
ejpam-6226	169	20	-	-	PUNCT
ejpam-6226	169	21	i	i	PRON
ejpam-6226	169	22	of	of	ADP
ejpam-6226	169	23	i.	i.	PROPN
ejpam-6226	169	24	proof	proof	PROPN
ejpam-6226	169	25	.	.	PUNCT
ejpam-6226	170	1	suppose	suppose	VERB
ejpam-6226	170	2	i	i	PRON
ejpam-6226	170	3	is	be	AUX
ejpam-6226	170	4	an	an	DET
ejpam-6226	170	5	implicative	implicative	ADJ
ejpam-6226	170	6	ink	ink	NOUN
ejpam-6226	170	7	-	-	PUNCT
ejpam-6226	170	8	algebra	algebra	NOUN
ejpam-6226	170	9	and	and	CCONJ
ejpam-6226	170	10	g	g	NOUN
ejpam-6226	170	11	is	be	AUX
ejpam-6226	170	12	an	an	DET
ejpam-6226	170	13	fink	fink	NOUN
ejpam-6226	170	14	-	-	PUNCT
ejpam-6226	170	15	i	i	PROPN
ejpam-6226	170	16	of	of	ADP
ejpam-6226	170	17	i.	i.	PROPN
ejpam-6226	170	18	then	then	ADV
ejpam-6226	170	19	by	by	ADP
ejpam-6226	170	20	(	(	PUNCT
ejpam-6226	170	21	c2	c2	PROPN
ejpam-6226	170	22	)	)	PUNCT
ejpam-6226	170	23	,	,	PUNCT
ejpam-6226	170	24	g(ϵ	g(ϵ	PROPN
ejpam-6226	170	25	)	)	PUNCT
ejpam-6226	170	26	≥	≥	NOUN
ejpam-6226	170	27	min{g(ϵ	min{g(ϵ	VERB
ejpam-6226	170	28	•	•	NUM
ejpam-6226	170	29	ς	ς	NOUN
ejpam-6226	170	30	)	)	PUNCT
ejpam-6226	170	31	,	,	PUNCT
ejpam-6226	170	32	g(ς	g(ς	PROPN
ejpam-6226	170	33	)	)	PUNCT
ejpam-6226	170	34	}	}	PUNCT
ejpam-6226	171	1	=	=	PUNCT
ejpam-6226	171	2	min{g((ϵ	min{g((ϵ	NOUN
ejpam-6226	172	1	•	•	NOUN
ejpam-6226	172	2	(	(	PUNCT
ejpam-6226	172	3	ξ	ξ	NOUN
ejpam-6226	172	4	•	•	NUM
ejpam-6226	172	5	ϵ	ϵ	NOUN
ejpam-6226	172	6	)	)	PUNCT
ejpam-6226	172	7	)	)	PUNCT
ejpam-6226	172	8	•	•	ADP
ejpam-6226	172	9	ς	ς	PROPN
ejpam-6226	172	10	)	)	PUNCT
ejpam-6226	172	11	,	,	PUNCT
ejpam-6226	172	12	g(ς	g(ς	PROPN
ejpam-6226	172	13	)	)	PUNCT
ejpam-6226	172	14	}	}	PUNCT
ejpam-6226	172	15	,	,	PUNCT
ejpam-6226	172	16	∀ϵ	∀ϵ	PROPN
ejpam-6226	172	17	,	,	PUNCT
ejpam-6226	172	18	ξ	ξ	PROPN
ejpam-6226	172	19	,	,	PUNCT
ejpam-6226	172	20	ς	ς	PROPN
ejpam-6226	172	21	∈	∈	PROPN
ejpam-6226	172	22	i.	i.	NOUN
ejpam-6226	172	23	it	it	PRON
ejpam-6226	172	24	follows	follow	VERB
ejpam-6226	172	25	that	that	SCONJ
ejpam-6226	172	26	g	g	PROPN
ejpam-6226	172	27	is	be	AUX
ejpam-6226	172	28	an	an	DET
ejpam-6226	172	29	fmink	fmink	NOUN
ejpam-6226	172	30	-	-	PUNCT
ejpam-6226	172	31	i	i	PRON
ejpam-6226	172	32	of	of	ADP
ejpam-6226	172	33	i.	i.	PROPN
ejpam-6226	172	34	theorem	theorem	VERB
ejpam-6226	172	35	5	5	NUM
ejpam-6226	172	36	.	.	PUNCT
ejpam-6226	173	1	every	every	DET
ejpam-6226	173	2	fpmink	fpmink	NOUN
ejpam-6226	173	3	-	-	PUNCT
ejpam-6226	173	4	i	i	PRON
ejpam-6226	173	5	of	of	ADP
ejpam-6226	173	6	an	an	DET
ejpam-6226	173	7	ink	ink	NOUN
ejpam-6226	173	8	-	-	PUNCT
ejpam-6226	173	9	algebra	algebra	NOUN
ejpam-6226	173	10	i	i	PRON
ejpam-6226	173	11	is	be	AUX
ejpam-6226	173	12	an	an	DET
ejpam-6226	173	13	fink	fink	NOUN
ejpam-6226	173	14	-	-	PUNCT
ejpam-6226	173	15	i	i	PROPN
ejpam-6226	173	16	of	of	ADP
ejpam-6226	173	17	i.	i.	PROPN
ejpam-6226	173	18	proof	proof	PROPN
ejpam-6226	173	19	.	.	PUNCT
ejpam-6226	174	1	let	let	VERB
ejpam-6226	174	2	g	g	PRON
ejpam-6226	174	3	be	be	AUX
ejpam-6226	174	4	an	an	DET
ejpam-6226	174	5	fpmink	fpmink	NOUN
ejpam-6226	174	6	-	-	PUNCT
ejpam-6226	174	7	i	i	PRON
ejpam-6226	174	8	of	of	ADP
ejpam-6226	174	9	an	an	DET
ejpam-6226	174	10	ink	ink	NOUN
ejpam-6226	174	11	-	-	PUNCT
ejpam-6226	174	12	algebra	algebra	NOUN
ejpam-6226	174	13	i.	i.	NOUN
ejpam-6226	174	14	substitute	substitute	PROPN
ejpam-6226	174	15	ς	ς	PROPN
ejpam-6226	174	16	=	=	NOUN
ejpam-6226	174	17	0	0	NUM
ejpam-6226	174	18	in	in	ADP
ejpam-6226	174	19	(	(	PUNCT
ejpam-6226	174	20	c4	c4	NOUN
ejpam-6226	174	21	)	)	PUNCT
ejpam-6226	174	22	,	,	PUNCT
ejpam-6226	174	23	g(ϵ•0	g(ϵ•0	VERB
ejpam-6226	174	24	)	)	PUNCT
ejpam-6226	174	25	≥	≥	X
ejpam-6226	175	1	min{g((ϵ	min{g((ϵ	NOUN
ejpam-6226	175	2	•	•	NUM
ejpam-6226	175	3	ξ	ξ	NOUN
ejpam-6226	175	4	)	)	PUNCT
ejpam-6226	175	5	•	•	NOUN
ejpam-6226	175	6	0	0	NUM
ejpam-6226	175	7	)	)	PUNCT
ejpam-6226	175	8	,	,	PUNCT
ejpam-6226	175	9	g(ξ	g(ξ	PROPN
ejpam-6226	175	10	•	•	NUM
ejpam-6226	175	11	0)},∀ϵ	0)},∀ϵ	PROPN
ejpam-6226	175	12	,	,	PUNCT
ejpam-6226	175	13	ξ	ξ	PROPN
ejpam-6226	175	14	∈	∈	PROPN
ejpam-6226	175	15	i	i	PRON
ejpam-6226	175	16	by	by	ADP
ejpam-6226	175	17	ink-3	ink-3	NOUN
ejpam-6226	175	18	.	.	PUNCT
ejpam-6226	176	1	thus	thus	ADV
ejpam-6226	176	2	,	,	PUNCT
ejpam-6226	176	3	g(ϵ	g(ϵ	PROPN
ejpam-6226	176	4	)	)	PUNCT
ejpam-6226	176	5	≥	≥	NOUN
ejpam-6226	176	6	min{g(ϵ	min{g(ϵ	VERB
ejpam-6226	176	7	•	•	NUM
ejpam-6226	176	8	ξ	ξ	NOUN
ejpam-6226	176	9	)	)	PUNCT
ejpam-6226	176	10	,	,	PUNCT
ejpam-6226	176	11	g(ξ	g(ξ	PROPN
ejpam-6226	176	12	)	)	PUNCT
ejpam-6226	176	13	}	}	PUNCT
ejpam-6226	176	14	.	.	PUNCT
ejpam-6226	177	1	this	this	PRON
ejpam-6226	177	2	shows	show	VERB
ejpam-6226	177	3	that	that	SCONJ
ejpam-6226	177	4	g	g	PROPN
ejpam-6226	177	5	satisfies	satisfie	NOUN
ejpam-6226	177	6	(	(	PUNCT
ejpam-6226	177	7	c2	c2	PROPN
ejpam-6226	177	8	)	)	PUNCT
ejpam-6226	177	9	.	.	PUNCT
ejpam-6226	178	1	combining	combine	VERB
ejpam-6226	178	2	(	(	PUNCT
ejpam-6226	178	3	c1	c1	PROPN
ejpam-6226	178	4	)	)	PUNCT
ejpam-6226	178	5	,	,	PUNCT
ejpam-6226	178	6	g	g	PROPN
ejpam-6226	178	7	is	be	AUX
ejpam-6226	178	8	an	an	DET
ejpam-6226	178	9	fink	fink	NOUN
ejpam-6226	178	10	-	-	PUNCT
ejpam-6226	178	11	i	i	PROPN
ejpam-6226	178	12	of	of	ADP
ejpam-6226	178	13	i.	i.	NOUN
ejpam-6226	178	14	the	the	DET
ejpam-6226	178	15	following	follow	VERB
ejpam-6226	178	16	example	example	NOUN
ejpam-6226	178	17	shows	show	VERB
ejpam-6226	178	18	that	that	SCONJ
ejpam-6226	178	19	the	the	DET
ejpam-6226	178	20	converse	converse	NOUN
ejpam-6226	178	21	of	of	ADP
ejpam-6226	178	22	theorem	theorem	NOUN
ejpam-6226	178	23	5	5	NUM
ejpam-6226	178	24	does	do	AUX
ejpam-6226	178	25	not	not	PART
ejpam-6226	178	26	hold	hold	VERB
ejpam-6226	178	27	.	.	PUNCT
ejpam-6226	178	28	example	example	NOUN
ejpam-6226	179	1	5	5	NUM
ejpam-6226	179	2	.	.	X
ejpam-6226	179	3	consider	consider	VERB
ejpam-6226	179	4	an	an	DET
ejpam-6226	179	5	ink	ink	NOUN
ejpam-6226	179	6	-	-	PUNCT
ejpam-6226	179	7	algebra	algebra	NOUN
ejpam-6226	179	8	i	i	NOUN
ejpam-6226	179	9	=	=	PUNCT
ejpam-6226	179	10	{	{	PUNCT
ejpam-6226	179	11	0	0	NUM
ejpam-6226	179	12	,	,	PUNCT
ejpam-6226	179	13	ă	ă	PROPN
ejpam-6226	179	14	,	,	PUNCT
ejpam-6226	179	15	b̆	b̆	NOUN
ejpam-6226	179	16	,	,	PUNCT
ejpam-6226	179	17	c̆	c̆	NOUN
ejpam-6226	179	18	}	}	PUNCT
ejpam-6226	179	19	with	with	ADP
ejpam-6226	179	20	the	the	DET
ejpam-6226	179	21	following	follow	VERB
ejpam-6226	179	22	cayley	cayley	ADJ
ejpam-6226	179	23	table	table	NOUN
ejpam-6226	179	24	:	:	PUNCT
ejpam-6226	179	25	•	•	NOUN
ejpam-6226	179	26	0	0	NUM
ejpam-6226	179	27	ă	ă	PROPN
ejpam-6226	179	28	b̆	b̆	CCONJ
ejpam-6226	179	29	c̆	c̆	ADV
ejpam-6226	179	30	0	0	NUM
ejpam-6226	179	31	0	0	NUM
ejpam-6226	180	1	ă	ă	NOUN
ejpam-6226	180	2	b̆	b̆	NOUN
ejpam-6226	180	3	c̆	c̆	ADP
ejpam-6226	180	4	ă	ă	PROPN
ejpam-6226	180	5	ă	ă	PROPN
ejpam-6226	180	6	0	0	PUNCT
ejpam-6226	181	1	c̆	c̆	ADV
ejpam-6226	181	2	b̆	b̆	NOUN
ejpam-6226	181	3	b̆	b̆	NOUN
ejpam-6226	182	1	b̆	b̆	NOUN
ejpam-6226	182	2	c̆	c̆	ADV
ejpam-6226	182	3	0	0	PUNCT
ejpam-6226	183	1	ă	ă	PROPN
ejpam-6226	183	2	c̆	c̆	ADV
ejpam-6226	183	3	c̆	c̆	ADV
ejpam-6226	183	4	b̆	b̆	NOUN
ejpam-6226	183	5	ă	ă	PROPN
ejpam-6226	183	6	0	0	PUNCT
ejpam-6226	184	1	r.	r.	PROPN
ejpam-6226	184	2	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	184	3	et	et	PROPN
ejpam-6226	184	4	al	al	PROPN
ejpam-6226	184	5	.	.	PUNCT
ejpam-6226	184	6	/	/	SYM
ejpam-6226	184	7	eur	eur	PROPN
ejpam-6226	184	8	.	.	PUNCT
ejpam-6226	185	1	j.	j.	PROPN
ejpam-6226	185	2	pure	pure	PROPN
ejpam-6226	185	3	appl	appl	PROPN
ejpam-6226	185	4	.	.	PROPN
ejpam-6226	185	5	math	math	PROPN
ejpam-6226	185	6	,	,	PUNCT
ejpam-6226	185	7	18	18	NUM
ejpam-6226	185	8	(	(	PUNCT
ejpam-6226	185	9	3	3	NUM
ejpam-6226	185	10	)	)	PUNCT
ejpam-6226	185	11	(	(	PUNCT
ejpam-6226	185	12	2025	2025	NUM
ejpam-6226	185	13	)	)	PUNCT
ejpam-6226	185	14	,	,	PUNCT
ejpam-6226	185	15	6226	6226	NUM
ejpam-6226	185	16	9	9	NUM
ejpam-6226	185	17	of	of	ADP
ejpam-6226	185	18	19	19	NUM
ejpam-6226	185	19	define	define	VERB
ejpam-6226	185	20	an	an	DET
ejpam-6226	185	21	fs	fs	NOUN
ejpam-6226	185	22	g	g	NOUN
ejpam-6226	185	23	:	:	PUNCT
ejpam-6226	185	24	i	i	PRON
ejpam-6226	185	25	→	→	PUNCT
ejpam-6226	186	1	[	[	X
ejpam-6226	186	2	0	0	NUM
ejpam-6226	186	3	,	,	PUNCT
ejpam-6226	186	4	1	1	NUM
ejpam-6226	186	5	]	]	PUNCT
ejpam-6226	186	6	by	by	ADP
ejpam-6226	186	7	0	0	NUM
ejpam-6226	186	8	ă	ă	PROPN
ejpam-6226	186	9	b̆	b̆	ADV
ejpam-6226	186	10	c̆	c̆	ADV
ejpam-6226	186	11	g	g	PROPN
ejpam-6226	186	12	0.5	0.5	NUM
ejpam-6226	186	13	0.3	0.3	NUM
ejpam-6226	186	14	0.3	0.3	NUM
ejpam-6226	186	15	0.5	0.5	NUM
ejpam-6226	186	16	then	then	ADV
ejpam-6226	186	17	,	,	PUNCT
ejpam-6226	186	18	the	the	DET
ejpam-6226	186	19	above	above	ADJ
ejpam-6226	186	20	table	table	NOUN
ejpam-6226	186	21	satisfies	satisfy	VERB
ejpam-6226	186	22	the	the	DET
ejpam-6226	186	23	fink	fink	PROPN
ejpam-6226	186	24	-	-	PUNCT
ejpam-6226	186	25	i	i	PRON
ejpam-6226	186	26	conditions	condition	NOUN
ejpam-6226	186	27	but	but	CCONJ
ejpam-6226	186	28	not	not	PART
ejpam-6226	186	29	the	the	DET
ejpam-6226	186	30	fpmink	fpmink	NOUN
ejpam-6226	186	31	-	-	PUNCT
ejpam-6226	186	32	i	i	PRON
ejpam-6226	186	33	of	of	ADP
ejpam-6226	186	34	i.	i.	PROPN
ejpam-6226	186	35	3.2	3.2	NUM
ejpam-6226	186	36	.	.	PUNCT
ejpam-6226	187	1	intersection	intersection	NOUN
ejpam-6226	187	2	of	of	ADP
ejpam-6226	187	3	fuzzy	fuzzy	ADJ
ejpam-6226	187	4	implicative	implicative	ADJ
ejpam-6226	187	5	and	and	CCONJ
ejpam-6226	187	6	fuzzy	fuzzy	ADJ
ejpam-6226	187	7	positive	positive	ADJ
ejpam-6226	187	8	implicative	implicative	ADJ
ejpam-6226	187	9	inkideals	inkideal	NOUN
ejpam-6226	187	10	of	of	ADP
ejpam-6226	187	11	ink	ink	NOUN
ejpam-6226	187	12	-	-	PUNCT
ejpam-6226	187	13	algebras	algebras	NOUN
ejpam-6226	187	14	after	after	ADP
ejpam-6226	187	15	introducing	introduce	VERB
ejpam-6226	187	16	fmink	fmink	NOUN
ejpam-6226	187	17	-	-	PUNCT
ejpam-6226	187	18	is	be	AUX
ejpam-6226	187	19	and	and	CCONJ
ejpam-6226	187	20	fpmink	fpmink	NOUN
ejpam-6226	187	21	-	-	PUNCT
ejpam-6226	187	22	is	be	AUX
ejpam-6226	187	23	,	,	PUNCT
ejpam-6226	187	24	it	it	PRON
ejpam-6226	187	25	is	be	AUX
ejpam-6226	187	26	natural	natural	ADJ
ejpam-6226	187	27	to	to	PART
ejpam-6226	187	28	investigate	investigate	VERB
ejpam-6226	187	29	their	their	PRON
ejpam-6226	187	30	behavior	behavior	NOUN
ejpam-6226	187	31	under	under	ADP
ejpam-6226	187	32	set	set	NOUN
ejpam-6226	187	33	-	-	PUNCT
ejpam-6226	187	34	theoretic	theoretic	NOUN
ejpam-6226	187	35	operations	operation	NOUN
ejpam-6226	187	36	.	.	PUNCT
ejpam-6226	188	1	in	in	ADP
ejpam-6226	188	2	this	this	DET
ejpam-6226	188	3	subsection	subsection	NOUN
ejpam-6226	188	4	,	,	PUNCT
ejpam-6226	188	5	we	we	PRON
ejpam-6226	188	6	analyze	analyze	VERB
ejpam-6226	188	7	the	the	DET
ejpam-6226	188	8	intersection	intersection	NOUN
ejpam-6226	188	9	and	and	CCONJ
ejpam-6226	188	10	union	union	NOUN
ejpam-6226	188	11	of	of	ADP
ejpam-6226	188	12	fmink	fmink	NOUN
ejpam-6226	188	13	-	-	PUNCT
ejpam-6226	188	14	is	be	AUX
ejpam-6226	188	15	and	and	CCONJ
ejpam-6226	188	16	fpmink	fpmink	NOUN
ejpam-6226	188	17	-	-	PUNCT
ejpam-6226	188	18	is	be	AUX
ejpam-6226	188	19	.	.	PUNCT
ejpam-6226	189	1	we	we	PRON
ejpam-6226	189	2	demonstrate	demonstrate	VERB
ejpam-6226	189	3	that	that	SCONJ
ejpam-6226	189	4	the	the	DET
ejpam-6226	189	5	intersection	intersection	NOUN
ejpam-6226	189	6	of	of	ADP
ejpam-6226	189	7	any	any	DET
ejpam-6226	189	8	two	two	NUM
ejpam-6226	189	9	fmink	fmink	NOUN
ejpam-6226	189	10	-	-	PUNCT
ejpam-6226	189	11	is	be	AUX
ejpam-6226	189	12	(	(	PUNCT
ejpam-6226	189	13	respectively	respectively	ADV
ejpam-6226	189	14	,	,	PUNCT
ejpam-6226	189	15	fpmink	fpmink	NOUN
ejpam-6226	189	16	-	-	PUNCT
ejpam-6226	189	17	is	be	AUX
ejpam-6226	189	18	)	)	PUNCT
ejpam-6226	189	19	yields	yield	VERB
ejpam-6226	189	20	another	another	DET
ejpam-6226	189	21	ideal	ideal	NOUN
ejpam-6226	189	22	of	of	ADP
ejpam-6226	189	23	the	the	DET
ejpam-6226	189	24	same	same	ADJ
ejpam-6226	189	25	type	type	NOUN
ejpam-6226	189	26	,	,	PUNCT
ejpam-6226	189	27	thus	thus	ADV
ejpam-6226	189	28	proving	prove	VERB
ejpam-6226	189	29	the	the	DET
ejpam-6226	189	30	closure	closure	NOUN
ejpam-6226	189	31	property	property	NOUN
ejpam-6226	189	32	under	under	ADP
ejpam-6226	189	33	intersection	intersection	NOUN
ejpam-6226	189	34	.	.	PUNCT
ejpam-6226	190	1	however	however	ADV
ejpam-6226	190	2	,	,	PUNCT
ejpam-6226	190	3	through	through	ADP
ejpam-6226	190	4	counterexamples	counterexample	NOUN
ejpam-6226	190	5	,	,	PUNCT
ejpam-6226	190	6	we	we	PRON
ejpam-6226	190	7	also	also	ADV
ejpam-6226	190	8	show	show	VERB
ejpam-6226	190	9	that	that	SCONJ
ejpam-6226	190	10	such	such	ADJ
ejpam-6226	190	11	closure	closure	NOUN
ejpam-6226	190	12	does	do	AUX
ejpam-6226	190	13	not	not	PART
ejpam-6226	190	14	hold	hold	VERB
ejpam-6226	190	15	in	in	ADP
ejpam-6226	190	16	general	general	ADJ
ejpam-6226	190	17	for	for	ADP
ejpam-6226	190	18	union	union	NOUN
ejpam-6226	190	19	.	.	PUNCT
ejpam-6226	191	1	these	these	DET
ejpam-6226	191	2	results	result	NOUN
ejpam-6226	191	3	highlight	highlight	VERB
ejpam-6226	191	4	the	the	DET
ejpam-6226	191	5	structural	structural	ADJ
ejpam-6226	191	6	stability	stability	NOUN
ejpam-6226	191	7	of	of	ADP
ejpam-6226	191	8	fmink	fmink	ADJ
ejpam-6226	191	9	-	-	PUNCT
ejpam-6226	191	10	i	i	PRON
ejpam-6226	191	11	and	and	CCONJ
ejpam-6226	191	12	fpmink	fpmink	NOUN
ejpam-6226	191	13	-	-	PUNCT
ejpam-6226	191	14	i	i	PRON
ejpam-6226	191	15	under	under	ADP
ejpam-6226	191	16	intersection	intersection	NOUN
ejpam-6226	191	17	,	,	PUNCT
ejpam-6226	191	18	while	while	SCONJ
ejpam-6226	191	19	also	also	ADV
ejpam-6226	191	20	identifying	identify	VERB
ejpam-6226	191	21	the	the	DET
ejpam-6226	191	22	limitations	limitation	NOUN
ejpam-6226	191	23	of	of	ADP
ejpam-6226	191	24	union	union	NOUN
ejpam-6226	191	25	in	in	ADP
ejpam-6226	191	26	preserving	preserve	VERB
ejpam-6226	191	27	implicative	implicative	ADJ
ejpam-6226	191	28	properties	property	NOUN
ejpam-6226	191	29	.	.	PUNCT
ejpam-6226	192	1	theorem	theorem	VERB
ejpam-6226	192	2	6	6	NUM
ejpam-6226	192	3	.	.	PUNCT
ejpam-6226	193	1	let	let	VERB
ejpam-6226	193	2	g	g	NOUN
ejpam-6226	193	3	and	and	CCONJ
ejpam-6226	193	4	h	h	NOUN
ejpam-6226	193	5	be	be	VERB
ejpam-6226	193	6	two	two	NUM
ejpam-6226	193	7	fmink	fmink	NOUN
ejpam-6226	193	8	-	-	PUNCT
ejpam-6226	193	9	is	be	AUX
ejpam-6226	193	10	of	of	ADP
ejpam-6226	193	11	an	an	DET
ejpam-6226	193	12	ink	ink	NOUN
ejpam-6226	193	13	-	-	PUNCT
ejpam-6226	193	14	algebra	algebra	NOUN
ejpam-6226	193	15	i.	i.	NOUN
ejpam-6226	193	16	then	then	ADV
ejpam-6226	193	17	g	g	PROPN
ejpam-6226	193	18	∩	∩	ADJ
ejpam-6226	193	19	h	h	NOUN
ejpam-6226	193	20	is	be	AUX
ejpam-6226	193	21	also	also	ADV
ejpam-6226	193	22	an	an	DET
ejpam-6226	193	23	fmink	fmink	NOUN
ejpam-6226	193	24	-	-	PUNCT
ejpam-6226	193	25	i	i	PRON
ejpam-6226	193	26	of	of	ADP
ejpam-6226	193	27	i.	i.	PROPN
ejpam-6226	193	28	proof	proof	PROPN
ejpam-6226	193	29	.	.	PUNCT
ejpam-6226	194	1	let	let	VERB
ejpam-6226	194	2	ϵ	ϵ	PRON
ejpam-6226	194	3	,	,	PUNCT
ejpam-6226	194	4	ξ	ξ	PROPN
ejpam-6226	194	5	,	,	PUNCT
ejpam-6226	194	6	ς	ς	PROPN
ejpam-6226	194	7	∈	∈	PROPN
ejpam-6226	194	8	i.	i.	NOUN
ejpam-6226	194	9	then	then	ADV
ejpam-6226	194	10	(	(	PUNCT
ejpam-6226	194	11	g	g	PROPN
ejpam-6226	194	12	∩	∩	NOUN
ejpam-6226	194	13	h)(ϵ	h)(ϵ	PRON
ejpam-6226	194	14	)	)	PUNCT
ejpam-6226	194	15	=	=	SYM
ejpam-6226	194	16	min{g(ϵ	min{g(ϵ	PROPN
ejpam-6226	194	17	)	)	PUNCT
ejpam-6226	194	18	,	,	PUNCT
ejpam-6226	194	19	h(ϵ	h(ϵ	PROPN
ejpam-6226	194	20	)	)	PUNCT
ejpam-6226	194	21	}	}	PUNCT
ejpam-6226	194	22	≥	≥	AUX
ejpam-6226	194	23	min{min{g((ϵ	min{min{g((ϵ	NOUN
ejpam-6226	194	24	•	•	INTJ
ejpam-6226	194	25	(	(	PUNCT
ejpam-6226	194	26	ξ	ξ	PROPN
ejpam-6226	194	27	•	•	NUM
ejpam-6226	194	28	ϵ	ϵ	NOUN
ejpam-6226	194	29	)	)	PUNCT
ejpam-6226	194	30	)	)	PUNCT
ejpam-6226	194	31	•	•	ADP
ejpam-6226	194	32	ς	ς	NOUN
ejpam-6226	194	33	)	)	PUNCT
ejpam-6226	194	34	,	,	PUNCT
ejpam-6226	194	35	g(ς)},min{h((ϵ	g(ς)},min{h((ϵ	VERB
ejpam-6226	194	36	•	•	NOUN
ejpam-6226	194	37	(	(	PUNCT
ejpam-6226	194	38	ξ	ξ	NOUN
ejpam-6226	194	39	•	•	NUM
ejpam-6226	194	40	ϵ	ϵ	NOUN
ejpam-6226	194	41	)	)	PUNCT
ejpam-6226	194	42	)	)	PUNCT
ejpam-6226	194	43	•	•	ADP
ejpam-6226	194	44	ς	ς	PROPN
ejpam-6226	194	45	)	)	PUNCT
ejpam-6226	194	46	,	,	PUNCT
ejpam-6226	194	47	h(ς	h(ς	PROPN
ejpam-6226	194	48	)	)	PUNCT
ejpam-6226	194	49	}	}	PUNCT
ejpam-6226	194	50	}	}	PUNCT
ejpam-6226	195	1	=	=	PUNCT
ejpam-6226	195	2	min{min{g((ϵ	min{min{g((ϵ	NOUN
ejpam-6226	195	3	•	•	INTJ
ejpam-6226	195	4	(	(	PUNCT
ejpam-6226	195	5	ξ	ξ	PROPN
ejpam-6226	195	6	•	•	NUM
ejpam-6226	195	7	ϵ	ϵ	NOUN
ejpam-6226	195	8	)	)	PUNCT
ejpam-6226	195	9	)	)	PUNCT
ejpam-6226	195	10	•	•	ADP
ejpam-6226	195	11	ς	ς	PROPN
ejpam-6226	195	12	)	)	PUNCT
ejpam-6226	195	13	,	,	PUNCT
ejpam-6226	195	14	h((ϵ	h((ϵ	PROPN
ejpam-6226	195	15	•	•	NOUN
ejpam-6226	195	16	(	(	PUNCT
ejpam-6226	195	17	ξ	ξ	PROPN
ejpam-6226	195	18	•	•	NUM
ejpam-6226	195	19	ϵ	ϵ	NOUN
ejpam-6226	195	20	)	)	PUNCT
ejpam-6226	195	21	)	)	PUNCT
ejpam-6226	195	22	•	•	ADP
ejpam-6226	195	23	ς)},min{g(ς	ς)},min{g(ς	PROPN
ejpam-6226	195	24	)	)	PUNCT
ejpam-6226	195	25	,	,	PUNCT
ejpam-6226	195	26	h(ς	h(ς	PROPN
ejpam-6226	195	27	)	)	PUNCT
ejpam-6226	195	28	}	}	PUNCT
ejpam-6226	195	29	}	}	PUNCT
ejpam-6226	195	30	≥	≥	NOUN
ejpam-6226	195	31	min{(g	min{(g	NOUN
ejpam-6226	195	32	∩	∩	NOUN
ejpam-6226	195	33	h)((ϵ	h)((ϵ	VERB
ejpam-6226	195	34	•	•	NOUN
ejpam-6226	195	35	(	(	PUNCT
ejpam-6226	195	36	ξ	ξ	NOUN
ejpam-6226	195	37	•	•	NUM
ejpam-6226	195	38	ϵ	ϵ	NOUN
ejpam-6226	195	39	)	)	PUNCT
ejpam-6226	195	40	)	)	PUNCT
ejpam-6226	195	41	•	•	ADP
ejpam-6226	195	42	ς	ς	NOUN
ejpam-6226	195	43	)	)	PUNCT
ejpam-6226	195	44	,	,	PUNCT
ejpam-6226	195	45	(	(	PUNCT
ejpam-6226	195	46	g	g	PROPN
ejpam-6226	195	47	∩	∩	NOUN
ejpam-6226	195	48	h)(ς	h)(ς	NUM
ejpam-6226	195	49	)	)	PUNCT
ejpam-6226	195	50	}	}	PUNCT
ejpam-6226	195	51	.	.	PUNCT
ejpam-6226	196	1	hence	hence	ADV
ejpam-6226	196	2	,	,	PUNCT
ejpam-6226	196	3	g	g	PROPN
ejpam-6226	196	4	∩	∩	ADJ
ejpam-6226	196	5	h	h	NOUN
ejpam-6226	196	6	is	be	AUX
ejpam-6226	196	7	an	an	DET
ejpam-6226	196	8	fmink	fmink	NOUN
ejpam-6226	196	9	-	-	PUNCT
ejpam-6226	196	10	i	i	PRON
ejpam-6226	196	11	of	of	ADP
ejpam-6226	196	12	i.	i.	PROPN
ejpam-6226	196	13	note	note	PROPN
ejpam-6226	196	14	:	:	PUNCT
ejpam-6226	196	15	the	the	DET
ejpam-6226	196	16	union	union	NOUN
ejpam-6226	196	17	of	of	ADP
ejpam-6226	196	18	two	two	NUM
ejpam-6226	196	19	fmink	fmink	NOUN
ejpam-6226	196	20	-	-	PUNCT
ejpam-6226	196	21	is	be	AUX
ejpam-6226	196	22	of	of	ADP
ejpam-6226	196	23	an	an	DET
ejpam-6226	196	24	ink	ink	NOUN
ejpam-6226	196	25	-	-	PUNCT
ejpam-6226	196	26	algebra	algebra	NOUN
ejpam-6226	196	27	need	need	AUX
ejpam-6226	196	28	not	not	PART
ejpam-6226	196	29	be	be	AUX
ejpam-6226	196	30	an	an	DET
ejpam-6226	196	31	fmink	fmink	ADJ
ejpam-6226	196	32	-	-	PUNCT
ejpam-6226	196	33	i.	i.	NOUN
ejpam-6226	196	34	example	example	NOUN
ejpam-6226	196	35	6	6	NUM
ejpam-6226	196	36	.	.	PUNCT
ejpam-6226	197	1	consider	consider	VERB
ejpam-6226	197	2	an	an	DET
ejpam-6226	197	3	ink	ink	NOUN
ejpam-6226	197	4	-	-	PUNCT
ejpam-6226	197	5	algebra	algebra	NOUN
ejpam-6226	197	6	i	i	NOUN
ejpam-6226	197	7	=	=	PUNCT
ejpam-6226	197	8	{	{	PUNCT
ejpam-6226	197	9	0	0	NUM
ejpam-6226	197	10	,	,	PUNCT
ejpam-6226	197	11	2	2	NUM
ejpam-6226	197	12	,	,	PUNCT
ejpam-6226	197	13	4	4	NUM
ejpam-6226	197	14	}	}	PUNCT
ejpam-6226	197	15	with	with	ADP
ejpam-6226	197	16	the	the	DET
ejpam-6226	197	17	following	follow	VERB
ejpam-6226	197	18	cayley	cayley	ADJ
ejpam-6226	197	19	table	table	NOUN
ejpam-6226	197	20	:	:	PUNCT
ejpam-6226	197	21	•	•	NOUN
ejpam-6226	197	22	0	0	NUM
ejpam-6226	197	23	2	2	NUM
ejpam-6226	197	24	4	4	NUM
ejpam-6226	197	25	0	0	NUM
ejpam-6226	197	26	0	0	NUM
ejpam-6226	197	27	0	0	NUM
ejpam-6226	197	28	0	0	NUM
ejpam-6226	197	29	2	2	NUM
ejpam-6226	197	30	2	2	NUM
ejpam-6226	197	31	0	0	NUM
ejpam-6226	197	32	2	2	NUM
ejpam-6226	197	33	4	4	NUM
ejpam-6226	197	34	4	4	NUM
ejpam-6226	197	35	4	4	NUM
ejpam-6226	197	36	0	0	NUM
ejpam-6226	197	37	define	define	VERB
ejpam-6226	197	38	an	an	DET
ejpam-6226	197	39	fs	fs	NOUN
ejpam-6226	197	40	g	g	NOUN
ejpam-6226	197	41	:	:	PUNCT
ejpam-6226	197	42	i	i	PRON
ejpam-6226	197	43	→	→	PUNCT
ejpam-6226	198	1	[	[	X
ejpam-6226	198	2	0	0	NUM
ejpam-6226	198	3	,	,	PUNCT
ejpam-6226	198	4	1	1	NUM
ejpam-6226	198	5	]	]	PUNCT
ejpam-6226	198	6	by	by	ADP
ejpam-6226	198	7	0	0	NUM
ejpam-6226	198	8	2	2	NUM
ejpam-6226	198	9	4	4	NUM
ejpam-6226	198	10	g	g	NOUN
ejpam-6226	198	11	0.3	0.3	NUM
ejpam-6226	198	12	0.4	0.4	NUM
ejpam-6226	198	13	0.6	0.6	NUM
ejpam-6226	198	14	define	define	VERB
ejpam-6226	198	15	an	an	DET
ejpam-6226	198	16	fs	fs	ADJ
ejpam-6226	198	17	h	h	NOUN
ejpam-6226	198	18	:	:	PUNCT
ejpam-6226	199	1	i	i	PRON
ejpam-6226	199	2	→	→	PUNCT
ejpam-6226	200	1	[	[	X
ejpam-6226	200	2	0	0	NUM
ejpam-6226	200	3	,	,	PUNCT
ejpam-6226	200	4	1	1	NUM
ejpam-6226	200	5	]	]	PUNCT
ejpam-6226	200	6	by	by	ADP
ejpam-6226	200	7	r.	r.	PROPN
ejpam-6226	200	8	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	200	9	et	et	PROPN
ejpam-6226	200	10	al	al	PROPN
ejpam-6226	200	11	.	.	PUNCT
ejpam-6226	200	12	/	/	SYM
ejpam-6226	200	13	eur	eur	PROPN
ejpam-6226	200	14	.	.	PUNCT
ejpam-6226	201	1	j.	j.	PROPN
ejpam-6226	201	2	pure	pure	PROPN
ejpam-6226	201	3	appl	appl	PROPN
ejpam-6226	201	4	.	.	PROPN
ejpam-6226	201	5	math	math	PROPN
ejpam-6226	201	6	,	,	PUNCT
ejpam-6226	201	7	18	18	NUM
ejpam-6226	201	8	(	(	PUNCT
ejpam-6226	201	9	3	3	NUM
ejpam-6226	201	10	)	)	PUNCT
ejpam-6226	201	11	(	(	PUNCT
ejpam-6226	201	12	2025	2025	NUM
ejpam-6226	201	13	)	)	PUNCT
ejpam-6226	201	14	,	,	PUNCT
ejpam-6226	201	15	6226	6226	NUM
ejpam-6226	201	16	10	10	NUM
ejpam-6226	201	17	of	of	ADP
ejpam-6226	201	18	19	19	NUM
ejpam-6226	201	19	0	0	NUM
ejpam-6226	201	20	2	2	NUM
ejpam-6226	201	21	4	4	NUM
ejpam-6226	201	22	h	h	NOUN
ejpam-6226	201	23	0.5	0.5	NUM
ejpam-6226	201	24	0.3	0.3	NUM
ejpam-6226	201	25	0.5	0.5	NUM
ejpam-6226	201	26	clearly	clearly	ADV
ejpam-6226	201	27	,	,	PUNCT
ejpam-6226	201	28	g	g	PROPN
ejpam-6226	201	29	and	and	CCONJ
ejpam-6226	201	30	h	h	NOUN
ejpam-6226	201	31	are	be	AUX
ejpam-6226	201	32	two	two	NUM
ejpam-6226	201	33	fmink	fmink	NOUN
ejpam-6226	201	34	-	-	PUNCT
ejpam-6226	201	35	is	be	AUX
ejpam-6226	201	36	of	of	ADP
ejpam-6226	201	37	i.	i.	NOUN
ejpam-6226	201	38	here	here	ADV
ejpam-6226	201	39	tg∪h(0	tg∪h(0	PROPN
ejpam-6226	201	40	)	)	PUNCT
ejpam-6226	201	41	=	=	PUNCT
ejpam-6226	201	42	0.3	0.3	NUM
ejpam-6226	201	43	,	,	PUNCT
ejpam-6226	201	44	but	but	CCONJ
ejpam-6226	201	45	it	it	PRON
ejpam-6226	201	46	is	be	AUX
ejpam-6226	201	47	not	not	PART
ejpam-6226	201	48	greater	great	ADJ
ejpam-6226	201	49	than	than	ADP
ejpam-6226	201	50	or	or	CCONJ
ejpam-6226	201	51	equal	equal	ADJ
ejpam-6226	201	52	to	to	ADP
ejpam-6226	201	53	0.5	0.5	NUM
ejpam-6226	201	54	=	=	NOUN
ejpam-6226	201	55	min{tg∪h((0	min{tg∪h((0	NOUN
ejpam-6226	201	56	•	•	NOUN
ejpam-6226	201	57	(	(	PUNCT
ejpam-6226	201	58	2	2	NUM
ejpam-6226	201	59	•	•	NUM
ejpam-6226	201	60	0	0	NUM
ejpam-6226	201	61	)	)	PUNCT
ejpam-6226	201	62	)	)	PUNCT
ejpam-6226	202	1	•	•	ADP
ejpam-6226	202	2	4	4	NUM
ejpam-6226	202	3	)	)	PUNCT
ejpam-6226	202	4	,	,	PUNCT
ejpam-6226	202	5	tg∪h(4	tg∪h(4	PROPN
ejpam-6226	202	6	)	)	PUNCT
ejpam-6226	202	7	}	}	PUNCT
ejpam-6226	202	8	.	.	PUNCT
ejpam-6226	203	1	thus	thus	ADV
ejpam-6226	203	2	,	,	PUNCT
ejpam-6226	203	3	the	the	DET
ejpam-6226	203	4	union	union	NOUN
ejpam-6226	203	5	of	of	ADP
ejpam-6226	203	6	fmink	fmink	NOUN
ejpam-6226	203	7	-	-	PUNCT
ejpam-6226	203	8	is	be	AUX
ejpam-6226	203	9	of	of	ADP
ejpam-6226	203	10	an	an	DET
ejpam-6226	203	11	ink	ink	NOUN
ejpam-6226	203	12	-	-	PUNCT
ejpam-6226	203	13	algebra	algebra	NOUN
ejpam-6226	203	14	is	be	AUX
ejpam-6226	203	15	not	not	PART
ejpam-6226	203	16	an	an	DET
ejpam-6226	203	17	fmink	fmink	ADJ
ejpam-6226	203	18	-	-	PUNCT
ejpam-6226	203	19	i.	i.	NOUN
ejpam-6226	203	20	theorem	theorem	NOUN
ejpam-6226	203	21	7	7	NUM
ejpam-6226	203	22	.	.	PUNCT
ejpam-6226	204	1	let	let	VERB
ejpam-6226	204	2	g	g	NOUN
ejpam-6226	204	3	and	and	CCONJ
ejpam-6226	204	4	h	h	NOUN
ejpam-6226	204	5	be	be	VERB
ejpam-6226	204	6	two	two	NUM
ejpam-6226	204	7	fmink	fmink	NOUN
ejpam-6226	204	8	-	-	PUNCT
ejpam-6226	204	9	is	be	AUX
ejpam-6226	204	10	of	of	ADP
ejpam-6226	204	11	an	an	DET
ejpam-6226	204	12	ink	ink	NOUN
ejpam-6226	204	13	-	-	PUNCT
ejpam-6226	204	14	algebra	algebra	NOUN
ejpam-6226	204	15	i.	i.	NOUN
ejpam-6226	204	16	if	if	SCONJ
ejpam-6226	204	17	g	g	PROPN
ejpam-6226	204	18	⊆	⊆	NUM
ejpam-6226	204	19	h	h	NOUN
ejpam-6226	204	20	or	or	CCONJ
ejpam-6226	204	21	h	h	NOUN
ejpam-6226	204	22	⊆	⊆	NUM
ejpam-6226	204	23	g	g	NOUN
ejpam-6226	204	24	,	,	PUNCT
ejpam-6226	204	25	then	then	ADV
ejpam-6226	204	26	g	g	PROPN
ejpam-6226	204	27	∪	∪	PROPN
ejpam-6226	204	28	h	h	NOUN
ejpam-6226	204	29	is	be	AUX
ejpam-6226	204	30	an	an	DET
ejpam-6226	204	31	fmink	fmink	NOUN
ejpam-6226	204	32	-	-	PUNCT
ejpam-6226	204	33	i	i	PRON
ejpam-6226	204	34	of	of	ADP
ejpam-6226	204	35	i.	i.	PROPN
ejpam-6226	204	36	proof	proof	PROPN
ejpam-6226	204	37	.	.	PUNCT
ejpam-6226	205	1	obvious	obvious	ADJ
ejpam-6226	205	2	.	.	PUNCT
ejpam-6226	206	1	theorem	theorem	VERB
ejpam-6226	206	2	8	8	NUM
ejpam-6226	206	3	.	.	PUNCT
ejpam-6226	207	1	let	let	VERB
ejpam-6226	207	2	g	g	NOUN
ejpam-6226	207	3	and	and	CCONJ
ejpam-6226	207	4	h	h	NOUN
ejpam-6226	207	5	be	be	VERB
ejpam-6226	207	6	two	two	NUM
ejpam-6226	207	7	fpmink	fpmink	NOUN
ejpam-6226	207	8	-	-	PUNCT
ejpam-6226	207	9	is	be	AUX
ejpam-6226	207	10	of	of	ADP
ejpam-6226	207	11	an	an	DET
ejpam-6226	207	12	ink	ink	NOUN
ejpam-6226	207	13	-	-	PUNCT
ejpam-6226	207	14	algebra	algebra	NOUN
ejpam-6226	207	15	i.	i.	NOUN
ejpam-6226	207	16	then	then	ADV
ejpam-6226	207	17	g	g	PROPN
ejpam-6226	207	18	∩	∩	ADJ
ejpam-6226	207	19	h	h	NOUN
ejpam-6226	207	20	is	be	AUX
ejpam-6226	207	21	also	also	ADV
ejpam-6226	207	22	an	an	DET
ejpam-6226	207	23	fpmink	fpmink	NOUN
ejpam-6226	207	24	-	-	PUNCT
ejpam-6226	207	25	i	i	PRON
ejpam-6226	207	26	of	of	ADP
ejpam-6226	207	27	i.	i.	PROPN
ejpam-6226	207	28	proof	proof	PROPN
ejpam-6226	207	29	.	.	PUNCT
ejpam-6226	208	1	the	the	DET
ejpam-6226	208	2	proof	proof	NOUN
ejpam-6226	208	3	is	be	AUX
ejpam-6226	208	4	similar	similar	ADJ
ejpam-6226	208	5	to	to	AUX
ejpam-6226	208	6	theorem	theorem	VERB
ejpam-6226	208	7	6	6	NUM
ejpam-6226	208	8	.	.	PUNCT
ejpam-6226	209	1	note	note	NOUN
ejpam-6226	209	2	:	:	PUNCT
ejpam-6226	209	3	the	the	DET
ejpam-6226	209	4	union	union	NOUN
ejpam-6226	209	5	of	of	ADP
ejpam-6226	209	6	two	two	NUM
ejpam-6226	209	7	fpmink	fpmink	NOUN
ejpam-6226	209	8	-	-	PUNCT
ejpam-6226	209	9	is	be	AUX
ejpam-6226	209	10	of	of	ADP
ejpam-6226	209	11	an	an	DET
ejpam-6226	209	12	ink	ink	NOUN
ejpam-6226	209	13	-	-	PUNCT
ejpam-6226	209	14	algebra	algebra	NOUN
ejpam-6226	209	15	need	need	AUX
ejpam-6226	209	16	not	not	PART
ejpam-6226	209	17	be	be	AUX
ejpam-6226	209	18	an	an	DET
ejpam-6226	209	19	fpmink	fpmink	ADJ
ejpam-6226	209	20	-	-	PUNCT
ejpam-6226	209	21	i.	i.	NOUN
ejpam-6226	209	22	example	example	NOUN
ejpam-6226	209	23	7	7	NUM
ejpam-6226	209	24	.	.	PUNCT
ejpam-6226	209	25	from	from	ADP
ejpam-6226	209	26	example	example	NOUN
ejpam-6226	209	27	6	6	NUM
ejpam-6226	209	28	,	,	PUNCT
ejpam-6226	209	29	g	g	PROPN
ejpam-6226	209	30	and	and	CCONJ
ejpam-6226	209	31	h	h	NOUN
ejpam-6226	209	32	are	be	AUX
ejpam-6226	209	33	two	two	NUM
ejpam-6226	209	34	fpmink	fpmink	NOUN
ejpam-6226	209	35	-	-	PUNCT
ejpam-6226	209	36	is	be	AUX
ejpam-6226	209	37	of	of	ADP
ejpam-6226	209	38	i.	i.	NOUN
ejpam-6226	209	39	here	here	ADV
ejpam-6226	209	40	,	,	PUNCT
ejpam-6226	209	41	tg∪h(0•2	tg∪h(0•2	NOUN
ejpam-6226	209	42	)	)	PUNCT
ejpam-6226	209	43	=	=	SYM
ejpam-6226	209	44	0.3	0.3	NUM
ejpam-6226	209	45	,	,	PUNCT
ejpam-6226	209	46	but	but	CCONJ
ejpam-6226	209	47	it	it	PRON
ejpam-6226	209	48	is	be	AUX
ejpam-6226	209	49	not	not	PART
ejpam-6226	209	50	greater	great	ADJ
ejpam-6226	209	51	than	than	ADP
ejpam-6226	209	52	or	or	CCONJ
ejpam-6226	209	53	equal	equal	ADJ
ejpam-6226	209	54	to	to	ADP
ejpam-6226	209	55	0.4	0.4	NUM
ejpam-6226	209	56	=	=	SYM
ejpam-6226	209	57	min{tg∪h((0	min{tg∪h((0	NOUN
ejpam-6226	209	58	•	•	NOUN
ejpam-6226	209	59	2	2	NUM
ejpam-6226	209	60	)	)	PUNCT
ejpam-6226	209	61	•	•	NUM
ejpam-6226	209	62	4	4	NUM
ejpam-6226	209	63	)	)	PUNCT
ejpam-6226	209	64	,	,	PUNCT
ejpam-6226	209	65	tg∪h(2	tg∪h(2	PROPN
ejpam-6226	209	66	•	•	NOUN
ejpam-6226	209	67	4	4	NUM
ejpam-6226	209	68	)	)	PUNCT
ejpam-6226	209	69	}	}	PUNCT
ejpam-6226	209	70	.	.	PUNCT
ejpam-6226	210	1	thus	thus	ADV
ejpam-6226	210	2	,	,	PUNCT
ejpam-6226	210	3	the	the	DET
ejpam-6226	210	4	union	union	NOUN
ejpam-6226	210	5	of	of	ADP
ejpam-6226	210	6	fpmink	fpmink	NOUN
ejpam-6226	210	7	-	-	PUNCT
ejpam-6226	210	8	i	i	PRON
ejpam-6226	210	9	of	of	ADP
ejpam-6226	210	10	i	i	PRON
ejpam-6226	210	11	is	be	AUX
ejpam-6226	210	12	not	not	PART
ejpam-6226	210	13	an	an	DET
ejpam-6226	210	14	fpmink	fpmink	ADJ
ejpam-6226	210	15	-	-	PUNCT
ejpam-6226	210	16	i.	i.	NOUN
ejpam-6226	210	17	theorem	theorem	NOUN
ejpam-6226	210	18	9	9	NUM
ejpam-6226	210	19	.	.	PUNCT
ejpam-6226	211	1	let	let	VERB
ejpam-6226	211	2	g	g	NOUN
ejpam-6226	211	3	and	and	CCONJ
ejpam-6226	211	4	h	h	NOUN
ejpam-6226	211	5	be	be	VERB
ejpam-6226	211	6	two	two	NUM
ejpam-6226	211	7	fpmink	fpmink	NOUN
ejpam-6226	211	8	-	-	PUNCT
ejpam-6226	211	9	is	be	AUX
ejpam-6226	211	10	of	of	ADP
ejpam-6226	211	11	an	an	DET
ejpam-6226	211	12	ink	ink	NOUN
ejpam-6226	211	13	-	-	PUNCT
ejpam-6226	211	14	algebra	algebra	NOUN
ejpam-6226	211	15	i.	i.	NOUN
ejpam-6226	211	16	if	if	SCONJ
ejpam-6226	211	17	g	g	PROPN
ejpam-6226	211	18	⊆	⊆	NUM
ejpam-6226	211	19	h	h	NOUN
ejpam-6226	211	20	or	or	CCONJ
ejpam-6226	211	21	h	h	NOUN
ejpam-6226	211	22	⊆	⊆	NUM
ejpam-6226	211	23	g	g	NOUN
ejpam-6226	211	24	,	,	PUNCT
ejpam-6226	211	25	then	then	ADV
ejpam-6226	211	26	g	g	PROPN
ejpam-6226	211	27	∪	∪	PROPN
ejpam-6226	211	28	h	h	NOUN
ejpam-6226	211	29	is	be	AUX
ejpam-6226	211	30	an	an	DET
ejpam-6226	211	31	fpmink	fpmink	NOUN
ejpam-6226	211	32	-	-	PUNCT
ejpam-6226	211	33	i	i	PRON
ejpam-6226	211	34	of	of	ADP
ejpam-6226	211	35	i.	i.	PROPN
ejpam-6226	211	36	proof	proof	PROPN
ejpam-6226	211	37	.	.	PUNCT
ejpam-6226	212	1	obvious	obvious	ADJ
ejpam-6226	212	2	.	.	PUNCT
ejpam-6226	213	1	3.3	3.3	NUM
ejpam-6226	213	2	.	.	PUNCT
ejpam-6226	214	1	homomorphism	homomorphism	NOUN
ejpam-6226	214	2	of	of	ADP
ejpam-6226	214	3	fuzzy	fuzzy	ADJ
ejpam-6226	214	4	implicative	implicative	ADJ
ejpam-6226	214	5	and	and	CCONJ
ejpam-6226	214	6	positive	positive	ADJ
ejpam-6226	214	7	implicative	implicative	ADJ
ejpam-6226	214	8	inkideals	inkideal	NOUN
ejpam-6226	214	9	of	of	ADP
ejpam-6226	214	10	ink	ink	NOUN
ejpam-6226	214	11	-	-	PUNCT
ejpam-6226	214	12	algebras	algebras	PROPN
ejpam-6226	214	13	homomorphisms	homomorphism	NOUN
ejpam-6226	214	14	play	play	VERB
ejpam-6226	214	15	a	a	DET
ejpam-6226	214	16	crucial	crucial	ADJ
ejpam-6226	214	17	role	role	NOUN
ejpam-6226	214	18	in	in	ADP
ejpam-6226	214	19	algebra	algebra	NOUN
ejpam-6226	214	20	by	by	ADP
ejpam-6226	214	21	preserving	preserve	VERB
ejpam-6226	214	22	structural	structural	ADJ
ejpam-6226	214	23	properties	property	NOUN
ejpam-6226	214	24	across	across	ADP
ejpam-6226	214	25	different	different	ADJ
ejpam-6226	214	26	algebraic	algebraic	ADJ
ejpam-6226	214	27	systems	system	NOUN
ejpam-6226	214	28	.	.	PUNCT
ejpam-6226	215	1	in	in	ADP
ejpam-6226	215	2	this	this	DET
ejpam-6226	215	3	subsection	subsection	NOUN
ejpam-6226	215	4	,	,	PUNCT
ejpam-6226	215	5	we	we	PRON
ejpam-6226	215	6	examine	examine	VERB
ejpam-6226	215	7	the	the	DET
ejpam-6226	215	8	behavior	behavior	NOUN
ejpam-6226	215	9	of	of	ADP
ejpam-6226	215	10	fuzzy	fuzzy	ADJ
ejpam-6226	215	11	implicative	implicative	ADJ
ejpam-6226	215	12	ink	ink	NOUN
ejpam-6226	215	13	-	-	PUNCT
ejpam-6226	215	14	ideals	ideal	NOUN
ejpam-6226	215	15	(	(	PUNCT
ejpam-6226	215	16	fmink	fmink	NOUN
ejpam-6226	215	17	-	-	PUNCT
ejpam-6226	215	18	i	i	NOUN
ejpam-6226	215	19	)	)	PUNCT
ejpam-6226	215	20	and	and	CCONJ
ejpam-6226	215	21	fuzzy	fuzzy	ADJ
ejpam-6226	215	22	positive	positive	ADJ
ejpam-6226	215	23	implicative	implicative	ADJ
ejpam-6226	215	24	ink	ink	NOUN
ejpam-6226	215	25	-	-	PUNCT
ejpam-6226	215	26	ideals	ideal	NOUN
ejpam-6226	215	27	(	(	PUNCT
ejpam-6226	215	28	fpmink	fpmink	NOUN
ejpam-6226	215	29	-	-	PUNCT
ejpam-6226	215	30	i	i	NOUN
ejpam-6226	215	31	)	)	PUNCT
ejpam-6226	215	32	under	under	ADP
ejpam-6226	215	33	homomorphic	homomorphic	ADJ
ejpam-6226	215	34	mappings	mapping	NOUN
ejpam-6226	215	35	between	between	ADP
ejpam-6226	215	36	ink	ink	NOUN
ejpam-6226	215	37	-	-	PUNCT
ejpam-6226	215	38	algebras	algebras	PROPN
ejpam-6226	215	39	.	.	PUNCT
ejpam-6226	216	1	specifically	specifically	ADV
ejpam-6226	216	2	,	,	PUNCT
ejpam-6226	216	3	we	we	PRON
ejpam-6226	216	4	focus	focus	VERB
ejpam-6226	216	5	on	on	ADP
ejpam-6226	216	6	the	the	DET
ejpam-6226	216	7	preimages	preimage	NOUN
ejpam-6226	216	8	of	of	ADP
ejpam-6226	216	9	these	these	DET
ejpam-6226	216	10	ideals	ideal	NOUN
ejpam-6226	216	11	and	and	CCONJ
ejpam-6226	216	12	prove	prove	VERB
ejpam-6226	216	13	that	that	SCONJ
ejpam-6226	216	14	such	such	ADJ
ejpam-6226	216	15	pre	pre	NOUN
ejpam-6226	216	16	-	-	NOUN
ejpam-6226	216	17	images	image	NOUN
ejpam-6226	216	18	retain	retain	VERB
ejpam-6226	216	19	the	the	DET
ejpam-6226	216	20	implicative	implicative	ADJ
ejpam-6226	216	21	and	and	CCONJ
ejpam-6226	216	22	positive	positive	ADJ
ejpam-6226	216	23	implicative	implicative	ADJ
ejpam-6226	216	24	properties	property	NOUN
ejpam-6226	216	25	of	of	ADP
ejpam-6226	216	26	the	the	DET
ejpam-6226	216	27	original	original	ADJ
ejpam-6226	216	28	fuzzy	fuzzy	ADJ
ejpam-6226	216	29	ideals	ideal	NOUN
ejpam-6226	216	30	.	.	PUNCT
ejpam-6226	217	1	these	these	DET
ejpam-6226	217	2	results	result	NOUN
ejpam-6226	217	3	establish	establish	VERB
ejpam-6226	217	4	the	the	DET
ejpam-6226	217	5	invariance	invariance	NOUN
ejpam-6226	217	6	of	of	ADP
ejpam-6226	217	7	fmink	fmink	ADJ
ejpam-6226	217	8	-	-	PUNCT
ejpam-6226	217	9	i	i	PRON
ejpam-6226	217	10	and	and	CCONJ
ejpam-6226	217	11	fpmink	fpmink	NOUN
ejpam-6226	217	12	-	-	PUNCT
ejpam-6226	217	13	i	i	PRON
ejpam-6226	217	14	under	under	ADP
ejpam-6226	217	15	structure	structure	NOUN
ejpam-6226	217	16	-	-	PUNCT
ejpam-6226	217	17	preserving	preserve	VERB
ejpam-6226	217	18	transformations	transformation	NOUN
ejpam-6226	217	19	,	,	PUNCT
ejpam-6226	217	20	thereby	thereby	ADV
ejpam-6226	217	21	confirming	confirm	VERB
ejpam-6226	217	22	their	their	PRON
ejpam-6226	217	23	robustness	robustness	NOUN
ejpam-6226	217	24	across	across	ADP
ejpam-6226	217	25	algebraic	algebraic	ADJ
ejpam-6226	217	26	homomorphic	homomorphic	ADJ
ejpam-6226	217	27	images	image	NOUN
ejpam-6226	217	28	.	.	PUNCT
ejpam-6226	218	1	definition	definition	NOUN
ejpam-6226	218	2	17	17	NUM
ejpam-6226	218	3	.	.	PUNCT
ejpam-6226	219	1	let	let	VERB
ejpam-6226	219	2	κ	κ	NOUN
ejpam-6226	219	3	:	:	PUNCT
ejpam-6226	219	4	i	i	PRON
ejpam-6226	219	5	→	→	PUNCT
ejpam-6226	219	6	ĭ	ĭ	NOUN
ejpam-6226	219	7	be	be	AUX
ejpam-6226	219	8	a	a	DET
ejpam-6226	219	9	homomorphism	homomorphism	NOUN
ejpam-6226	219	10	of	of	ADP
ejpam-6226	219	11	ink	ink	NOUN
ejpam-6226	219	12	-	-	PUNCT
ejpam-6226	219	13	algebras	algebras	PROPN
ejpam-6226	219	14	and	and	CCONJ
ejpam-6226	219	15	g	g	PROPN
ejpam-6226	219	16	be	be	AUX
ejpam-6226	219	17	the	the	DET
ejpam-6226	219	18	fs	f	NOUN
ejpam-6226	219	19	in	in	ADP
ejpam-6226	219	20	ĭ.	ĭ.	PROPN
ejpam-6226	219	21	then	then	ADV
ejpam-6226	219	22	the	the	DET
ejpam-6226	219	23	fs	fs	PROPN
ejpam-6226	219	24	g[κ	g[κ	X
ejpam-6226	219	25	]	]	X
ejpam-6226	219	26	in	in	ADP
ejpam-6226	219	27	i	i	PRON
ejpam-6226	219	28	is	be	AUX
ejpam-6226	219	29	defined	define	VERB
ejpam-6226	219	30	by	by	ADP
ejpam-6226	219	31	g[κ](ϵ	g[κ](ϵ	X
ejpam-6226	219	32	)	)	PUNCT
ejpam-6226	219	33	=	=	SYM
ejpam-6226	219	34	g(κ(ϵ	g(κ(ϵ	PROPN
ejpam-6226	219	35	)	)	PUNCT
ejpam-6226	219	36	)	)	PUNCT
ejpam-6226	219	37	for	for	ADP
ejpam-6226	219	38	every	every	DET
ejpam-6226	219	39	ϵ	ϵ	PROPN
ejpam-6226	219	40	∈	∈	PROPN
ejpam-6226	219	41	i	i	PRON
ejpam-6226	219	42	is	be	AUX
ejpam-6226	219	43	called	call	VERB
ejpam-6226	219	44	the	the	DET
ejpam-6226	219	45	pre	pre	NOUN
ejpam-6226	219	46	-	-	NOUN
ejpam-6226	219	47	image	image	NOUN
ejpam-6226	219	48	of	of	ADP
ejpam-6226	219	49	g	g	NOUN
ejpam-6226	219	50	under	under	ADP
ejpam-6226	219	51	κ	κ	PROPN
ejpam-6226	219	52	.	.	PUNCT
ejpam-6226	220	1	theorem	theorem	NOUN
ejpam-6226	220	2	10	10	NUM
ejpam-6226	220	3	.	.	PUNCT
ejpam-6226	221	1	a	a	DET
ejpam-6226	221	2	homomorphic	homomorphic	ADJ
ejpam-6226	221	3	pre	pre	NOUN
ejpam-6226	221	4	-	-	NOUN
ejpam-6226	221	5	image	image	NOUN
ejpam-6226	221	6	of	of	ADP
ejpam-6226	221	7	an	an	DET
ejpam-6226	221	8	fmink	fmink	NOUN
ejpam-6226	221	9	-	-	PUNCT
ejpam-6226	221	10	i	i	PRON
ejpam-6226	221	11	of	of	ADP
ejpam-6226	221	12	an	an	DET
ejpam-6226	221	13	ink	ink	NOUN
ejpam-6226	221	14	-	-	PUNCT
ejpam-6226	221	15	algebra	algebra	NOUN
ejpam-6226	221	16	is	be	AUX
ejpam-6226	221	17	an	an	DET
ejpam-6226	221	18	fminki	fminki	PROPN
ejpam-6226	221	19	.	.	PUNCT
ejpam-6226	222	1	r.	r.	PROPN
ejpam-6226	222	2	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	222	3	et	et	PROPN
ejpam-6226	222	4	al	al	PROPN
ejpam-6226	222	5	.	.	PUNCT
ejpam-6226	222	6	/	/	SYM
ejpam-6226	222	7	eur	eur	PROPN
ejpam-6226	222	8	.	.	PUNCT
ejpam-6226	223	1	j.	j.	PROPN
ejpam-6226	223	2	pure	pure	PROPN
ejpam-6226	223	3	appl	appl	PROPN
ejpam-6226	223	4	.	.	PROPN
ejpam-6226	223	5	math	math	PROPN
ejpam-6226	223	6	,	,	PUNCT
ejpam-6226	223	7	18	18	NUM
ejpam-6226	223	8	(	(	PUNCT
ejpam-6226	223	9	3	3	NUM
ejpam-6226	223	10	)	)	PUNCT
ejpam-6226	223	11	(	(	PUNCT
ejpam-6226	223	12	2025	2025	NUM
ejpam-6226	223	13	)	)	PUNCT
ejpam-6226	223	14	,	,	PUNCT
ejpam-6226	223	15	6226	6226	NUM
ejpam-6226	223	16	11	11	NUM
ejpam-6226	223	17	of	of	ADP
ejpam-6226	223	18	19	19	NUM
ejpam-6226	223	19	proof	proof	NOUN
ejpam-6226	223	20	.	.	PUNCT
ejpam-6226	224	1	let	let	VERB
ejpam-6226	224	2	κ	κ	NOUN
ejpam-6226	224	3	:	:	PUNCT
ejpam-6226	224	4	i	i	PRON
ejpam-6226	224	5	→	→	PUNCT
ejpam-6226	224	6	ĭ	ĭ	NOUN
ejpam-6226	224	7	be	be	AUX
ejpam-6226	224	8	a	a	DET
ejpam-6226	224	9	homomorphism	homomorphism	NOUN
ejpam-6226	224	10	of	of	ADP
ejpam-6226	224	11	ink	ink	NOUN
ejpam-6226	224	12	-	-	PUNCT
ejpam-6226	224	13	algebras	algebras	NOUN
ejpam-6226	224	14	.	.	PUNCT
ejpam-6226	225	1	if	if	SCONJ
ejpam-6226	225	2	g	g	PROPN
ejpam-6226	225	3	is	be	AUX
ejpam-6226	225	4	an	an	DET
ejpam-6226	225	5	fmink	fmink	NOUN
ejpam-6226	225	6	-	-	PUNCT
ejpam-6226	225	7	i	i	PRON
ejpam-6226	225	8	of	of	ADP
ejpam-6226	225	9	an	an	DET
ejpam-6226	225	10	ink	ink	NOUN
ejpam-6226	225	11	-	-	PUNCT
ejpam-6226	225	12	algebra	algebra	NOUN
ejpam-6226	225	13	ĭ	ĭ	NOUN
ejpam-6226	225	14	,	,	PUNCT
ejpam-6226	225	15	then	then	ADV
ejpam-6226	225	16	g[κ](ϵ	g[κ](ϵ	X
ejpam-6226	225	17	)	)	PUNCT
ejpam-6226	225	18	=	=	SYM
ejpam-6226	225	19	g(κ(ϵ	g(κ(ϵ	PROPN
ejpam-6226	225	20	)	)	PUNCT
ejpam-6226	225	21	)	)	PUNCT
ejpam-6226	225	22	≥	≥	PROPN
ejpam-6226	225	23	g(0	g(0	NOUN
ejpam-6226	225	24	)	)	PUNCT
ejpam-6226	225	25	=	=	SYM
ejpam-6226	225	26	g(κ(0	g(κ(0	NOUN
ejpam-6226	225	27	)	)	PUNCT
ejpam-6226	225	28	)	)	PUNCT
ejpam-6226	226	1	=	=	SYM
ejpam-6226	226	2	g[κ](0),∀ϵ	g[κ](0),∀ϵ	PROPN
ejpam-6226	226	3	∈	∈	PROPN
ejpam-6226	226	4	i.	i.	NOUN
ejpam-6226	226	5	let	let	VERB
ejpam-6226	226	6	ϵ	ϵ	NUM
ejpam-6226	226	7	,	,	PUNCT
ejpam-6226	226	8	ξ	ξ	PROPN
ejpam-6226	226	9	,	,	PUNCT
ejpam-6226	226	10	ς	ς	PROPN
ejpam-6226	226	11	∈	∈	PROPN
ejpam-6226	226	12	i.	i.	NOUN
ejpam-6226	226	13	then	then	ADV
ejpam-6226	226	14	min{g[κ]((ϵ	min{g[κ]((ϵ	VERB
ejpam-6226	226	15	•	•	NOUN
ejpam-6226	226	16	(	(	PUNCT
ejpam-6226	226	17	ξ	ξ	NOUN
ejpam-6226	226	18	•	•	NUM
ejpam-6226	226	19	ϵ	ϵ	NOUN
ejpam-6226	226	20	)	)	PUNCT
ejpam-6226	226	21	)	)	PUNCT
ejpam-6226	226	22	•	•	ADP
ejpam-6226	226	23	ς	ς	NOUN
ejpam-6226	226	24	)	)	PUNCT
ejpam-6226	226	25	,	,	PUNCT
ejpam-6226	226	26	g[κ](ς	g[κ](ς	NOUN
ejpam-6226	226	27	)	)	PUNCT
ejpam-6226	226	28	}	}	PUNCT
ejpam-6226	227	1	=	=	PUNCT
ejpam-6226	227	2	min{g(κ((ϵ	min{g(κ((ϵ	ADJ
ejpam-6226	227	3	•	•	INTJ
ejpam-6226	227	4	(	(	PUNCT
ejpam-6226	227	5	ξ	ξ	NOUN
ejpam-6226	227	6	•	•	NUM
ejpam-6226	227	7	ϵ	ϵ	NOUN
ejpam-6226	227	8	)	)	PUNCT
ejpam-6226	227	9	)	)	PUNCT
ejpam-6226	227	10	•	•	NUM
ejpam-6226	227	11	ς	ς	PROPN
ejpam-6226	227	12	)	)	PUNCT
ejpam-6226	227	13	)	)	PUNCT
ejpam-6226	227	14	,	,	PUNCT
ejpam-6226	227	15	g(κ(ς	g(κ(ς	PROPN
ejpam-6226	227	16	)	)	PUNCT
ejpam-6226	227	17	)	)	PUNCT
ejpam-6226	227	18	}	}	PUNCT
ejpam-6226	228	1	=	=	PUNCT
ejpam-6226	228	2	min{g(κ(ϵ	min{g(κ(ϵ	PROPN
ejpam-6226	228	3	•	•	NUM
ejpam-6226	228	4	ς	ς	PROPN
ejpam-6226	228	5	)	)	PUNCT
ejpam-6226	228	6	)	)	PUNCT
ejpam-6226	228	7	,	,	PUNCT
ejpam-6226	228	8	g(κ(ς	g(κ(ς	PROPN
ejpam-6226	228	9	)	)	PUNCT
ejpam-6226	228	10	)	)	PUNCT
ejpam-6226	228	11	}	}	PUNCT
ejpam-6226	228	12	=	=	SYM
ejpam-6226	228	13	g(κ(ϵ	g(κ(ϵ	PROPN
ejpam-6226	228	14	)	)	PUNCT
ejpam-6226	228	15	)	)	PUNCT
ejpam-6226	229	1	=	=	PUNCT
ejpam-6226	229	2	g[κ](ϵ	g[κ](ϵ	ADJ
ejpam-6226	229	3	)	)	PUNCT
ejpam-6226	229	4	.	.	PUNCT
ejpam-6226	230	1	hence	hence	ADV
ejpam-6226	230	2	,	,	PUNCT
ejpam-6226	230	3	g[κ	g[κ	PROPN
ejpam-6226	230	4	]	]	X
ejpam-6226	230	5	is	be	AUX
ejpam-6226	230	6	an	an	DET
ejpam-6226	230	7	fmink	fmink	NOUN
ejpam-6226	230	8	-	-	PUNCT
ejpam-6226	230	9	i	i	PRON
ejpam-6226	230	10	of	of	ADP
ejpam-6226	230	11	ĭ.	ĭ.	NOUN
ejpam-6226	230	12	theorem	theorem	VERB
ejpam-6226	230	13	11	11	NUM
ejpam-6226	230	14	.	.	PUNCT
ejpam-6226	231	1	a	a	DET
ejpam-6226	231	2	homomorphic	homomorphic	ADJ
ejpam-6226	231	3	pre	pre	NOUN
ejpam-6226	231	4	-	-	NOUN
ejpam-6226	231	5	image	image	NOUN
ejpam-6226	231	6	of	of	ADP
ejpam-6226	231	7	an	an	DET
ejpam-6226	231	8	fpmink	fpmink	NOUN
ejpam-6226	231	9	-	-	PUNCT
ejpam-6226	231	10	i	i	PRON
ejpam-6226	231	11	of	of	ADP
ejpam-6226	231	12	ink	ink	NOUN
ejpam-6226	231	13	-	-	PUNCT
ejpam-6226	231	14	algebras	algebras	PROPN
ejpam-6226	231	15	is	be	AUX
ejpam-6226	231	16	an	an	DET
ejpam-6226	231	17	fpminki	fpminki	NOUN
ejpam-6226	231	18	.	.	PUNCT
ejpam-6226	232	1	proof	proof	NOUN
ejpam-6226	232	2	.	.	PUNCT
ejpam-6226	233	1	the	the	DET
ejpam-6226	233	2	proof	proof	NOUN
ejpam-6226	233	3	is	be	AUX
ejpam-6226	233	4	similar	similar	ADJ
ejpam-6226	233	5	to	to	ADP
ejpam-6226	233	6	theorem	theorem	VERB
ejpam-6226	233	7	10	10	NUM
ejpam-6226	233	8	.	.	PUNCT
ejpam-6226	233	9	4	4	NUM
ejpam-6226	233	10	.	.	X
ejpam-6226	233	11	neutrosophic	neutrosophic	ADJ
ejpam-6226	233	12	implicative	implicative	ADJ
ejpam-6226	233	13	and	and	CCONJ
ejpam-6226	233	14	positive	positive	ADJ
ejpam-6226	233	15	implicative	implicative	ADJ
ejpam-6226	233	16	ink	ink	NOUN
ejpam-6226	233	17	-	-	PUNCT
ejpam-6226	233	18	ideals	ideal	NOUN
ejpam-6226	233	19	of	of	ADP
ejpam-6226	233	20	ink	ink	NOUN
ejpam-6226	233	21	-	-	PUNCT
ejpam-6226	233	22	algebras	algebras	NOUN
ejpam-6226	233	23	expanding	expand	VERB
ejpam-6226	233	24	on	on	ADP
ejpam-6226	233	25	the	the	DET
ejpam-6226	233	26	fuzzy	fuzzy	ADJ
ejpam-6226	233	27	framework	framework	NOUN
ejpam-6226	233	28	,	,	PUNCT
ejpam-6226	233	29	we	we	PRON
ejpam-6226	233	30	now	now	ADV
ejpam-6226	233	31	extend	extend	VERB
ejpam-6226	233	32	the	the	DET
ejpam-6226	233	33	notions	notion	NOUN
ejpam-6226	233	34	of	of	ADP
ejpam-6226	233	35	mink	mink	NOUN
ejpam-6226	233	36	-	-	PUNCT
ejpam-6226	233	37	is	be	AUX
ejpam-6226	233	38	and	and	CCONJ
ejpam-6226	233	39	pmink	pmink	NOUN
ejpam-6226	233	40	-	-	PUNCT
ejpam-6226	233	41	is	be	AUX
ejpam-6226	233	42	to	to	ADP
ejpam-6226	233	43	the	the	DET
ejpam-6226	233	44	setting	setting	NOUN
ejpam-6226	233	45	of	of	ADP
ejpam-6226	233	46	nss	ns	NOUN
ejpam-6226	233	47	,	,	PUNCT
ejpam-6226	233	48	which	which	PRON
ejpam-6226	233	49	provide	provide	VERB
ejpam-6226	233	50	a	a	DET
ejpam-6226	233	51	more	more	ADV
ejpam-6226	233	52	expressive	expressive	ADJ
ejpam-6226	233	53	structure	structure	NOUN
ejpam-6226	233	54	for	for	ADP
ejpam-6226	233	55	capturing	capture	VERB
ejpam-6226	233	56	uncertainty	uncertainty	NOUN
ejpam-6226	233	57	,	,	PUNCT
ejpam-6226	233	58	indeterminacy	indeterminacy	NOUN
ejpam-6226	233	59	,	,	PUNCT
ejpam-6226	233	60	and	and	CCONJ
ejpam-6226	233	61	inconsistency	inconsistency	NOUN
ejpam-6226	233	62	.	.	PUNCT
ejpam-6226	234	1	in	in	ADP
ejpam-6226	234	2	this	this	DET
ejpam-6226	234	3	section	section	NOUN
ejpam-6226	234	4	,	,	PUNCT
ejpam-6226	234	5	we	we	PRON
ejpam-6226	234	6	introduce	introduce	VERB
ejpam-6226	234	7	the	the	DET
ejpam-6226	234	8	concepts	concept	NOUN
ejpam-6226	234	9	of	of	ADP
ejpam-6226	234	10	neutrosophic	neutrosophic	ADJ
ejpam-6226	234	11	implicative	implicative	ADJ
ejpam-6226	234	12	ink	ink	NOUN
ejpam-6226	234	13	-	-	PUNCT
ejpam-6226	234	14	ideals	ideal	NOUN
ejpam-6226	234	15	(	(	PUNCT
ejpam-6226	234	16	nmink	nmink	NOUN
ejpam-6226	234	17	-	-	PUNCT
ejpam-6226	234	18	is	be	AUX
ejpam-6226	234	19	)	)	PUNCT
ejpam-6226	234	20	and	and	CCONJ
ejpam-6226	234	21	neutrosophic	neutrosophic	ADJ
ejpam-6226	234	22	positive	positive	ADJ
ejpam-6226	234	23	implicative	implicative	ADJ
ejpam-6226	234	24	ink	ink	NOUN
ejpam-6226	234	25	-	-	PUNCT
ejpam-6226	234	26	ideals	ideal	NOUN
ejpam-6226	234	27	(	(	PUNCT
ejpam-6226	234	28	npmink	npmink	NOUN
ejpam-6226	234	29	-	-	PUNCT
ejpam-6226	234	30	is	be	AUX
ejpam-6226	234	31	)	)	PUNCT
ejpam-6226	234	32	in	in	ADP
ejpam-6226	234	33	ink	ink	NOUN
ejpam-6226	234	34	-	-	PUNCT
ejpam-6226	234	35	algebras	algebras	PROPN
ejpam-6226	234	36	.	.	PUNCT
ejpam-6226	235	1	these	these	DET
ejpam-6226	235	2	definitions	definition	NOUN
ejpam-6226	235	3	are	be	AUX
ejpam-6226	235	4	formulated	formulate	VERB
ejpam-6226	235	5	in	in	ADP
ejpam-6226	235	6	terms	term	NOUN
ejpam-6226	235	7	of	of	ADP
ejpam-6226	235	8	the	the	DET
ejpam-6226	235	9	three	three	NUM
ejpam-6226	235	10	-	-	PUNCT
ejpam-6226	235	11	valued	value	VERB
ejpam-6226	235	12	membership	membership	NOUN
ejpam-6226	235	13	functions	function	NOUN
ejpam-6226	235	14	of	of	ADP
ejpam-6226	235	15	neutrosophic	neutrosophic	ADJ
ejpam-6226	235	16	sets	set	NOUN
ejpam-6226	235	17	—	—	PUNCT
ejpam-6226	235	18	truth	truth	NOUN
ejpam-6226	235	19	,	,	PUNCT
ejpam-6226	235	20	indeterminacy	indeterminacy	NOUN
ejpam-6226	235	21	,	,	PUNCT
ejpam-6226	235	22	and	and	CCONJ
ejpam-6226	235	23	falsity	falsity	NOUN
ejpam-6226	235	24	—	—	PUNCT
ejpam-6226	235	25	and	and	CCONJ
ejpam-6226	235	26	are	be	AUX
ejpam-6226	235	27	motivated	motivate	VERB
ejpam-6226	235	28	by	by	ADP
ejpam-6226	235	29	their	their	PRON
ejpam-6226	235	30	capacity	capacity	NOUN
ejpam-6226	235	31	to	to	PART
ejpam-6226	235	32	model	model	VERB
ejpam-6226	235	33	more	more	ADV
ejpam-6226	235	34	complex	complex	ADJ
ejpam-6226	235	35	decision	decision	NOUN
ejpam-6226	235	36	-	-	PUNCT
ejpam-6226	235	37	making	make	VERB
ejpam-6226	235	38	environments	environment	NOUN
ejpam-6226	235	39	.	.	PUNCT
ejpam-6226	236	1	we	we	PRON
ejpam-6226	236	2	present	present	VERB
ejpam-6226	236	3	key	key	ADJ
ejpam-6226	236	4	properties	property	NOUN
ejpam-6226	236	5	,	,	PUNCT
ejpam-6226	236	6	establish	establish	VERB
ejpam-6226	236	7	their	their	PRON
ejpam-6226	236	8	relationships	relationship	NOUN
ejpam-6226	236	9	with	with	ADP
ejpam-6226	236	10	standard	standard	ADJ
ejpam-6226	236	11	neutrosophic	neutrosophic	ADJ
ejpam-6226	236	12	ideals	ideal	NOUN
ejpam-6226	236	13	,	,	PUNCT
ejpam-6226	236	14	and	and	CCONJ
ejpam-6226	236	15	explore	explore	VERB
ejpam-6226	236	16	the	the	DET
ejpam-6226	236	17	conditions	condition	NOUN
ejpam-6226	236	18	under	under	ADP
ejpam-6226	236	19	which	which	PRON
ejpam-6226	236	20	they	they	PRON
ejpam-6226	236	21	are	be	AUX
ejpam-6226	236	22	preserved	preserve	VERB
ejpam-6226	236	23	or	or	CCONJ
ejpam-6226	236	24	extended	extend	VERB
ejpam-6226	236	25	.	.	PUNCT
ejpam-6226	237	1	examples	example	NOUN
ejpam-6226	237	2	are	be	AUX
ejpam-6226	237	3	provided	provide	VERB
ejpam-6226	237	4	to	to	PART
ejpam-6226	237	5	illustrate	illustrate	VERB
ejpam-6226	237	6	the	the	DET
ejpam-6226	237	7	distinctions	distinction	NOUN
ejpam-6226	237	8	between	between	ADP
ejpam-6226	237	9	nmink	nmink	NOUN
ejpam-6226	237	10	-	-	PUNCT
ejpam-6226	237	11	is	be	AUX
ejpam-6226	237	12	/	/	SYM
ejpam-6226	237	13	npmink	npmink	NOUN
ejpam-6226	237	14	-	-	PUNCT
ejpam-6226	237	15	is	be	AUX
ejpam-6226	237	16	and	and	CCONJ
ejpam-6226	237	17	general	general	ADJ
ejpam-6226	237	18	neutrosophic	neutrosophic	ADJ
ejpam-6226	237	19	ideals	ideal	NOUN
ejpam-6226	237	20	.	.	PUNCT
ejpam-6226	238	1	definition	definition	NOUN
ejpam-6226	238	2	18	18	NUM
ejpam-6226	238	3	.	.	PUNCT
ejpam-6226	239	1	an	an	DET
ejpam-6226	239	2	ns	ns	ADJ
ejpam-6226	239	3	g	g	NOUN
ejpam-6226	239	4	=	=	PUNCT
ejpam-6226	239	5	(	(	PUNCT
ejpam-6226	239	6	gt	gt	INTJ
ejpam-6226	239	7	,	,	PUNCT
ejpam-6226	239	8	gi	gi	INTJ
ejpam-6226	239	9	,	,	PUNCT
ejpam-6226	239	10	gf	gf	NOUN
ejpam-6226	239	11	)	)	PUNCT
ejpam-6226	239	12	in	in	ADP
ejpam-6226	239	13	an	an	DET
ejpam-6226	239	14	ink	ink	NOUN
ejpam-6226	239	15	-	-	PUNCT
ejpam-6226	239	16	algebra	algebra	NOUN
ejpam-6226	239	17	i	i	PRON
ejpam-6226	239	18	is	be	AUX
ejpam-6226	239	19	entitled	entitle	VERB
ejpam-6226	239	20	as	as	ADP
ejpam-6226	239	21	a	a	DET
ejpam-6226	239	22	neutrosophic	neutrosophic	ADJ
ejpam-6226	239	23	implicative	implicative	ADJ
ejpam-6226	239	24	ink	ink	NOUN
ejpam-6226	239	25	-	-	PUNCT
ejpam-6226	239	26	ideal	ideal	NOUN
ejpam-6226	239	27	(	(	PUNCT
ejpam-6226	239	28	nmink	nmink	NOUN
ejpam-6226	239	29	-	-	PUNCT
ejpam-6226	239	30	i	i	PROPN
ejpam-6226	239	31	)	)	PUNCT
ejpam-6226	239	32	of	of	ADP
ejpam-6226	239	33	i	i	PRON
ejpam-6226	239	34	if	if	SCONJ
ejpam-6226	239	35	it	it	PRON
ejpam-6226	239	36	gratifies	gratify	VERB
ejpam-6226	239	37	(	(	PUNCT
ejpam-6226	239	38	d4	d4	PROPN
ejpam-6226	239	39	)	)	PUNCT
ejpam-6226	239	40	and	and	CCONJ
ejpam-6226	239	41	(	(	PUNCT
ejpam-6226	239	42	d11	d11	PROPN
ejpam-6226	239	43	)	)	PUNCT
ejpam-6226	239	44	gt	gt	PROPN
ejpam-6226	239	45	(	(	PUNCT
ejpam-6226	239	46	ϵ	ϵ	X
ejpam-6226	239	47	)	)	PUNCT
ejpam-6226	239	48	≥	≥	NOUN
ejpam-6226	239	49	min{gt	min{gt	X
ejpam-6226	239	50	(	(	PUNCT
ejpam-6226	239	51	(	(	PUNCT
ejpam-6226	239	52	ϵ	ϵ	PART
ejpam-6226	239	53	•	•	PRON
ejpam-6226	239	54	(	(	PUNCT
ejpam-6226	239	55	ξ	ξ	PROPN
ejpam-6226	239	56	•	•	NUM
ejpam-6226	239	57	ϵ	ϵ	NOUN
ejpam-6226	239	58	)	)	PUNCT
ejpam-6226	239	59	)	)	PUNCT
ejpam-6226	239	60	•	•	ADP
ejpam-6226	239	61	ς	ς	PROPN
ejpam-6226	239	62	)	)	PUNCT
ejpam-6226	239	63	,	,	PUNCT
ejpam-6226	239	64	gt	gt	PROPN
ejpam-6226	239	65	(	(	PUNCT
ejpam-6226	239	66	ς	ς	NOUN
ejpam-6226	239	67	)	)	PUNCT
ejpam-6226	239	68	}	}	PUNCT
ejpam-6226	239	69	(	(	PUNCT
ejpam-6226	239	70	d12	d12	NOUN
ejpam-6226	239	71	)	)	PUNCT
ejpam-6226	239	72	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	239	73	)	)	PUNCT
ejpam-6226	239	74	≤	≤	NUM
ejpam-6226	240	1	max{gi((ϵ	max{gi((ϵ	ADV
ejpam-6226	240	2	•	•	ADP
ejpam-6226	240	3	(	(	PUNCT
ejpam-6226	240	4	ξ	ξ	NOUN
ejpam-6226	240	5	•	•	NUM
ejpam-6226	240	6	ϵ	ϵ	NOUN
ejpam-6226	240	7	)	)	PUNCT
ejpam-6226	240	8	)	)	PUNCT
ejpam-6226	240	9	•	•	ADP
ejpam-6226	240	10	ς	ς	NOUN
ejpam-6226	240	11	)	)	PUNCT
ejpam-6226	240	12	,	,	PUNCT
ejpam-6226	240	13	gi(ς	gi(ς	NOUN
ejpam-6226	240	14	)	)	PUNCT
ejpam-6226	240	15	}	}	PUNCT
ejpam-6226	240	16	(	(	PUNCT
ejpam-6226	240	17	d13	d13	NOUN
ejpam-6226	240	18	)	)	PUNCT
ejpam-6226	240	19	gf	gf	NOUN
ejpam-6226	240	20	(	(	PUNCT
ejpam-6226	240	21	ϵ	ϵ	NOUN
ejpam-6226	240	22	)	)	PUNCT
ejpam-6226	240	23	≤	≤	NOUN
ejpam-6226	240	24	max{gf	max{gf	PUNCT
ejpam-6226	240	25	(	(	PUNCT
ejpam-6226	240	26	(	(	PUNCT
ejpam-6226	240	27	ϵ	ϵ	PART
ejpam-6226	240	28	•	•	PRON
ejpam-6226	240	29	(	(	PUNCT
ejpam-6226	240	30	ξ	ξ	PROPN
ejpam-6226	240	31	•	•	NUM
ejpam-6226	240	32	ϵ	ϵ	NOUN
ejpam-6226	240	33	)	)	PUNCT
ejpam-6226	240	34	)	)	PUNCT
ejpam-6226	240	35	•	•	ADP
ejpam-6226	240	36	ς	ς	NOUN
ejpam-6226	240	37	)	)	PUNCT
ejpam-6226	240	38	,	,	PUNCT
ejpam-6226	240	39	gf	gf	X
ejpam-6226	240	40	(	(	PUNCT
ejpam-6226	240	41	ς	ς	NOUN
ejpam-6226	240	42	)	)	PUNCT
ejpam-6226	240	43	}	}	PUNCT
ejpam-6226	240	44	,	,	PUNCT
ejpam-6226	240	45	∀ϵ	∀ϵ	PROPN
ejpam-6226	240	46	,	,	PUNCT
ejpam-6226	240	47	ξ	ξ	PROPN
ejpam-6226	240	48	,	,	PUNCT
ejpam-6226	240	49	ς	ς	PROPN
ejpam-6226	240	50	∈	∈	PROPN
ejpam-6226	240	51	i.	i.	NOUN
ejpam-6226	240	52	definition	definition	NOUN
ejpam-6226	240	53	19	19	NUM
ejpam-6226	240	54	.	.	PUNCT
ejpam-6226	241	1	an	an	DET
ejpam-6226	241	2	ns	ns	ADJ
ejpam-6226	241	3	g	g	NOUN
ejpam-6226	241	4	=	=	PUNCT
ejpam-6226	241	5	(	(	PUNCT
ejpam-6226	241	6	gt	gt	INTJ
ejpam-6226	241	7	,	,	PUNCT
ejpam-6226	241	8	gi	gi	INTJ
ejpam-6226	241	9	,	,	PUNCT
ejpam-6226	241	10	gf	gf	NOUN
ejpam-6226	241	11	)	)	PUNCT
ejpam-6226	241	12	in	in	ADP
ejpam-6226	241	13	an	an	DET
ejpam-6226	241	14	ink	ink	NOUN
ejpam-6226	241	15	-	-	PUNCT
ejpam-6226	241	16	algebra	algebra	NOUN
ejpam-6226	241	17	i	i	PRON
ejpam-6226	241	18	is	be	AUX
ejpam-6226	241	19	entitled	entitle	VERB
ejpam-6226	241	20	as	as	ADP
ejpam-6226	241	21	a	a	DET
ejpam-6226	241	22	neutrosophic	neutrosophic	ADJ
ejpam-6226	241	23	positive	positive	ADJ
ejpam-6226	241	24	implicative	implicative	ADJ
ejpam-6226	241	25	ink	ink	NOUN
ejpam-6226	241	26	-	-	PUNCT
ejpam-6226	241	27	ideal	ideal	NOUN
ejpam-6226	241	28	(	(	PUNCT
ejpam-6226	241	29	npmink	npmink	NOUN
ejpam-6226	241	30	-	-	PUNCT
ejpam-6226	241	31	i	i	PROPN
ejpam-6226	241	32	)	)	PUNCT
ejpam-6226	241	33	of	of	ADP
ejpam-6226	241	34	i	i	PRON
ejpam-6226	241	35	if	if	SCONJ
ejpam-6226	241	36	it	it	PRON
ejpam-6226	241	37	gratifies	gratify	VERB
ejpam-6226	241	38	(	(	PUNCT
ejpam-6226	241	39	d4	d4	PROPN
ejpam-6226	241	40	)	)	PUNCT
ejpam-6226	241	41	and	and	CCONJ
ejpam-6226	241	42	(	(	PUNCT
ejpam-6226	241	43	d14	d14	PROPN
ejpam-6226	241	44	)	)	PUNCT
ejpam-6226	241	45	gt	gt	PROPN
ejpam-6226	241	46	(	(	PUNCT
ejpam-6226	241	47	ϵ	ϵ	NOUN
ejpam-6226	241	48	•	•	NUM
ejpam-6226	241	49	ς	ς	PROPN
ejpam-6226	241	50	)	)	PUNCT
ejpam-6226	241	51	≥	≥	NOUN
ejpam-6226	241	52	min{gt	min{gt	X
ejpam-6226	241	53	(	(	PUNCT
ejpam-6226	241	54	(	(	PUNCT
ejpam-6226	241	55	ϵ	ϵ	PART
ejpam-6226	241	56	•	•	NUM
ejpam-6226	241	57	ξ	ξ	NOUN
ejpam-6226	241	58	)	)	PUNCT
ejpam-6226	241	59	•	•	NUM
ejpam-6226	241	60	ς	ς	PROPN
ejpam-6226	241	61	)	)	PUNCT
ejpam-6226	241	62	,	,	PUNCT
ejpam-6226	241	63	gt	gt	PROPN
ejpam-6226	241	64	(	(	PUNCT
ejpam-6226	241	65	ξ	ξ	PROPN
ejpam-6226	241	66	•	•	NUM
ejpam-6226	241	67	ς	ς	NOUN
ejpam-6226	241	68	)	)	PUNCT
ejpam-6226	241	69	}	}	PUNCT
ejpam-6226	241	70	(	(	PUNCT
ejpam-6226	241	71	d15	d15	NOUN
ejpam-6226	241	72	)	)	PUNCT
ejpam-6226	241	73	gi(ϵ	gi(ϵ	VERB
ejpam-6226	241	74	•	•	ADP
ejpam-6226	241	75	ς	ς	NOUN
ejpam-6226	241	76	)	)	PUNCT
ejpam-6226	241	77	≤	≤	NUM
ejpam-6226	242	1	max{gi((ϵ	max{gi((ϵ	ADV
ejpam-6226	242	2	•	•	NUM
ejpam-6226	242	3	ξ	ξ	NOUN
ejpam-6226	242	4	)	)	PUNCT
ejpam-6226	242	5	•	•	NUM
ejpam-6226	242	6	ς	ς	NOUN
ejpam-6226	242	7	)	)	PUNCT
ejpam-6226	242	8	,	,	PUNCT
ejpam-6226	242	9	gi(ξ	gi(ξ	X
ejpam-6226	242	10	•	•	ADP
ejpam-6226	242	11	ς	ς	NOUN
ejpam-6226	242	12	)	)	PUNCT
ejpam-6226	242	13	}	}	PUNCT
ejpam-6226	242	14	(	(	PUNCT
ejpam-6226	242	15	d16	d16	NOUN
ejpam-6226	242	16	)	)	PUNCT
ejpam-6226	242	17	gf	gf	NOUN
ejpam-6226	242	18	(	(	PUNCT
ejpam-6226	242	19	ϵ	ϵ	NOUN
ejpam-6226	242	20	•	•	NUM
ejpam-6226	242	21	ς	ς	PROPN
ejpam-6226	242	22	)	)	PUNCT
ejpam-6226	242	23	≤	≤	NOUN
ejpam-6226	242	24	max{gf	max{gf	PUNCT
ejpam-6226	242	25	(	(	PUNCT
ejpam-6226	242	26	(	(	PUNCT
ejpam-6226	242	27	ϵ	ϵ	PART
ejpam-6226	242	28	•	•	NUM
ejpam-6226	242	29	ξ	ξ	NOUN
ejpam-6226	242	30	)	)	PUNCT
ejpam-6226	242	31	•	•	NUM
ejpam-6226	242	32	ς	ς	NOUN
ejpam-6226	242	33	)	)	PUNCT
ejpam-6226	242	34	,	,	PUNCT
ejpam-6226	242	35	gf	gf	X
ejpam-6226	242	36	(	(	PUNCT
ejpam-6226	242	37	ξ	ξ	NOUN
ejpam-6226	242	38	•	•	NUM
ejpam-6226	242	39	ς)},∀ϵ	ς)},∀ϵ	NUM
ejpam-6226	242	40	,	,	PUNCT
ejpam-6226	242	41	ξ	ξ	PROPN
ejpam-6226	242	42	,	,	PUNCT
ejpam-6226	242	43	ς	ς	PROPN
ejpam-6226	242	44	∈	∈	PROPN
ejpam-6226	242	45	i.	i.	PROPN
ejpam-6226	242	46	r.	r.	PROPN
ejpam-6226	242	47	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	242	48	et	et	PROPN
ejpam-6226	242	49	al	al	PROPN
ejpam-6226	242	50	.	.	PUNCT
ejpam-6226	242	51	/	/	SYM
ejpam-6226	242	52	eur	eur	PROPN
ejpam-6226	242	53	.	.	PUNCT
ejpam-6226	243	1	j.	j.	PROPN
ejpam-6226	243	2	pure	pure	PROPN
ejpam-6226	243	3	appl	appl	PROPN
ejpam-6226	243	4	.	.	PROPN
ejpam-6226	243	5	math	math	PROPN
ejpam-6226	243	6	,	,	PUNCT
ejpam-6226	243	7	18	18	NUM
ejpam-6226	243	8	(	(	PUNCT
ejpam-6226	243	9	3	3	NUM
ejpam-6226	243	10	)	)	PUNCT
ejpam-6226	243	11	(	(	PUNCT
ejpam-6226	243	12	2025	2025	NUM
ejpam-6226	243	13	)	)	PUNCT
ejpam-6226	243	14	,	,	PUNCT
ejpam-6226	243	15	6226	6226	NUM
ejpam-6226	243	16	12	12	NUM
ejpam-6226	243	17	of	of	ADP
ejpam-6226	243	18	19	19	NUM
ejpam-6226	243	19	example	example	NOUN
ejpam-6226	243	20	8	8	NUM
ejpam-6226	243	21	.	.	PUNCT
ejpam-6226	243	22	consider	consider	VERB
ejpam-6226	243	23	an	an	DET
ejpam-6226	243	24	ink	ink	NOUN
ejpam-6226	243	25	-	-	PUNCT
ejpam-6226	243	26	algebra	algebra	NOUN
ejpam-6226	243	27	(	(	PUNCT
ejpam-6226	243	28	i	i	PROPN
ejpam-6226	243	29	,	,	PUNCT
ejpam-6226	243	30	•	•	PROPN
ejpam-6226	243	31	,	,	PUNCT
ejpam-6226	243	32	0	0	NUM
ejpam-6226	243	33	)	)	PUNCT
ejpam-6226	243	34	from	from	ADP
ejpam-6226	243	35	example	example	NOUN
ejpam-6226	243	36	3	3	NUM
ejpam-6226	243	37	.	.	PUNCT
ejpam-6226	243	38	define	define	VERB
ejpam-6226	243	39	an	an	DET
ejpam-6226	243	40	ns	ns	ADJ
ejpam-6226	243	41	g	g	NOUN
ejpam-6226	243	42	=	=	PUNCT
ejpam-6226	243	43	(	(	PUNCT
ejpam-6226	243	44	gt	gt	INTJ
ejpam-6226	243	45	,	,	PUNCT
ejpam-6226	243	46	gi	gi	INTJ
ejpam-6226	243	47	,	,	PUNCT
ejpam-6226	243	48	gf	gf	PROPN
ejpam-6226	243	49	)	)	PUNCT
ejpam-6226	243	50	of	of	ADP
ejpam-6226	243	51	i	i	PRON
ejpam-6226	243	52	by	by	ADP
ejpam-6226	243	53	0	0	NUM
ejpam-6226	243	54	ă	ă	PROPN
ejpam-6226	244	1	b̆	b̆	PROPN
ejpam-6226	244	2	gt	gt	PROPN
ejpam-6226	244	3	0.4	0.4	NUM
ejpam-6226	244	4	0.3	0.3	NUM
ejpam-6226	244	5	0.3	0.3	NUM
ejpam-6226	244	6	gi	gi	NOUN
ejpam-6226	244	7	0.2	0.2	NUM
ejpam-6226	244	8	0.4	0.4	NUM
ejpam-6226	244	9	0.4	0.4	NUM
ejpam-6226	245	1	gf	gf	NOUN
ejpam-6226	245	2	0.3	0.3	NUM
ejpam-6226	245	3	0.3	0.3	NUM
ejpam-6226	245	4	0.5	0.5	NUM
ejpam-6226	245	5	then	then	ADV
ejpam-6226	245	6	,	,	PUNCT
ejpam-6226	245	7	g	g	PROPN
ejpam-6226	245	8	=	=	SYM
ejpam-6226	245	9	(	(	PUNCT
ejpam-6226	245	10	gt	gt	INTJ
ejpam-6226	245	11	,	,	PUNCT
ejpam-6226	245	12	gi	gi	INTJ
ejpam-6226	245	13	,	,	PUNCT
ejpam-6226	245	14	gf	gf	PROPN
ejpam-6226	245	15	)	)	PUNCT
ejpam-6226	245	16	is	be	AUX
ejpam-6226	245	17	an	an	DET
ejpam-6226	245	18	nmink	nmink	NOUN
ejpam-6226	245	19	-	-	PUNCT
ejpam-6226	245	20	i	i	PRON
ejpam-6226	245	21	and	and	CCONJ
ejpam-6226	245	22	npmink	npmink	NOUN
ejpam-6226	245	23	-	-	PUNCT
ejpam-6226	245	24	i	i	PRON
ejpam-6226	245	25	of	of	ADP
ejpam-6226	245	26	i.	i.	PROPN
ejpam-6226	245	27	theorem	theorem	PROPN
ejpam-6226	245	28	12	12	NUM
ejpam-6226	245	29	.	.	PUNCT
ejpam-6226	246	1	every	every	DET
ejpam-6226	246	2	nmink	nmink	NOUN
ejpam-6226	246	3	-	-	PUNCT
ejpam-6226	246	4	i	i	PRON
ejpam-6226	246	5	of	of	ADP
ejpam-6226	246	6	an	an	DET
ejpam-6226	246	7	ink	ink	NOUN
ejpam-6226	246	8	-	-	PUNCT
ejpam-6226	246	9	algebra	algebra	NOUN
ejpam-6226	246	10	i	i	PRON
ejpam-6226	246	11	is	be	AUX
ejpam-6226	246	12	an	an	DET
ejpam-6226	246	13	nink	nink	NOUN
ejpam-6226	246	14	-	-	PUNCT
ejpam-6226	246	15	i.	i.	NOUN
ejpam-6226	246	16	proof	proof	NOUN
ejpam-6226	246	17	.	.	PUNCT
ejpam-6226	247	1	let	let	VERB
ejpam-6226	247	2	g	g	PROPN
ejpam-6226	247	3	=	=	SYM
ejpam-6226	247	4	(	(	PUNCT
ejpam-6226	247	5	gt	gt	INTJ
ejpam-6226	247	6	,	,	PUNCT
ejpam-6226	247	7	gi	gi	INTJ
ejpam-6226	247	8	,	,	PUNCT
ejpam-6226	247	9	gf	gf	PROPN
ejpam-6226	247	10	)	)	PUNCT
ejpam-6226	247	11	be	be	AUX
ejpam-6226	247	12	an	an	DET
ejpam-6226	247	13	nmink	nmink	NOUN
ejpam-6226	247	14	-	-	PUNCT
ejpam-6226	247	15	i	i	PRON
ejpam-6226	247	16	of	of	ADP
ejpam-6226	247	17	an	an	DET
ejpam-6226	247	18	ink	ink	NOUN
ejpam-6226	247	19	-	-	PUNCT
ejpam-6226	247	20	algebra	algebra	NOUN
ejpam-6226	247	21	i.	i.	NOUN
ejpam-6226	247	22	let	let	VERB
ejpam-6226	247	23	ϵ	ϵ	ADP
ejpam-6226	247	24	,	,	PUNCT
ejpam-6226	247	25	ξ	ξ	PROPN
ejpam-6226	247	26	,	,	PUNCT
ejpam-6226	247	27	ς	ς	PROPN
ejpam-6226	247	28	∈	∈	PROPN
ejpam-6226	247	29	i.	i.	NOUN
ejpam-6226	247	30	then	then	ADV
ejpam-6226	247	31	by	by	ADP
ejpam-6226	247	32	(	(	PUNCT
ejpam-6226	247	33	d11	d11	PROPN
ejpam-6226	247	34	)	)	PUNCT
ejpam-6226	247	35	,	,	PUNCT
ejpam-6226	247	36	we	we	PRON
ejpam-6226	247	37	have	have	VERB
ejpam-6226	247	38	gt	gt	PROPN
ejpam-6226	247	39	(	(	PUNCT
ejpam-6226	247	40	ϵ	ϵ	NOUN
ejpam-6226	247	41	)	)	PUNCT
ejpam-6226	247	42	≥	≥	NOUN
ejpam-6226	247	43	min{gt	min{gt	X
ejpam-6226	247	44	(	(	PUNCT
ejpam-6226	247	45	(	(	PUNCT
ejpam-6226	247	46	ϵ	ϵ	X
ejpam-6226	247	47	•	•	NOUN
ejpam-6226	247	48	(	(	PUNCT
ejpam-6226	247	49	0	0	NUM
ejpam-6226	247	50	•	•	NUM
ejpam-6226	247	51	ϵ	ϵ	NOUN
ejpam-6226	247	52	)	)	PUNCT
ejpam-6226	247	53	)	)	PUNCT
ejpam-6226	247	54	•	•	ADP
ejpam-6226	247	55	ς	ς	PROPN
ejpam-6226	247	56	)	)	PUNCT
ejpam-6226	247	57	,	,	PUNCT
ejpam-6226	247	58	gt	gt	PROPN
ejpam-6226	247	59	(	(	PUNCT
ejpam-6226	247	60	ς	ς	NOUN
ejpam-6226	247	61	)	)	PUNCT
ejpam-6226	247	62	}	}	PUNCT
ejpam-6226	247	63	=	=	SYM
ejpam-6226	247	64	min{gt	min{gt	NOUN
ejpam-6226	247	65	(	(	PUNCT
ejpam-6226	247	66	(	(	PUNCT
ejpam-6226	247	67	ϵ	ϵ	INTJ
ejpam-6226	247	68	•	•	NOUN
ejpam-6226	247	69	0	0	NUM
ejpam-6226	247	70	)	)	PUNCT
ejpam-6226	247	71	•	•	NUM
ejpam-6226	247	72	ς	ς	NOUN
ejpam-6226	247	73	)	)	PUNCT
ejpam-6226	247	74	)	)	PUNCT
ejpam-6226	247	75	,	,	PUNCT
ejpam-6226	247	76	gt	gt	PROPN
ejpam-6226	247	77	(	(	PUNCT
ejpam-6226	247	78	ς	ς	NOUN
ejpam-6226	247	79	)	)	PUNCT
ejpam-6226	247	80	}	}	PUNCT
ejpam-6226	248	1	=	=	SYM
ejpam-6226	248	2	min{gt	min{gt	NOUN
ejpam-6226	248	3	(	(	PUNCT
ejpam-6226	248	4	ϵ	ϵ	SYM
ejpam-6226	248	5	•	•	NUM
ejpam-6226	248	6	ς	ς	PROPN
ejpam-6226	248	7	)	)	PUNCT
ejpam-6226	248	8	,	,	PUNCT
ejpam-6226	248	9	gt	gt	PROPN
ejpam-6226	248	10	(	(	PUNCT
ejpam-6226	248	11	ς	ς	NOUN
ejpam-6226	248	12	)	)	PUNCT
ejpam-6226	248	13	}	}	PUNCT
ejpam-6226	248	14	.	.	PUNCT
ejpam-6226	249	1	this	this	PRON
ejpam-6226	249	2	shows	show	VERB
ejpam-6226	249	3	that	that	SCONJ
ejpam-6226	249	4	gt	gt	PROPN
ejpam-6226	249	5	gratifies	gratify	VERB
ejpam-6226	249	6	(	(	PUNCT
ejpam-6226	249	7	d5	d5	NOUN
ejpam-6226	249	8	)	)	PUNCT
ejpam-6226	249	9	.	.	PUNCT
ejpam-6226	250	1	by	by	ADP
ejpam-6226	250	2	(	(	PUNCT
ejpam-6226	250	3	d12	d12	PROPN
ejpam-6226	250	4	)	)	PUNCT
ejpam-6226	250	5	,	,	PUNCT
ejpam-6226	250	6	we	we	PRON
ejpam-6226	250	7	have	have	AUX
ejpam-6226	250	8	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	250	9	)	)	PUNCT
ejpam-6226	250	10	≤	≤	NUM
ejpam-6226	250	11	max{gi((ϵ	max{gi((ϵ	ADV
ejpam-6226	250	12	•	•	ADP
ejpam-6226	250	13	(	(	PUNCT
ejpam-6226	250	14	0	0	NUM
ejpam-6226	250	15	•	•	NUM
ejpam-6226	250	16	ϵ	ϵ	NOUN
ejpam-6226	250	17	)	)	PUNCT
ejpam-6226	250	18	)	)	PUNCT
ejpam-6226	250	19	•	•	ADP
ejpam-6226	250	20	ς	ς	NOUN
ejpam-6226	250	21	)	)	PUNCT
ejpam-6226	250	22	,	,	PUNCT
ejpam-6226	250	23	gi(ς	gi(ς	NOUN
ejpam-6226	250	24	)	)	PUNCT
ejpam-6226	250	25	}	}	PUNCT
ejpam-6226	250	26	=	=	PUNCT
ejpam-6226	251	1	max{gi((ϵ	max{gi((ϵ	ADV
ejpam-6226	251	2	•	•	NOUN
ejpam-6226	251	3	0	0	NUM
ejpam-6226	251	4	)	)	PUNCT
ejpam-6226	251	5	•	•	NUM
ejpam-6226	251	6	ς	ς	NOUN
ejpam-6226	251	7	)	)	PUNCT
ejpam-6226	251	8	)	)	PUNCT
ejpam-6226	251	9	,	,	PUNCT
ejpam-6226	251	10	gi(ς	gi(ς	NOUN
ejpam-6226	251	11	)	)	PUNCT
ejpam-6226	251	12	}	}	PUNCT
ejpam-6226	251	13	=	=	PUNCT
ejpam-6226	251	14	max{gi(ϵ	max{gi(ϵ	NUM
ejpam-6226	251	15	•	•	NUM
ejpam-6226	251	16	ς	ς	NOUN
ejpam-6226	251	17	)	)	PUNCT
ejpam-6226	251	18	,	,	PUNCT
ejpam-6226	251	19	gi(ς	gi(ς	NOUN
ejpam-6226	251	20	)	)	PUNCT
ejpam-6226	251	21	}	}	PUNCT
ejpam-6226	251	22	.	.	PUNCT
ejpam-6226	252	1	this	this	PRON
ejpam-6226	252	2	shows	show	VERB
ejpam-6226	252	3	that	that	SCONJ
ejpam-6226	252	4	gi	gi	PROPN
ejpam-6226	252	5	gratifies	gratify	VERB
ejpam-6226	252	6	(	(	PUNCT
ejpam-6226	252	7	d6	d6	NOUN
ejpam-6226	252	8	)	)	PUNCT
ejpam-6226	252	9	.	.	PUNCT
ejpam-6226	253	1	by	by	ADP
ejpam-6226	253	2	(	(	PUNCT
ejpam-6226	253	3	d13	d13	NOUN
ejpam-6226	253	4	)	)	PUNCT
ejpam-6226	253	5	,	,	PUNCT
ejpam-6226	253	6	we	we	PRON
ejpam-6226	253	7	have	have	VERB
ejpam-6226	253	8	gf	gf	VERB
ejpam-6226	253	9	(	(	PUNCT
ejpam-6226	253	10	ϵ	ϵ	NOUN
ejpam-6226	253	11	)	)	PUNCT
ejpam-6226	253	12	≤	≤	NOUN
ejpam-6226	253	13	max{gf	max{gf	PUNCT
ejpam-6226	253	14	(	(	PUNCT
ejpam-6226	253	15	(	(	PUNCT
ejpam-6226	253	16	ϵ	ϵ	X
ejpam-6226	253	17	•	•	NOUN
ejpam-6226	253	18	(	(	PUNCT
ejpam-6226	253	19	0	0	NUM
ejpam-6226	253	20	•	•	NUM
ejpam-6226	253	21	ϵ	ϵ	NOUN
ejpam-6226	253	22	)	)	PUNCT
ejpam-6226	253	23	)	)	PUNCT
ejpam-6226	253	24	•	•	ADP
ejpam-6226	253	25	ς	ς	NOUN
ejpam-6226	253	26	)	)	PUNCT
ejpam-6226	253	27	,	,	PUNCT
ejpam-6226	253	28	gf	gf	X
ejpam-6226	253	29	(	(	PUNCT
ejpam-6226	253	30	ς	ς	NOUN
ejpam-6226	253	31	)	)	PUNCT
ejpam-6226	253	32	}	}	PUNCT
ejpam-6226	253	33	=	=	SYM
ejpam-6226	253	34	max{gf	max{gf	X
ejpam-6226	254	1	(	(	PUNCT
ejpam-6226	254	2	(	(	PUNCT
ejpam-6226	254	3	ϵ	ϵ	INTJ
ejpam-6226	254	4	•	•	NOUN
ejpam-6226	254	5	0	0	NUM
ejpam-6226	254	6	)	)	PUNCT
ejpam-6226	254	7	•	•	NUM
ejpam-6226	254	8	ς	ς	NOUN
ejpam-6226	254	9	)	)	PUNCT
ejpam-6226	254	10	)	)	PUNCT
ejpam-6226	254	11	,	,	PUNCT
ejpam-6226	254	12	gf	gf	X
ejpam-6226	254	13	(	(	PUNCT
ejpam-6226	254	14	ς	ς	NOUN
ejpam-6226	254	15	)	)	PUNCT
ejpam-6226	254	16	}	}	PUNCT
ejpam-6226	255	1	=	=	SYM
ejpam-6226	255	2	max{gf	max{gf	X
ejpam-6226	255	3	(	(	PUNCT
ejpam-6226	255	4	ϵ	ϵ	PROPN
ejpam-6226	255	5	•	•	NUM
ejpam-6226	255	6	ς	ς	PROPN
ejpam-6226	255	7	)	)	PUNCT
ejpam-6226	255	8	,	,	PUNCT
ejpam-6226	255	9	gf	gf	X
ejpam-6226	255	10	(	(	PUNCT
ejpam-6226	255	11	ς	ς	NOUN
ejpam-6226	255	12	)	)	PUNCT
ejpam-6226	255	13	}	}	PUNCT
ejpam-6226	255	14	.	.	PUNCT
ejpam-6226	256	1	this	this	PRON
ejpam-6226	256	2	shows	show	VERB
ejpam-6226	256	3	that	that	SCONJ
ejpam-6226	256	4	gf	gf	PROPN
ejpam-6226	256	5	gratifies	gratify	VERB
ejpam-6226	256	6	(	(	PUNCT
ejpam-6226	256	7	d7	d7	PROPN
ejpam-6226	256	8	)	)	PUNCT
ejpam-6226	256	9	.	.	PUNCT
ejpam-6226	257	1	by	by	ADP
ejpam-6226	257	2	combining	combine	VERB
ejpam-6226	257	3	(	(	PUNCT
ejpam-6226	257	4	d4	d4	PROPN
ejpam-6226	257	5	)	)	PUNCT
ejpam-6226	257	6	,	,	PUNCT
ejpam-6226	257	7	g	g	PROPN
ejpam-6226	257	8	is	be	AUX
ejpam-6226	257	9	an	an	DET
ejpam-6226	257	10	nink	nink	NOUN
ejpam-6226	257	11	-	-	PUNCT
ejpam-6226	257	12	i	i	PRON
ejpam-6226	257	13	of	of	ADP
ejpam-6226	257	14	i.	i.	PROPN
ejpam-6226	257	15	note	note	PROPN
ejpam-6226	257	16	:	:	PUNCT
ejpam-6226	257	17	every	every	DET
ejpam-6226	257	18	nmink	nmink	NOUN
ejpam-6226	257	19	-	-	PUNCT
ejpam-6226	257	20	i	i	PRON
ejpam-6226	257	21	of	of	ADP
ejpam-6226	257	22	an	an	DET
ejpam-6226	257	23	ink	ink	NOUN
ejpam-6226	257	24	-	-	PUNCT
ejpam-6226	257	25	algebra	algebra	NOUN
ejpam-6226	257	26	is	be	AUX
ejpam-6226	257	27	an	an	DET
ejpam-6226	257	28	nink	nink	NOUN
ejpam-6226	257	29	-	-	PUNCT
ejpam-6226	257	30	i	i	NOUN
ejpam-6226	257	31	,	,	PUNCT
ejpam-6226	257	32	but	but	CCONJ
ejpam-6226	257	33	the	the	DET
ejpam-6226	257	34	converse	converse	NOUN
ejpam-6226	257	35	is	be	AUX
ejpam-6226	257	36	not	not	PART
ejpam-6226	257	37	valid	valid	ADJ
ejpam-6226	257	38	.	.	PUNCT
ejpam-6226	258	1	example	example	NOUN
ejpam-6226	258	2	9	9	NUM
ejpam-6226	258	3	.	.	X
ejpam-6226	258	4	consider	consider	VERB
ejpam-6226	258	5	an	an	DET
ejpam-6226	258	6	ink	ink	NOUN
ejpam-6226	258	7	-	-	PUNCT
ejpam-6226	258	8	algebra	algebra	NOUN
ejpam-6226	259	1	i	i	NOUN
ejpam-6226	259	2	=	=	PUNCT
ejpam-6226	259	3	{	{	PUNCT
ejpam-6226	259	4	0	0	NUM
ejpam-6226	259	5	,	,	PUNCT
ejpam-6226	259	6	ă	ă	NOUN
ejpam-6226	259	7	,	,	PUNCT
ejpam-6226	259	8	b̆	b̆	NOUN
ejpam-6226	259	9	}	}	PUNCT
ejpam-6226	259	10	with	with	ADP
ejpam-6226	259	11	the	the	DET
ejpam-6226	259	12	following	follow	VERB
ejpam-6226	259	13	cayley	cayley	ADJ
ejpam-6226	259	14	table	table	NOUN
ejpam-6226	259	15	:	:	PUNCT
ejpam-6226	259	16	•	•	NOUN
ejpam-6226	259	17	0	0	X
ejpam-6226	259	18	ă	ă	PROPN
ejpam-6226	259	19	b̆	b̆	NOUN
ejpam-6226	259	20	0	0	NUM
ejpam-6226	259	21	0	0	NUM
ejpam-6226	259	22	b̆	b̆	NOUN
ejpam-6226	259	23	ă	ă	NOUN
ejpam-6226	259	24	ă	ă	PROPN
ejpam-6226	259	25	ă	ă	PROPN
ejpam-6226	259	26	0	0	NUM
ejpam-6226	260	1	b̆	b̆	NOUN
ejpam-6226	260	2	b̆	b̆	NOUN
ejpam-6226	260	3	b̆	b̆	PROPN
ejpam-6226	260	4	ă	ă	PROPN
ejpam-6226	260	5	0	0	NUM
ejpam-6226	261	1	define	define	VERB
ejpam-6226	261	2	an	an	DET
ejpam-6226	261	3	ns	ns	ADJ
ejpam-6226	261	4	g	g	NOUN
ejpam-6226	261	5	=	=	PUNCT
ejpam-6226	261	6	(	(	PUNCT
ejpam-6226	261	7	gt	gt	INTJ
ejpam-6226	261	8	,	,	PUNCT
ejpam-6226	261	9	gi	gi	INTJ
ejpam-6226	261	10	,	,	PUNCT
ejpam-6226	261	11	gf	gf	PROPN
ejpam-6226	261	12	)	)	PUNCT
ejpam-6226	261	13	of	of	ADP
ejpam-6226	261	14	i	i	PRON
ejpam-6226	261	15	by	by	ADP
ejpam-6226	261	16	0	0	NUM
ejpam-6226	261	17	ă	ă	PROPN
ejpam-6226	261	18	b̆	b̆	NOUN
ejpam-6226	262	1	gt	gt	PROPN
ejpam-6226	262	2	0.6	0.6	NUM
ejpam-6226	262	3	0.3	0.3	NUM
ejpam-6226	262	4	0.3	0.3	NUM
ejpam-6226	262	5	gi	gi	NOUN
ejpam-6226	262	6	0.5	0.5	NUM
ejpam-6226	262	7	0.4	0.4	NUM
ejpam-6226	262	8	0.4	0.4	NUM
ejpam-6226	262	9	gf	gf	NOUN
ejpam-6226	262	10	0.8	0.8	NUM
ejpam-6226	262	11	0.4	0.4	NUM
ejpam-6226	262	12	0.4	0.4	NUM
ejpam-6226	262	13	r.	r.	PROPN
ejpam-6226	262	14	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	262	15	et	et	PROPN
ejpam-6226	262	16	al	al	PROPN
ejpam-6226	262	17	.	.	PUNCT
ejpam-6226	262	18	/	/	SYM
ejpam-6226	262	19	eur	eur	PROPN
ejpam-6226	262	20	.	.	PUNCT
ejpam-6226	263	1	j.	j.	PROPN
ejpam-6226	263	2	pure	pure	PROPN
ejpam-6226	263	3	appl	appl	PROPN
ejpam-6226	263	4	.	.	PROPN
ejpam-6226	263	5	math	math	PROPN
ejpam-6226	263	6	,	,	PUNCT
ejpam-6226	263	7	18	18	NUM
ejpam-6226	263	8	(	(	PUNCT
ejpam-6226	263	9	3	3	NUM
ejpam-6226	263	10	)	)	PUNCT
ejpam-6226	263	11	(	(	PUNCT
ejpam-6226	263	12	2025	2025	NUM
ejpam-6226	263	13	)	)	PUNCT
ejpam-6226	263	14	,	,	PUNCT
ejpam-6226	263	15	6226	6226	NUM
ejpam-6226	263	16	13	13	NUM
ejpam-6226	263	17	of	of	ADP
ejpam-6226	263	18	19	19	NUM
ejpam-6226	263	19	then	then	ADV
ejpam-6226	263	20	,	,	PUNCT
ejpam-6226	263	21	the	the	DET
ejpam-6226	263	22	above	above	ADJ
ejpam-6226	263	23	table	table	NOUN
ejpam-6226	263	24	satisfies	satisfy	VERB
ejpam-6226	263	25	the	the	DET
ejpam-6226	263	26	nink	nink	VERB
ejpam-6226	263	27	-	-	PUNCT
ejpam-6226	263	28	i	i	PRON
ejpam-6226	263	29	conditions	condition	NOUN
ejpam-6226	263	30	but	but	CCONJ
ejpam-6226	263	31	does	do	AUX
ejpam-6226	263	32	not	not	PART
ejpam-6226	263	33	satisfy	satisfy	VERB
ejpam-6226	263	34	the	the	DET
ejpam-6226	263	35	conditions	condition	NOUN
ejpam-6226	263	36	of	of	ADP
ejpam-6226	263	37	nmink	nmink	NOUN
ejpam-6226	263	38	-	-	PUNCT
ejpam-6226	263	39	i	i	PRON
ejpam-6226	263	40	of	of	ADP
ejpam-6226	263	41	i.	i.	PROPN
ejpam-6226	263	42	theorem	theorem	VERB
ejpam-6226	263	43	13	13	NUM
ejpam-6226	263	44	.	.	PUNCT
ejpam-6226	264	1	if	if	SCONJ
ejpam-6226	264	2	i	i	PRON
ejpam-6226	264	3	is	be	AUX
ejpam-6226	264	4	an	an	DET
ejpam-6226	264	5	implicative	implicative	ADJ
ejpam-6226	264	6	ink	ink	NOUN
ejpam-6226	264	7	-	-	PUNCT
ejpam-6226	264	8	algebra	algebra	NOUN
ejpam-6226	264	9	,	,	PUNCT
ejpam-6226	264	10	then	then	ADV
ejpam-6226	264	11	every	every	DET
ejpam-6226	264	12	nink	nink	NOUN
ejpam-6226	264	13	-	-	PUNCT
ejpam-6226	264	14	i	i	PRON
ejpam-6226	264	15	of	of	ADP
ejpam-6226	264	16	i	i	PRON
ejpam-6226	264	17	is	be	AUX
ejpam-6226	264	18	an	an	DET
ejpam-6226	264	19	nmink	nmink	NOUN
ejpam-6226	264	20	-	-	PUNCT
ejpam-6226	264	21	i.	i.	NOUN
ejpam-6226	264	22	proof	proof	NOUN
ejpam-6226	264	23	.	.	PUNCT
ejpam-6226	265	1	since	since	SCONJ
ejpam-6226	265	2	i	i	PRON
ejpam-6226	265	3	is	be	AUX
ejpam-6226	265	4	an	an	DET
ejpam-6226	265	5	implicative	implicative	ADJ
ejpam-6226	265	6	ink	ink	NOUN
ejpam-6226	265	7	-	-	PUNCT
ejpam-6226	265	8	algebra	algebra	NOUN
ejpam-6226	265	9	,	,	PUNCT
ejpam-6226	265	10	it	it	PRON
ejpam-6226	265	11	follows	follow	VERB
ejpam-6226	265	12	that	that	SCONJ
ejpam-6226	265	13	ϵ	ϵ	PROPN
ejpam-6226	265	14	=	=	SYM
ejpam-6226	265	15	ϵ•(ξ•ϵ	ϵ•(ξ•ϵ	PROPN
ejpam-6226	265	16	)	)	PUNCT
ejpam-6226	265	17	,	,	PUNCT
ejpam-6226	265	18	∀ϵ	∀ϵ	PROPN
ejpam-6226	265	19	,	,	PUNCT
ejpam-6226	265	20	ξ	ξ	PROPN
ejpam-6226	265	21	∈	∈	PROPN
ejpam-6226	265	22	i.	i.	NOUN
ejpam-6226	265	23	let	let	VERB
ejpam-6226	265	24	g	g	PROPN
ejpam-6226	265	25	=	=	SYM
ejpam-6226	265	26	(	(	PUNCT
ejpam-6226	265	27	gt	gt	INTJ
ejpam-6226	265	28	,	,	PUNCT
ejpam-6226	265	29	gi	gi	INTJ
ejpam-6226	265	30	,	,	PUNCT
ejpam-6226	265	31	gf	gf	PROPN
ejpam-6226	265	32	)	)	PUNCT
ejpam-6226	265	33	be	be	AUX
ejpam-6226	265	34	an	an	DET
ejpam-6226	265	35	nink	nink	NOUN
ejpam-6226	265	36	-	-	PUNCT
ejpam-6226	265	37	i	i	PRON
ejpam-6226	265	38	of	of	ADP
ejpam-6226	265	39	i.	i.	PROPN
ejpam-6226	265	40	then	then	ADV
ejpam-6226	265	41	by	by	ADP
ejpam-6226	265	42	(	(	PUNCT
ejpam-6226	265	43	d5	d5	NOUN
ejpam-6226	265	44	)	)	PUNCT
ejpam-6226	265	45	,	,	PUNCT
ejpam-6226	265	46	gt	gt	PROPN
ejpam-6226	265	47	(	(	PUNCT
ejpam-6226	265	48	ϵ	ϵ	X
ejpam-6226	265	49	)	)	PUNCT
ejpam-6226	265	50	≥	≥	NOUN
ejpam-6226	265	51	min{gt	min{gt	X
ejpam-6226	265	52	(	(	PUNCT
ejpam-6226	265	53	ϵ	ϵ	SYM
ejpam-6226	265	54	•	•	NUM
ejpam-6226	265	55	ς	ς	PROPN
ejpam-6226	265	56	)	)	PUNCT
ejpam-6226	265	57	,	,	PUNCT
ejpam-6226	265	58	gt	gt	PROPN
ejpam-6226	265	59	(	(	PUNCT
ejpam-6226	265	60	ς)},∀ϵ	ς)},∀ϵ	NUM
ejpam-6226	265	61	,	,	PUNCT
ejpam-6226	265	62	ξ	ξ	PROPN
ejpam-6226	265	63	,	,	PUNCT
ejpam-6226	265	64	ς	ς	PROPN
ejpam-6226	265	65	∈	∈	PROPN
ejpam-6226	266	1	i	i	PRON
ejpam-6226	266	2	,	,	PUNCT
ejpam-6226	266	3	so	so	ADV
ejpam-6226	266	4	gt	gt	INTJ
ejpam-6226	266	5	(	(	PUNCT
ejpam-6226	266	6	ϵ	ϵ	X
ejpam-6226	266	7	)	)	PUNCT
ejpam-6226	266	8	≥	≥	NOUN
ejpam-6226	266	9	min{gt	min{gt	X
ejpam-6226	266	10	(	(	PUNCT
ejpam-6226	266	11	(	(	PUNCT
ejpam-6226	266	12	ϵ	ϵ	PART
ejpam-6226	266	13	•	•	PRON
ejpam-6226	266	14	(	(	PUNCT
ejpam-6226	266	15	ξ	ξ	PROPN
ejpam-6226	266	16	•	•	NUM
ejpam-6226	266	17	ϵ	ϵ	NOUN
ejpam-6226	266	18	)	)	PUNCT
ejpam-6226	266	19	)	)	PUNCT
ejpam-6226	266	20	•	•	ADP
ejpam-6226	266	21	ς	ς	PROPN
ejpam-6226	266	22	)	)	PUNCT
ejpam-6226	266	23	,	,	PUNCT
ejpam-6226	266	24	gt	gt	PROPN
ejpam-6226	266	25	(	(	PUNCT
ejpam-6226	266	26	ς	ς	NOUN
ejpam-6226	266	27	)	)	PUNCT
ejpam-6226	266	28	}	}	PUNCT
ejpam-6226	266	29	.	.	PUNCT
ejpam-6226	267	1	similarly	similarly	ADV
ejpam-6226	267	2	,	,	PUNCT
ejpam-6226	267	3	by	by	ADP
ejpam-6226	267	4	(	(	PUNCT
ejpam-6226	267	5	d6	d6	NOUN
ejpam-6226	267	6	)	)	PUNCT
ejpam-6226	267	7	,	,	PUNCT
ejpam-6226	267	8	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	267	9	)	)	PUNCT
ejpam-6226	267	10	≤	≤	NUM
ejpam-6226	267	11	max{gi(ϵ	max{gi(ϵ	NOUN
ejpam-6226	267	12	•	•	NUM
ejpam-6226	267	13	ς	ς	NOUN
ejpam-6226	267	14	)	)	PUNCT
ejpam-6226	267	15	,	,	PUNCT
ejpam-6226	267	16	gi(ς	gi(ς	NOUN
ejpam-6226	267	17	)	)	PUNCT
ejpam-6226	267	18	}	}	PUNCT
ejpam-6226	267	19	,	,	PUNCT
ejpam-6226	267	20	so	so	CCONJ
ejpam-6226	267	21	gi(ϵ	gi(ϵ	NOUN
ejpam-6226	267	22	)	)	PUNCT
ejpam-6226	267	23	≤	≤	NUM
ejpam-6226	268	1	max{gi((ϵ	max{gi((ϵ	ADV
ejpam-6226	268	2	•	•	ADP
ejpam-6226	268	3	(	(	PUNCT
ejpam-6226	268	4	ξ	ξ	NOUN
ejpam-6226	268	5	•	•	NUM
ejpam-6226	268	6	ϵ	ϵ	NOUN
ejpam-6226	268	7	)	)	PUNCT
ejpam-6226	268	8	)	)	PUNCT
ejpam-6226	268	9	•	•	ADP
ejpam-6226	268	10	ς	ς	NOUN
ejpam-6226	268	11	)	)	PUNCT
ejpam-6226	268	12	,	,	PUNCT
ejpam-6226	268	13	gi(ς	gi(ς	NOUN
ejpam-6226	268	14	)	)	PUNCT
ejpam-6226	268	15	}	}	PUNCT
ejpam-6226	268	16	.	.	PUNCT
ejpam-6226	269	1	also	also	ADV
ejpam-6226	269	2	by	by	ADP
ejpam-6226	269	3	(	(	PUNCT
ejpam-6226	269	4	d7	d7	PROPN
ejpam-6226	269	5	)	)	PUNCT
ejpam-6226	269	6	,	,	PUNCT
ejpam-6226	269	7	gf	gf	X
ejpam-6226	269	8	(	(	PUNCT
ejpam-6226	269	9	ϵ	ϵ	NOUN
ejpam-6226	269	10	)	)	PUNCT
ejpam-6226	269	11	≤	≤	NOUN
ejpam-6226	269	12	max{gf	max{gf	PUNCT
ejpam-6226	269	13	(	(	PUNCT
ejpam-6226	269	14	ϵ	ϵ	PROPN
ejpam-6226	269	15	•	•	NUM
ejpam-6226	269	16	ς	ς	PROPN
ejpam-6226	269	17	)	)	PUNCT
ejpam-6226	269	18	,	,	PUNCT
ejpam-6226	269	19	gf	gf	X
ejpam-6226	269	20	(	(	PUNCT
ejpam-6226	269	21	ς	ς	NOUN
ejpam-6226	269	22	)	)	PUNCT
ejpam-6226	269	23	}	}	PUNCT
ejpam-6226	269	24	,	,	PUNCT
ejpam-6226	269	25	so	so	ADV
ejpam-6226	269	26	gf	gf	X
ejpam-6226	269	27	(	(	PUNCT
ejpam-6226	269	28	ϵ	ϵ	NOUN
ejpam-6226	269	29	)	)	PUNCT
ejpam-6226	269	30	≤	≤	NOUN
ejpam-6226	269	31	max{gf	max{gf	PUNCT
ejpam-6226	269	32	(	(	PUNCT
ejpam-6226	269	33	(	(	PUNCT
ejpam-6226	269	34	ϵ	ϵ	PART
ejpam-6226	269	35	•	•	PRON
ejpam-6226	269	36	(	(	PUNCT
ejpam-6226	269	37	ξ	ξ	PROPN
ejpam-6226	269	38	•	•	NUM
ejpam-6226	269	39	ϵ	ϵ	NOUN
ejpam-6226	269	40	)	)	PUNCT
ejpam-6226	269	41	)	)	PUNCT
ejpam-6226	269	42	•	•	ADP
ejpam-6226	269	43	ς	ς	NOUN
ejpam-6226	269	44	)	)	PUNCT
ejpam-6226	269	45	,	,	PUNCT
ejpam-6226	269	46	gf	gf	X
ejpam-6226	269	47	(	(	PUNCT
ejpam-6226	269	48	ς	ς	NOUN
ejpam-6226	269	49	)	)	PUNCT
ejpam-6226	269	50	}	}	PUNCT
ejpam-6226	269	51	.	.	PUNCT
ejpam-6226	270	1	hence	hence	ADV
ejpam-6226	270	2	,	,	PUNCT
ejpam-6226	270	3	g	g	PROPN
ejpam-6226	270	4	is	be	AUX
ejpam-6226	270	5	an	an	DET
ejpam-6226	270	6	nmink	nmink	NOUN
ejpam-6226	270	7	-	-	PUNCT
ejpam-6226	270	8	i	i	PRON
ejpam-6226	270	9	of	of	ADP
ejpam-6226	270	10	i.	i.	PROPN
ejpam-6226	270	11	theorem	theorem	VERB
ejpam-6226	270	12	14	14	NUM
ejpam-6226	270	13	.	.	PUNCT
ejpam-6226	271	1	every	every	DET
ejpam-6226	271	2	npmink	npmink	NOUN
ejpam-6226	271	3	-	-	PUNCT
ejpam-6226	271	4	i	i	PRON
ejpam-6226	271	5	of	of	ADP
ejpam-6226	271	6	an	an	DET
ejpam-6226	271	7	ink	ink	NOUN
ejpam-6226	271	8	-	-	PUNCT
ejpam-6226	271	9	algebra	algebra	NOUN
ejpam-6226	271	10	i	i	PRON
ejpam-6226	271	11	is	be	AUX
ejpam-6226	271	12	an	an	DET
ejpam-6226	271	13	nink	nink	NOUN
ejpam-6226	271	14	-	-	PUNCT
ejpam-6226	271	15	i.	i.	NOUN
ejpam-6226	271	16	proof	proof	NOUN
ejpam-6226	271	17	.	.	PUNCT
ejpam-6226	272	1	the	the	DET
ejpam-6226	272	2	proof	proof	NOUN
ejpam-6226	272	3	is	be	AUX
ejpam-6226	272	4	similar	similar	ADJ
ejpam-6226	272	5	to	to	ADP
ejpam-6226	272	6	theorem	theorem	NOUN
ejpam-6226	272	7	12	12	NUM
ejpam-6226	272	8	.	.	PUNCT
ejpam-6226	273	1	note	note	NOUN
ejpam-6226	273	2	:	:	PUNCT
ejpam-6226	273	3	the	the	DET
ejpam-6226	273	4	following	follow	VERB
ejpam-6226	273	5	example	example	NOUN
ejpam-6226	273	6	shows	show	VERB
ejpam-6226	273	7	that	that	SCONJ
ejpam-6226	273	8	the	the	DET
ejpam-6226	273	9	converse	converse	NOUN
ejpam-6226	273	10	of	of	ADP
ejpam-6226	273	11	theorem	theorem	NOUN
ejpam-6226	273	12	14	14	NUM
ejpam-6226	273	13	does	do	AUX
ejpam-6226	273	14	not	not	PART
ejpam-6226	273	15	hold	hold	VERB
ejpam-6226	273	16	.	.	PUNCT
ejpam-6226	274	1	example	example	NOUN
ejpam-6226	274	2	10	10	NUM
ejpam-6226	274	3	.	.	PUNCT
ejpam-6226	275	1	consider	consider	VERB
ejpam-6226	275	2	an	an	DET
ejpam-6226	275	3	ink	ink	NOUN
ejpam-6226	275	4	-	-	PUNCT
ejpam-6226	275	5	algebra	algebra	NOUN
ejpam-6226	275	6	i	i	NOUN
ejpam-6226	275	7	=	=	PUNCT
ejpam-6226	275	8	{	{	PUNCT
ejpam-6226	275	9	0	0	NUM
ejpam-6226	275	10	,	,	PUNCT
ejpam-6226	275	11	ă	ă	PROPN
ejpam-6226	275	12	,	,	PUNCT
ejpam-6226	275	13	b̆	b̆	NOUN
ejpam-6226	275	14	,	,	PUNCT
ejpam-6226	275	15	c̆	c̆	NOUN
ejpam-6226	275	16	}	}	PUNCT
ejpam-6226	275	17	from	from	ADP
ejpam-6226	275	18	example	example	NOUN
ejpam-6226	275	19	5	5	NUM
ejpam-6226	275	20	.	.	PUNCT
ejpam-6226	275	21	define	define	VERB
ejpam-6226	275	22	an	an	DET
ejpam-6226	275	23	ns	ns	ADJ
ejpam-6226	275	24	g	g	NOUN
ejpam-6226	275	25	=	=	PUNCT
ejpam-6226	275	26	(	(	PUNCT
ejpam-6226	275	27	gt	gt	INTJ
ejpam-6226	275	28	,	,	PUNCT
ejpam-6226	275	29	gi	gi	INTJ
ejpam-6226	275	30	,	,	PUNCT
ejpam-6226	275	31	gf	gf	PROPN
ejpam-6226	275	32	)	)	PUNCT
ejpam-6226	275	33	of	of	ADP
ejpam-6226	275	34	i	i	PRON
ejpam-6226	275	35	by	by	ADP
ejpam-6226	275	36	0	0	NUM
ejpam-6226	275	37	ă	ă	PROPN
ejpam-6226	276	1	b̆	b̆	INTJ
ejpam-6226	277	1	c̆	c̆	ADV
ejpam-6226	277	2	gt	gt	PROPN
ejpam-6226	277	3	0.5	0.5	NUM
ejpam-6226	277	4	0.3	0.3	NUM
ejpam-6226	277	5	0.3	0.3	NUM
ejpam-6226	277	6	0.5	0.5	NUM
ejpam-6226	277	7	gi	gi	NOUN
ejpam-6226	277	8	0.2	0.2	NUM
ejpam-6226	277	9	0.4	0.4	NUM
ejpam-6226	277	10	0.4	0.4	NUM
ejpam-6226	277	11	0.2	0.2	NUM
ejpam-6226	277	12	gf	gf	NOUN
ejpam-6226	277	13	0.3	0.3	NUM
ejpam-6226	277	14	0.5	0.5	NUM
ejpam-6226	277	15	0.5	0.5	NUM
ejpam-6226	277	16	0.4	0.4	NUM
ejpam-6226	277	17	then	then	ADV
ejpam-6226	277	18	,	,	PUNCT
ejpam-6226	277	19	the	the	DET
ejpam-6226	277	20	above	above	ADJ
ejpam-6226	277	21	table	table	NOUN
ejpam-6226	277	22	satisfies	satisfy	VERB
ejpam-6226	277	23	the	the	DET
ejpam-6226	277	24	nink	nink	VERB
ejpam-6226	277	25	-	-	PUNCT
ejpam-6226	277	26	i	i	PRON
ejpam-6226	277	27	conditions	condition	NOUN
ejpam-6226	277	28	but	but	CCONJ
ejpam-6226	277	29	does	do	AUX
ejpam-6226	277	30	not	not	PART
ejpam-6226	277	31	satisfy	satisfy	VERB
ejpam-6226	277	32	the	the	DET
ejpam-6226	277	33	conditions	condition	NOUN
ejpam-6226	277	34	of	of	ADP
ejpam-6226	277	35	npmink	npmink	NOUN
ejpam-6226	277	36	-	-	PUNCT
ejpam-6226	277	37	i	i	PRON
ejpam-6226	277	38	of	of	ADP
ejpam-6226	277	39	i.	i.	PROPN
ejpam-6226	277	40	4.1	4.1	NUM
ejpam-6226	277	41	.	.	PUNCT
ejpam-6226	278	1	intersection	intersection	NOUN
ejpam-6226	278	2	of	of	ADP
ejpam-6226	278	3	neutrosophic	neutrosophic	ADJ
ejpam-6226	278	4	implicative	implicative	ADJ
ejpam-6226	278	5	and	and	CCONJ
ejpam-6226	278	6	positive	positive	ADJ
ejpam-6226	278	7	implicative	implicative	ADJ
ejpam-6226	278	8	inkideals	inkideal	NOUN
ejpam-6226	278	9	of	of	ADP
ejpam-6226	278	10	ink	ink	NOUN
ejpam-6226	278	11	-	-	PUNCT
ejpam-6226	278	12	algebras	algebras	NOUN
ejpam-6226	278	13	in	in	ADP
ejpam-6226	278	14	this	this	DET
ejpam-6226	278	15	subsection	subsection	NOUN
ejpam-6226	278	16	,	,	PUNCT
ejpam-6226	278	17	we	we	PRON
ejpam-6226	278	18	investigate	investigate	VERB
ejpam-6226	278	19	the	the	DET
ejpam-6226	278	20	stability	stability	NOUN
ejpam-6226	278	21	of	of	ADP
ejpam-6226	278	22	nmink	nmink	NOUN
ejpam-6226	278	23	-	-	PUNCT
ejpam-6226	278	24	is	be	AUX
ejpam-6226	278	25	and	and	CCONJ
ejpam-6226	278	26	npmink	npmink	VERB
ejpam-6226	278	27	-	-	PUNCT
ejpam-6226	278	28	is	be	AUX
ejpam-6226	278	29	under	under	ADP
ejpam-6226	278	30	intersection	intersection	NOUN
ejpam-6226	278	31	operation	operation	NOUN
ejpam-6226	278	32	.	.	PUNCT
ejpam-6226	279	1	understanding	understand	VERB
ejpam-6226	279	2	how	how	SCONJ
ejpam-6226	279	3	these	these	DET
ejpam-6226	279	4	classes	class	NOUN
ejpam-6226	279	5	of	of	ADP
ejpam-6226	279	6	ideals	ideal	NOUN
ejpam-6226	279	7	behave	behave	VERB
ejpam-6226	279	8	under	under	ADP
ejpam-6226	279	9	set	set	NOUN
ejpam-6226	279	10	-	-	PUNCT
ejpam-6226	279	11	theoretic	theoretic	NOUN
ejpam-6226	279	12	intersection	intersection	NOUN
ejpam-6226	279	13	is	be	AUX
ejpam-6226	279	14	crucial	crucial	ADJ
ejpam-6226	279	15	for	for	ADP
ejpam-6226	279	16	exploring	explore	VERB
ejpam-6226	279	17	their	their	PRON
ejpam-6226	279	18	algebraic	algebraic	ADJ
ejpam-6226	279	19	structure	structure	NOUN
ejpam-6226	279	20	and	and	CCONJ
ejpam-6226	279	21	for	for	ADP
ejpam-6226	279	22	constructing	construct	VERB
ejpam-6226	279	23	new	new	ADJ
ejpam-6226	279	24	ideals	ideal	NOUN
ejpam-6226	279	25	from	from	ADP
ejpam-6226	279	26	existing	exist	VERB
ejpam-6226	279	27	ones	one	NOUN
ejpam-6226	279	28	.	.	PUNCT
ejpam-6226	280	1	we	we	PRON
ejpam-6226	280	2	prove	prove	VERB
ejpam-6226	280	3	that	that	SCONJ
ejpam-6226	280	4	the	the	DET
ejpam-6226	280	5	intersection	intersection	NOUN
ejpam-6226	280	6	of	of	ADP
ejpam-6226	280	7	any	any	DET
ejpam-6226	280	8	two	two	NUM
ejpam-6226	280	9	nmink	nmink	NOUN
ejpam-6226	280	10	-	-	PUNCT
ejpam-6226	280	11	is	be	AUX
ejpam-6226	280	12	(	(	PUNCT
ejpam-6226	280	13	respectively	respectively	ADV
ejpam-6226	280	14	,	,	PUNCT
ejpam-6226	280	15	npmink	npmink	NOUN
ejpam-6226	280	16	-	-	PUNCT
ejpam-6226	280	17	is	be	AUX
ejpam-6226	280	18	)	)	PUNCT
ejpam-6226	280	19	results	result	NOUN
ejpam-6226	280	20	in	in	ADP
ejpam-6226	280	21	an	an	DET
ejpam-6226	280	22	ideal	ideal	NOUN
ejpam-6226	280	23	of	of	ADP
ejpam-6226	280	24	the	the	DET
ejpam-6226	280	25	same	same	ADJ
ejpam-6226	280	26	type	type	NOUN
ejpam-6226	280	27	,	,	PUNCT
ejpam-6226	280	28	thus	thus	ADV
ejpam-6226	280	29	demonstrating	demonstrate	VERB
ejpam-6226	280	30	the	the	DET
ejpam-6226	280	31	closure	closure	NOUN
ejpam-6226	280	32	property	property	NOUN
ejpam-6226	280	33	under	under	ADP
ejpam-6226	280	34	intersection	intersection	NOUN
ejpam-6226	280	35	.	.	PUNCT
ejpam-6226	281	1	we	we	PRON
ejpam-6226	281	2	also	also	ADV
ejpam-6226	281	3	provide	provide	VERB
ejpam-6226	281	4	illustrative	illustrative	ADJ
ejpam-6226	281	5	examples	example	NOUN
ejpam-6226	281	6	to	to	PART
ejpam-6226	281	7	confirm	confirm	VERB
ejpam-6226	281	8	the	the	DET
ejpam-6226	281	9	validity	validity	NOUN
ejpam-6226	281	10	of	of	ADP
ejpam-6226	281	11	the	the	DET
ejpam-6226	281	12	results	result	NOUN
ejpam-6226	281	13	and	and	CCONJ
ejpam-6226	281	14	highlight	highlight	VERB
ejpam-6226	281	15	that	that	SCONJ
ejpam-6226	281	16	,	,	PUNCT
ejpam-6226	281	17	unlike	unlike	ADP
ejpam-6226	281	18	intersection	intersection	NOUN
ejpam-6226	281	19	,	,	PUNCT
ejpam-6226	281	20	the	the	DET
ejpam-6226	281	21	union	union	NOUN
ejpam-6226	281	22	of	of	ADP
ejpam-6226	281	23	such	such	ADJ
ejpam-6226	281	24	ideals	ideal	NOUN
ejpam-6226	281	25	does	do	AUX
ejpam-6226	281	26	not	not	PART
ejpam-6226	281	27	necessarily	necessarily	ADV
ejpam-6226	281	28	preserve	preserve	VERB
ejpam-6226	281	29	the	the	DET
ejpam-6226	281	30	implicative	implicative	ADJ
ejpam-6226	281	31	properties	property	NOUN
ejpam-6226	281	32	.	.	PUNCT
ejpam-6226	282	1	definition	definition	NOUN
ejpam-6226	282	2	20	20	NUM
ejpam-6226	282	3	.	.	PUNCT
ejpam-6226	283	1	let	let	VERB
ejpam-6226	283	2	g	g	PROPN
ejpam-6226	283	3	=	=	SYM
ejpam-6226	283	4	(	(	PUNCT
ejpam-6226	283	5	gt	gt	INTJ
ejpam-6226	283	6	,	,	PUNCT
ejpam-6226	283	7	gi	gi	INTJ
ejpam-6226	283	8	,	,	PUNCT
ejpam-6226	283	9	gf	gf	PROPN
ejpam-6226	283	10	)	)	PUNCT
ejpam-6226	283	11	and	and	CCONJ
ejpam-6226	283	12	h	h	NOUN
ejpam-6226	283	13	=	=	SYM
ejpam-6226	283	14	(	(	PUNCT
ejpam-6226	283	15	ht	ht	INTJ
ejpam-6226	283	16	,	,	PUNCT
ejpam-6226	283	17	hi	hi	INTJ
ejpam-6226	283	18	,	,	PUNCT
ejpam-6226	283	19	hf	hf	INTJ
ejpam-6226	283	20	)	)	PUNCT
ejpam-6226	283	21	be	be	AUX
ejpam-6226	283	22	two	two	NUM
ejpam-6226	283	23	nss	ns	NOUN
ejpam-6226	283	24	in	in	ADP
ejpam-6226	283	25	i.	i.	NOUN
ejpam-6226	283	26	then	then	ADV
ejpam-6226	283	27	the	the	DET
ejpam-6226	283	28	intersection	intersection	NOUN
ejpam-6226	283	29	g	g	NOUN
ejpam-6226	283	30	∩	∩	ADJ
ejpam-6226	283	31	h	h	NOUN
ejpam-6226	283	32	=	=	SYM
ejpam-6226	283	33	(	(	PUNCT
ejpam-6226	283	34	tg∩h	tg∩h	PROPN
ejpam-6226	283	35	,	,	PUNCT
ejpam-6226	283	36	ig∩h	ig∩h	PROPN
ejpam-6226	283	37	,	,	PUNCT
ejpam-6226	283	38	fg∩h	fg∩h	PROPN
ejpam-6226	283	39	)	)	PUNCT
ejpam-6226	283	40	is	be	AUX
ejpam-6226	283	41	defined	define	VERB
ejpam-6226	283	42	as	as	SCONJ
ejpam-6226	283	43	follows	follow	VERB
ejpam-6226	283	44	:	:	PUNCT
ejpam-6226	283	45	(	(	PUNCT
ejpam-6226	283	46	i	i	NOUN
ejpam-6226	283	47	)	)	PUNCT
ejpam-6226	283	48	tg∩h(ϵ	tg∩h(ϵ	PROPN
ejpam-6226	283	49	)	)	PUNCT
ejpam-6226	283	50	≥	≥	NOUN
ejpam-6226	283	51	min{gt	min{gt	X
ejpam-6226	283	52	(	(	PUNCT
ejpam-6226	283	53	ϵ	ϵ	X
ejpam-6226	283	54	)	)	PUNCT
ejpam-6226	283	55	,	,	PUNCT
ejpam-6226	283	56	ht	ht	PROPN
ejpam-6226	283	57	(	(	PUNCT
ejpam-6226	283	58	ϵ	ϵ	NOUN
ejpam-6226	283	59	)	)	PUNCT
ejpam-6226	283	60	}	}	PUNCT
ejpam-6226	283	61	(	(	PUNCT
ejpam-6226	283	62	ii	ii	X
ejpam-6226	283	63	)	)	PUNCT
ejpam-6226	283	64	ig∩h(ϵ	ig∩h(ϵ	PROPN
ejpam-6226	283	65	)	)	PUNCT
ejpam-6226	283	66	≤	≤	NUM
ejpam-6226	283	67	max{gi(ϵ	max{gi(ϵ	NOUN
ejpam-6226	283	68	)	)	PUNCT
ejpam-6226	283	69	,	,	PUNCT
ejpam-6226	283	70	hi(ϵ	hi(ϵ	NOUN
ejpam-6226	283	71	)	)	PUNCT
ejpam-6226	283	72	}	}	PUNCT
ejpam-6226	283	73	(	(	PUNCT
ejpam-6226	283	74	iii	iii	X
ejpam-6226	283	75	)	)	PUNCT
ejpam-6226	283	76	fg∩h(ϵ	fg∩h(ϵ	PROPN
ejpam-6226	283	77	)	)	PUNCT
ejpam-6226	283	78	≤	≤	NUM
ejpam-6226	283	79	max{gf	max{gf	PUNCT
ejpam-6226	283	80	(	(	PUNCT
ejpam-6226	283	81	ϵ	ϵ	NOUN
ejpam-6226	283	82	)	)	PUNCT
ejpam-6226	283	83	,	,	PUNCT
ejpam-6226	283	84	hf	hf	X
ejpam-6226	283	85	(	(	PUNCT
ejpam-6226	283	86	ϵ)},∀ϵ	ϵ)},∀ϵ	PUNCT
ejpam-6226	283	87	∈	∈	PROPN
ejpam-6226	283	88	i.	i.	PROPN
ejpam-6226	283	89	r.	r.	PROPN
ejpam-6226	283	90	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	284	1	et	et	PROPN
ejpam-6226	284	2	al	al	PROPN
ejpam-6226	284	3	.	.	PUNCT
ejpam-6226	284	4	/	/	SYM
ejpam-6226	284	5	eur	eur	PROPN
ejpam-6226	284	6	.	.	PUNCT
ejpam-6226	285	1	j.	j.	PROPN
ejpam-6226	285	2	pure	pure	PROPN
ejpam-6226	285	3	appl	appl	PROPN
ejpam-6226	285	4	.	.	PROPN
ejpam-6226	285	5	math	math	PROPN
ejpam-6226	285	6	,	,	PUNCT
ejpam-6226	285	7	18	18	NUM
ejpam-6226	285	8	(	(	PUNCT
ejpam-6226	285	9	3	3	NUM
ejpam-6226	285	10	)	)	PUNCT
ejpam-6226	285	11	(	(	PUNCT
ejpam-6226	285	12	2025	2025	NUM
ejpam-6226	285	13	)	)	PUNCT
ejpam-6226	285	14	,	,	PUNCT
ejpam-6226	285	15	6226	6226	NUM
ejpam-6226	285	16	14	14	NUM
ejpam-6226	285	17	of	of	ADP
ejpam-6226	285	18	19	19	NUM
ejpam-6226	285	19	definition	definition	NOUN
ejpam-6226	285	20	21	21	NUM
ejpam-6226	285	21	.	.	PUNCT
ejpam-6226	286	1	let	let	VERB
ejpam-6226	286	2	g	g	PROPN
ejpam-6226	286	3	=	=	SYM
ejpam-6226	286	4	(	(	PUNCT
ejpam-6226	286	5	gt	gt	INTJ
ejpam-6226	286	6	,	,	PUNCT
ejpam-6226	286	7	gi	gi	INTJ
ejpam-6226	286	8	,	,	PUNCT
ejpam-6226	286	9	gf	gf	PROPN
ejpam-6226	286	10	)	)	PUNCT
ejpam-6226	286	11	and	and	CCONJ
ejpam-6226	286	12	h	h	NOUN
ejpam-6226	286	13	=	=	SYM
ejpam-6226	286	14	(	(	PUNCT
ejpam-6226	286	15	ht	ht	INTJ
ejpam-6226	286	16	,	,	PUNCT
ejpam-6226	286	17	hi	hi	INTJ
ejpam-6226	286	18	,	,	PUNCT
ejpam-6226	286	19	hf	hf	INTJ
ejpam-6226	286	20	)	)	PUNCT
ejpam-6226	286	21	be	be	AUX
ejpam-6226	286	22	two	two	NUM
ejpam-6226	286	23	nss	ns	NOUN
ejpam-6226	286	24	in	in	ADP
ejpam-6226	286	25	i.	i.	NOUN
ejpam-6226	286	26	then	then	ADV
ejpam-6226	286	27	the	the	DET
ejpam-6226	286	28	union	union	NOUN
ejpam-6226	286	29	g	g	NOUN
ejpam-6226	286	30	∪	∪	ADJ
ejpam-6226	286	31	h	h	NOUN
ejpam-6226	286	32	=	=	PUNCT
ejpam-6226	286	33	(	(	PUNCT
ejpam-6226	286	34	tg∪h	tg∪h	ADJ
ejpam-6226	286	35	,	,	PUNCT
ejpam-6226	286	36	ig∪h	ig∪h	NOUN
ejpam-6226	286	37	,	,	PUNCT
ejpam-6226	286	38	fg∪h	fg∪h	NOUN
ejpam-6226	286	39	)	)	PUNCT
ejpam-6226	286	40	is	be	AUX
ejpam-6226	286	41	defined	define	VERB
ejpam-6226	286	42	as	as	SCONJ
ejpam-6226	286	43	follows	follow	VERB
ejpam-6226	286	44	:	:	PUNCT
ejpam-6226	286	45	(	(	PUNCT
ejpam-6226	286	46	i	i	NOUN
ejpam-6226	286	47	)	)	PUNCT
ejpam-6226	286	48	tg∪h(ϵ	tg∪h(ϵ	PROPN
ejpam-6226	286	49	)	)	PUNCT
ejpam-6226	286	50	≤	≤	PROPN
ejpam-6226	286	51	max{gt	max{gt	ADV
ejpam-6226	286	52	(	(	PUNCT
ejpam-6226	286	53	ϵ	ϵ	X
ejpam-6226	286	54	)	)	PUNCT
ejpam-6226	286	55	,	,	PUNCT
ejpam-6226	286	56	ht	ht	PROPN
ejpam-6226	286	57	(	(	PUNCT
ejpam-6226	286	58	ϵ	ϵ	NOUN
ejpam-6226	286	59	)	)	PUNCT
ejpam-6226	286	60	}	}	PUNCT
ejpam-6226	286	61	(	(	PUNCT
ejpam-6226	286	62	ii	ii	NOUN
ejpam-6226	286	63	)	)	PUNCT
ejpam-6226	286	64	ig∪h(ϵ	ig∪h(ϵ	PROPN
ejpam-6226	286	65	)	)	PUNCT
ejpam-6226	286	66	≥	≥	NOUN
ejpam-6226	286	67	min{gi(ϵ	min{gi(ϵ	PROPN
ejpam-6226	286	68	)	)	PUNCT
ejpam-6226	286	69	,	,	PUNCT
ejpam-6226	286	70	hi(ϵ	hi(ϵ	NOUN
ejpam-6226	286	71	)	)	PUNCT
ejpam-6226	286	72	}	}	PUNCT
ejpam-6226	286	73	(	(	PUNCT
ejpam-6226	286	74	iii	iii	X
ejpam-6226	286	75	)	)	PUNCT
ejpam-6226	286	76	hg∪h(ϵ	hg∪h(ϵ	PROPN
ejpam-6226	286	77	)	)	PUNCT
ejpam-6226	286	78	≥	≥	PRON
ejpam-6226	286	79	min{gf	min{gf	X
ejpam-6226	286	80	(	(	PUNCT
ejpam-6226	286	81	ϵ	ϵ	NOUN
ejpam-6226	286	82	)	)	PUNCT
ejpam-6226	286	83	,	,	PUNCT
ejpam-6226	286	84	hf	hf	X
ejpam-6226	286	85	(	(	PUNCT
ejpam-6226	286	86	ϵ)},∀ϵ	ϵ)},∀ϵ	PUNCT
ejpam-6226	286	87	∈	∈	PROPN
ejpam-6226	286	88	i.	i.	NOUN
ejpam-6226	286	89	theorem	theorem	VERB
ejpam-6226	286	90	15	15	NUM
ejpam-6226	286	91	.	.	PUNCT
ejpam-6226	287	1	let	let	VERB
ejpam-6226	287	2	g	g	NOUN
ejpam-6226	287	3	=	=	SYM
ejpam-6226	287	4	(	(	PUNCT
ejpam-6226	287	5	gt	gt	INTJ
ejpam-6226	287	6	,	,	PUNCT
ejpam-6226	287	7	gi	gi	INTJ
ejpam-6226	287	8	,	,	PUNCT
ejpam-6226	287	9	gf	gf	PROPN
ejpam-6226	287	10	)	)	PUNCT
ejpam-6226	287	11	and	and	CCONJ
ejpam-6226	287	12	h	h	NOUN
ejpam-6226	287	13	=	=	SYM
ejpam-6226	287	14	(	(	PUNCT
ejpam-6226	287	15	ht	ht	INTJ
ejpam-6226	287	16	,	,	PUNCT
ejpam-6226	287	17	hi	hi	INTJ
ejpam-6226	287	18	,	,	PUNCT
ejpam-6226	287	19	hf	hf	INTJ
ejpam-6226	287	20	)	)	PUNCT
ejpam-6226	287	21	be	be	AUX
ejpam-6226	287	22	two	two	NUM
ejpam-6226	287	23	nmink	nmink	NOUN
ejpam-6226	287	24	-	-	PUNCT
ejpam-6226	287	25	is	be	AUX
ejpam-6226	287	26	of	of	ADP
ejpam-6226	287	27	an	an	DET
ejpam-6226	287	28	inkalgebra	inkalgebra	NOUN
ejpam-6226	287	29	i.	i.	NOUN
ejpam-6226	287	30	then	then	ADV
ejpam-6226	287	31	g	g	PROPN
ejpam-6226	287	32	∩	∩	ADJ
ejpam-6226	287	33	h	h	NOUN
ejpam-6226	287	34	=	=	SYM
ejpam-6226	287	35	(	(	PUNCT
ejpam-6226	287	36	tg∩h	tg∩h	PROPN
ejpam-6226	287	37	,	,	PUNCT
ejpam-6226	287	38	ig∩h	ig∩h	PROPN
ejpam-6226	287	39	,	,	PUNCT
ejpam-6226	287	40	fg∩h	fg∩h	PROPN
ejpam-6226	287	41	)	)	PUNCT
ejpam-6226	287	42	is	be	AUX
ejpam-6226	287	43	an	an	DET
ejpam-6226	287	44	nmink	nmink	NOUN
ejpam-6226	287	45	-	-	PUNCT
ejpam-6226	287	46	i	i	PRON
ejpam-6226	287	47	of	of	ADP
ejpam-6226	287	48	i.	i.	PROPN
ejpam-6226	287	49	proof	proof	PROPN
ejpam-6226	287	50	.	.	PUNCT
ejpam-6226	288	1	let	let	VERB
ejpam-6226	288	2	g	g	NOUN
ejpam-6226	288	3	and	and	CCONJ
ejpam-6226	288	4	h	h	NOUN
ejpam-6226	288	5	be	be	VERB
ejpam-6226	288	6	two	two	NUM
ejpam-6226	288	7	nmink	nmink	NOUN
ejpam-6226	288	8	-	-	PUNCT
ejpam-6226	288	9	is	be	AUX
ejpam-6226	288	10	of	of	ADP
ejpam-6226	288	11	an	an	DET
ejpam-6226	288	12	ink	ink	NOUN
ejpam-6226	288	13	-	-	PUNCT
ejpam-6226	288	14	algebra	algebra	NOUN
ejpam-6226	288	15	i.	i.	NOUN
ejpam-6226	288	16	let	let	VERB
ejpam-6226	288	17	ϵ	ϵ	ADP
ejpam-6226	288	18	,	,	PUNCT
ejpam-6226	288	19	ξ	ξ	PROPN
ejpam-6226	288	20	,	,	PUNCT
ejpam-6226	288	21	ς	ς	PROPN
ejpam-6226	288	22	∈	∈	PROPN
ejpam-6226	288	23	i.	i.	NOUN
ejpam-6226	288	24	then	then	ADV
ejpam-6226	288	25	tg∩h(ϵ	tg∩h(ϵ	PROPN
ejpam-6226	288	26	)	)	PUNCT
ejpam-6226	288	27	=	=	PRON
ejpam-6226	288	28	min{gt	min{gt	SYM
ejpam-6226	288	29	(	(	PUNCT
ejpam-6226	288	30	ϵ	ϵ	X
ejpam-6226	288	31	)	)	PUNCT
ejpam-6226	288	32	,	,	PUNCT
ejpam-6226	288	33	ht	ht	PROPN
ejpam-6226	288	34	(	(	PUNCT
ejpam-6226	288	35	ϵ	ϵ	NOUN
ejpam-6226	288	36	)	)	PUNCT
ejpam-6226	288	37	}	}	PUNCT
ejpam-6226	288	38	≥	≥	X
ejpam-6226	288	39	min{min{gt	min{min{gt	PRON
ejpam-6226	288	40	(	(	PUNCT
ejpam-6226	288	41	(	(	PUNCT
ejpam-6226	288	42	ϵ	ϵ	PART
ejpam-6226	288	43	•	•	NOUN
ejpam-6226	288	44	(	(	PUNCT
ejpam-6226	288	45	ξ	ξ	PROPN
ejpam-6226	288	46	•	•	NUM
ejpam-6226	288	47	ϵ	ϵ	NOUN
ejpam-6226	288	48	)	)	PUNCT
ejpam-6226	288	49	)	)	PUNCT
ejpam-6226	288	50	•	•	ADP
ejpam-6226	288	51	ς	ς	PROPN
ejpam-6226	288	52	)	)	PUNCT
ejpam-6226	288	53	,	,	PUNCT
ejpam-6226	288	54	gt	gt	PROPN
ejpam-6226	288	55	(	(	PUNCT
ejpam-6226	288	56	ς)},min{ht	ς)},min{ht	PROPN
ejpam-6226	288	57	(	(	PUNCT
ejpam-6226	288	58	(	(	PUNCT
ejpam-6226	288	59	ϵ	ϵ	PART
ejpam-6226	288	60	•	•	PRON
ejpam-6226	288	61	(	(	PUNCT
ejpam-6226	288	62	ξ	ξ	PROPN
ejpam-6226	288	63	•	•	NUM
ejpam-6226	288	64	ϵ	ϵ	NOUN
ejpam-6226	288	65	)	)	PUNCT
ejpam-6226	288	66	)	)	PUNCT
ejpam-6226	288	67	•	•	ADP
ejpam-6226	288	68	ς	ς	PROPN
ejpam-6226	288	69	)	)	PUNCT
ejpam-6226	288	70	,	,	PUNCT
ejpam-6226	288	71	ht	ht	PROPN
ejpam-6226	288	72	(	(	PUNCT
ejpam-6226	288	73	ς	ς	NOUN
ejpam-6226	288	74	)	)	PUNCT
ejpam-6226	288	75	}	}	PUNCT
ejpam-6226	288	76	}	}	PUNCT
ejpam-6226	288	77	=	=	SYM
ejpam-6226	288	78	min{min{gt	min{min{gt	PRON
ejpam-6226	288	79	(	(	PUNCT
ejpam-6226	288	80	(	(	PUNCT
ejpam-6226	288	81	ϵ	ϵ	PART
ejpam-6226	288	82	•	•	NOUN
ejpam-6226	288	83	(	(	PUNCT
ejpam-6226	288	84	ξ	ξ	PROPN
ejpam-6226	288	85	•	•	NUM
ejpam-6226	288	86	ϵ	ϵ	NOUN
ejpam-6226	288	87	)	)	PUNCT
ejpam-6226	288	88	)	)	PUNCT
ejpam-6226	288	89	•	•	ADP
ejpam-6226	288	90	ς	ς	PROPN
ejpam-6226	288	91	)	)	PUNCT
ejpam-6226	288	92	,	,	PUNCT
ejpam-6226	288	93	ht	ht	INTJ
ejpam-6226	288	94	(	(	PUNCT
ejpam-6226	288	95	(	(	PUNCT
ejpam-6226	288	96	ϵ	ϵ	PART
ejpam-6226	288	97	•	•	NOUN
ejpam-6226	288	98	(	(	PUNCT
ejpam-6226	288	99	ξ	ξ	PROPN
ejpam-6226	288	100	•	•	NUM
ejpam-6226	288	101	ϵ	ϵ	NOUN
ejpam-6226	288	102	)	)	PUNCT
ejpam-6226	288	103	)	)	PUNCT
ejpam-6226	289	1	•	•	ADP
ejpam-6226	289	2	ς)},min{gt	ς)},min{gt	PROPN
ejpam-6226	289	3	(	(	PUNCT
ejpam-6226	289	4	ς	ς	PROPN
ejpam-6226	289	5	)	)	PUNCT
ejpam-6226	289	6	,	,	PUNCT
ejpam-6226	289	7	ht	ht	PROPN
ejpam-6226	289	8	(	(	PUNCT
ejpam-6226	289	9	ς	ς	NOUN
ejpam-6226	289	10	)	)	PUNCT
ejpam-6226	289	11	}	}	PUNCT
ejpam-6226	289	12	}	}	PUNCT
ejpam-6226	289	13	≥	≥	X
ejpam-6226	289	14	min{tg∩h((ϵ	min{tg∩h((ϵ	ADJ
ejpam-6226	289	15	•	•	NOUN
ejpam-6226	289	16	(	(	PUNCT
ejpam-6226	289	17	ξ	ξ	PROPN
ejpam-6226	289	18	•	•	NUM
ejpam-6226	289	19	ϵ	ϵ	NOUN
ejpam-6226	289	20	)	)	PUNCT
ejpam-6226	289	21	)	)	PUNCT
ejpam-6226	289	22	•	•	ADP
ejpam-6226	289	23	ς	ς	PROPN
ejpam-6226	289	24	)	)	PUNCT
ejpam-6226	289	25	,	,	PUNCT
ejpam-6226	289	26	tg∩h(ς	tg∩h(ς	PROPN
ejpam-6226	289	27	)	)	PUNCT
ejpam-6226	289	28	}	}	PUNCT
ejpam-6226	289	29	,	,	PUNCT
ejpam-6226	289	30	ig∩h(ϵ	ig∩h(ϵ	PROPN
ejpam-6226	289	31	)	)	PUNCT
ejpam-6226	289	32	=	=	SYM
ejpam-6226	289	33	max{gi(ϵ	max{gi(ϵ	PROPN
ejpam-6226	289	34	)	)	PUNCT
ejpam-6226	289	35	,	,	PUNCT
ejpam-6226	289	36	hi(ϵ	hi(ϵ	NOUN
ejpam-6226	289	37	)	)	PUNCT
ejpam-6226	289	38	}	}	PUNCT
ejpam-6226	289	39	≤	≤	NUM
ejpam-6226	290	1	max{max{gi((ϵ	max{max{gi((ϵ	CCONJ
ejpam-6226	290	2	•	•	NOUN
ejpam-6226	290	3	(	(	PUNCT
ejpam-6226	290	4	ξ	ξ	NOUN
ejpam-6226	290	5	•	•	NUM
ejpam-6226	290	6	ϵ	ϵ	NOUN
ejpam-6226	290	7	)	)	PUNCT
ejpam-6226	290	8	)	)	PUNCT
ejpam-6226	290	9	•	•	ADP
ejpam-6226	291	1	ς	ς	NOUN
ejpam-6226	291	2	)	)	PUNCT
ejpam-6226	291	3	,	,	PUNCT
ejpam-6226	292	1	gi(ς)},max{hi((ϵ	gi(ς)},max{hi((ϵ	NOUN
ejpam-6226	292	2	•	•	ADV
ejpam-6226	292	3	(	(	PUNCT
ejpam-6226	292	4	ξ	ξ	PROPN
ejpam-6226	292	5	•	•	NUM
ejpam-6226	292	6	ϵ	ϵ	NOUN
ejpam-6226	292	7	)	)	PUNCT
ejpam-6226	292	8	)	)	PUNCT
ejpam-6226	292	9	•	•	ADP
ejpam-6226	292	10	ς	ς	NOUN
ejpam-6226	292	11	)	)	PUNCT
ejpam-6226	292	12	,	,	PUNCT
ejpam-6226	292	13	hi(ς	hi(ς	NOUN
ejpam-6226	292	14	)	)	PUNCT
ejpam-6226	292	15	}	}	PUNCT
ejpam-6226	292	16	}	}	PUNCT
ejpam-6226	292	17	=	=	PUNCT
ejpam-6226	292	18	max{max{gi((ϵ	max{max{gi((ϵ	CCONJ
ejpam-6226	292	19	•	•	NOUN
ejpam-6226	292	20	(	(	PUNCT
ejpam-6226	292	21	ξ	ξ	NOUN
ejpam-6226	292	22	•	•	NUM
ejpam-6226	292	23	ϵ	ϵ	NOUN
ejpam-6226	292	24	)	)	PUNCT
ejpam-6226	292	25	)	)	PUNCT
ejpam-6226	292	26	•	•	ADP
ejpam-6226	292	27	ς	ς	NOUN
ejpam-6226	292	28	)	)	PUNCT
ejpam-6226	292	29	,	,	PUNCT
ejpam-6226	292	30	hi((ϵ	hi((ϵ	ADV
ejpam-6226	292	31	•	•	NOUN
ejpam-6226	292	32	(	(	PUNCT
ejpam-6226	292	33	ξ	ξ	NOUN
ejpam-6226	292	34	•	•	NUM
ejpam-6226	292	35	ϵ	ϵ	NOUN
ejpam-6226	292	36	)	)	PUNCT
ejpam-6226	292	37	)	)	PUNCT
ejpam-6226	292	38	•	•	NUM
ejpam-6226	292	39	ς)},max{gi(ς	ς)},max{gi(ς	NOUN
ejpam-6226	292	40	)	)	PUNCT
ejpam-6226	292	41	,	,	PUNCT
ejpam-6226	292	42	hi(ς	hi(ς	NOUN
ejpam-6226	292	43	)	)	PUNCT
ejpam-6226	292	44	}	}	PUNCT
ejpam-6226	292	45	}	}	PUNCT
ejpam-6226	292	46	≤	≤	NUM
ejpam-6226	293	1	max{ig∩h((ϵ	max{ig∩h((ϵ	NOUN
ejpam-6226	293	2	•	•	NOUN
ejpam-6226	293	3	(	(	PUNCT
ejpam-6226	293	4	ξ	ξ	PROPN
ejpam-6226	293	5	•	•	NUM
ejpam-6226	293	6	ϵ	ϵ	NOUN
ejpam-6226	293	7	)	)	PUNCT
ejpam-6226	293	8	)	)	PUNCT
ejpam-6226	293	9	•	•	ADP
ejpam-6226	294	1	ς	ς	NOUN
ejpam-6226	294	2	)	)	PUNCT
ejpam-6226	294	3	,	,	PUNCT
ejpam-6226	294	4	ig∩h(ς	ig∩h(ς	PROPN
ejpam-6226	294	5	)	)	PUNCT
ejpam-6226	294	6	}	}	PUNCT
ejpam-6226	294	7	,	,	PUNCT
ejpam-6226	294	8	fg∩h(ϵ	fg∩h(ϵ	PROPN
ejpam-6226	294	9	)	)	PUNCT
ejpam-6226	294	10	=	=	X
ejpam-6226	294	11	max{gf	max{gf	X
ejpam-6226	294	12	(	(	PUNCT
ejpam-6226	294	13	ϵ	ϵ	NOUN
ejpam-6226	294	14	)	)	PUNCT
ejpam-6226	294	15	,	,	PUNCT
ejpam-6226	294	16	hf	hf	X
ejpam-6226	294	17	(	(	PUNCT
ejpam-6226	294	18	ϵ	ϵ	NOUN
ejpam-6226	294	19	)	)	PUNCT
ejpam-6226	294	20	}	}	PUNCT
ejpam-6226	294	21	≤	≤	ADV
ejpam-6226	294	22	max{max{gf	max{max{gf	X
ejpam-6226	294	23	(	(	PUNCT
ejpam-6226	294	24	(	(	PUNCT
ejpam-6226	294	25	ϵ	ϵ	PART
ejpam-6226	294	26	•	•	PRON
ejpam-6226	294	27	(	(	PUNCT
ejpam-6226	294	28	ξ	ξ	PROPN
ejpam-6226	294	29	•	•	NUM
ejpam-6226	294	30	ϵ	ϵ	NOUN
ejpam-6226	294	31	)	)	PUNCT
ejpam-6226	294	32	)	)	PUNCT
ejpam-6226	294	33	•	•	ADP
ejpam-6226	295	1	ς	ς	NOUN
ejpam-6226	295	2	)	)	PUNCT
ejpam-6226	295	3	,	,	PUNCT
ejpam-6226	295	4	gf	gf	PROPN
ejpam-6226	295	5	(	(	PUNCT
ejpam-6226	295	6	ς)},max{hf	ς)},max{hf	NOUN
ejpam-6226	295	7	(	(	PUNCT
ejpam-6226	295	8	(	(	PUNCT
ejpam-6226	295	9	ϵ	ϵ	PART
ejpam-6226	295	10	•	•	NOUN
ejpam-6226	295	11	(	(	PUNCT
ejpam-6226	295	12	ξ	ξ	PROPN
ejpam-6226	295	13	•	•	NUM
ejpam-6226	295	14	ϵ	ϵ	NOUN
ejpam-6226	295	15	)	)	PUNCT
ejpam-6226	295	16	)	)	PUNCT
ejpam-6226	295	17	•	•	ADP
ejpam-6226	295	18	ς	ς	NOUN
ejpam-6226	295	19	)	)	PUNCT
ejpam-6226	295	20	,	,	PUNCT
ejpam-6226	295	21	hf	hf	INTJ
ejpam-6226	295	22	(	(	PUNCT
ejpam-6226	295	23	ς	ς	NOUN
ejpam-6226	295	24	)	)	PUNCT
ejpam-6226	295	25	}	}	PUNCT
ejpam-6226	295	26	}	}	PUNCT
ejpam-6226	295	27	=	=	SYM
ejpam-6226	295	28	max{max{gf	max{max{gf	NOUN
ejpam-6226	295	29	(	(	PUNCT
ejpam-6226	295	30	(	(	PUNCT
ejpam-6226	295	31	ϵ	ϵ	PART
ejpam-6226	295	32	•	•	PRON
ejpam-6226	295	33	(	(	PUNCT
ejpam-6226	295	34	ξ	ξ	PROPN
ejpam-6226	295	35	•	•	NUM
ejpam-6226	295	36	ϵ	ϵ	NOUN
ejpam-6226	295	37	)	)	PUNCT
ejpam-6226	295	38	)	)	PUNCT
ejpam-6226	295	39	•	•	ADP
ejpam-6226	295	40	ς	ς	NOUN
ejpam-6226	295	41	)	)	PUNCT
ejpam-6226	295	42	,	,	PUNCT
ejpam-6226	295	43	hf	hf	X
ejpam-6226	295	44	(	(	PUNCT
ejpam-6226	295	45	(	(	PUNCT
ejpam-6226	295	46	ϵ	ϵ	PART
ejpam-6226	295	47	•	•	NOUN
ejpam-6226	295	48	(	(	PUNCT
ejpam-6226	295	49	ξ	ξ	PROPN
ejpam-6226	295	50	•	•	NUM
ejpam-6226	295	51	ϵ	ϵ	NOUN
ejpam-6226	295	52	)	)	PUNCT
ejpam-6226	295	53	)	)	PUNCT
ejpam-6226	295	54	•	•	ADP
ejpam-6226	296	1	ς)},max{gf	ς)},max{gf	ADJ
ejpam-6226	296	2	(	(	PUNCT
ejpam-6226	296	3	ς	ς	NOUN
ejpam-6226	296	4	)	)	PUNCT
ejpam-6226	296	5	,	,	PUNCT
ejpam-6226	296	6	hf	hf	INTJ
ejpam-6226	296	7	(	(	PUNCT
ejpam-6226	296	8	ς	ς	NOUN
ejpam-6226	296	9	)	)	PUNCT
ejpam-6226	296	10	}	}	PUNCT
ejpam-6226	296	11	}	}	PUNCT
ejpam-6226	296	12	≤	≤	NUM
ejpam-6226	296	13	max{fg∩h((ϵ	max{fg∩h((ϵ	NOUN
ejpam-6226	296	14	•	•	NOUN
ejpam-6226	296	15	(	(	PUNCT
ejpam-6226	296	16	ξ	ξ	NOUN
ejpam-6226	296	17	•	•	NUM
ejpam-6226	296	18	ϵ	ϵ	NOUN
ejpam-6226	296	19	)	)	PUNCT
ejpam-6226	296	20	)	)	PUNCT
ejpam-6226	296	21	•	•	ADP
ejpam-6226	296	22	ς	ς	PROPN
ejpam-6226	296	23	)	)	PUNCT
ejpam-6226	296	24	,	,	PUNCT
ejpam-6226	296	25	fg∩h(ς	fg∩h(ς	NOUN
ejpam-6226	296	26	)	)	PUNCT
ejpam-6226	296	27	}	}	PUNCT
ejpam-6226	296	28	.	.	PUNCT
ejpam-6226	297	1	hence	hence	ADV
ejpam-6226	297	2	,	,	PUNCT
ejpam-6226	297	3	g	g	PROPN
ejpam-6226	297	4	∩	∩	ADJ
ejpam-6226	297	5	h	h	NOUN
ejpam-6226	297	6	is	be	AUX
ejpam-6226	297	7	an	an	DET
ejpam-6226	297	8	nmink	nmink	NOUN
ejpam-6226	297	9	-	-	PUNCT
ejpam-6226	297	10	i	i	PRON
ejpam-6226	297	11	of	of	ADP
ejpam-6226	297	12	i.	i.	PROPN
ejpam-6226	297	13	note	note	PROPN
ejpam-6226	297	14	:	:	PUNCT
ejpam-6226	297	15	the	the	DET
ejpam-6226	297	16	union	union	NOUN
ejpam-6226	297	17	of	of	ADP
ejpam-6226	297	18	nmink	nmink	NOUN
ejpam-6226	297	19	-	-	PUNCT
ejpam-6226	297	20	is	be	AUX
ejpam-6226	297	21	of	of	ADP
ejpam-6226	297	22	an	an	DET
ejpam-6226	297	23	ink	ink	NOUN
ejpam-6226	297	24	-	-	PUNCT
ejpam-6226	297	25	algebra	algebra	NOUN
ejpam-6226	297	26	need	need	AUX
ejpam-6226	297	27	not	not	PART
ejpam-6226	297	28	be	be	AUX
ejpam-6226	297	29	an	an	DET
ejpam-6226	297	30	nmink	nmink	NOUN
ejpam-6226	297	31	-	-	PUNCT
ejpam-6226	297	32	i.	i.	NOUN
ejpam-6226	297	33	example	example	NOUN
ejpam-6226	297	34	11	11	NUM
ejpam-6226	297	35	.	.	PUNCT
ejpam-6226	298	1	consider	consider	VERB
ejpam-6226	298	2	an	an	DET
ejpam-6226	298	3	ink	ink	NOUN
ejpam-6226	298	4	-	-	PUNCT
ejpam-6226	298	5	algebra	algebra	NOUN
ejpam-6226	298	6	i	i	NOUN
ejpam-6226	298	7	=	=	PUNCT
ejpam-6226	298	8	{	{	PUNCT
ejpam-6226	298	9	0	0	NUM
ejpam-6226	298	10	,	,	PUNCT
ejpam-6226	298	11	2	2	NUM
ejpam-6226	298	12	,	,	PUNCT
ejpam-6226	298	13	4	4	NUM
ejpam-6226	298	14	}	}	PUNCT
ejpam-6226	298	15	from	from	ADP
ejpam-6226	298	16	example	example	NOUN
ejpam-6226	298	17	6	6	NUM
ejpam-6226	298	18	.	.	PUNCT
ejpam-6226	298	19	define	define	VERB
ejpam-6226	298	20	an	an	DET
ejpam-6226	298	21	ns	ns	ADJ
ejpam-6226	298	22	g	g	NOUN
ejpam-6226	298	23	=	=	PUNCT
ejpam-6226	298	24	(	(	PUNCT
ejpam-6226	298	25	gt	gt	INTJ
ejpam-6226	298	26	,	,	PUNCT
ejpam-6226	298	27	gi	gi	INTJ
ejpam-6226	298	28	,	,	PUNCT
ejpam-6226	298	29	gf	gf	PROPN
ejpam-6226	298	30	)	)	PUNCT
ejpam-6226	298	31	of	of	ADP
ejpam-6226	298	32	i	i	PRON
ejpam-6226	298	33	by	by	ADP
ejpam-6226	298	34	0	0	NUM
ejpam-6226	298	35	2	2	NUM
ejpam-6226	298	36	4	4	NUM
ejpam-6226	298	37	gt	gt	PROPN
ejpam-6226	298	38	0.3	0.3	NUM
ejpam-6226	298	39	0.4	0.4	NUM
ejpam-6226	298	40	0.6	0.6	NUM
ejpam-6226	298	41	gi	gi	NOUN
ejpam-6226	298	42	0.5	0.5	NUM
ejpam-6226	298	43	0.4	0.4	NUM
ejpam-6226	298	44	0.4	0.4	NUM
ejpam-6226	298	45	gf	gf	NOUN
ejpam-6226	298	46	0.4	0.4	NUM
ejpam-6226	298	47	0.5	0.5	NUM
ejpam-6226	298	48	0.6	0.6	NUM
ejpam-6226	298	49	define	define	VERB
ejpam-6226	298	50	an	an	DET
ejpam-6226	298	51	ns	ns	ADJ
ejpam-6226	298	52	h	h	NOUN
ejpam-6226	298	53	=	=	PUNCT
ejpam-6226	298	54	(	(	PUNCT
ejpam-6226	298	55	ht	ht	INTJ
ejpam-6226	298	56	,	,	PUNCT
ejpam-6226	298	57	hi	hi	INTJ
ejpam-6226	298	58	,	,	PUNCT
ejpam-6226	298	59	hf	hf	NOUN
ejpam-6226	298	60	)	)	PUNCT
ejpam-6226	298	61	of	of	ADP
ejpam-6226	298	62	i	i	PRON
ejpam-6226	298	63	by	by	ADP
ejpam-6226	298	64	0	0	NUM
ejpam-6226	298	65	2	2	NUM
ejpam-6226	298	66	4	4	NUM
ejpam-6226	298	67	ht	ht	PROPN
ejpam-6226	298	68	0.5	0.5	NUM
ejpam-6226	298	69	0.3	0.3	NUM
ejpam-6226	298	70	0.5	0.5	NUM
ejpam-6226	298	71	hi	hi	NOUN
ejpam-6226	298	72	0.4	0.4	NUM
ejpam-6226	298	73	0.6	0.6	NUM
ejpam-6226	298	74	0.6	0.6	NUM
ejpam-6226	298	75	hf	hf	ADP
ejpam-6226	298	76	0.6	0.6	NUM
ejpam-6226	298	77	0.5	0.5	NUM
ejpam-6226	298	78	0.5	0.5	NUM
ejpam-6226	298	79	r.	r.	PROPN
ejpam-6226	298	80	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	298	81	et	et	PROPN
ejpam-6226	298	82	al	al	PROPN
ejpam-6226	298	83	.	.	PUNCT
ejpam-6226	298	84	/	/	SYM
ejpam-6226	298	85	eur	eur	PROPN
ejpam-6226	298	86	.	.	PUNCT
ejpam-6226	299	1	j.	j.	PROPN
ejpam-6226	299	2	pure	pure	PROPN
ejpam-6226	299	3	appl	appl	PROPN
ejpam-6226	299	4	.	.	PROPN
ejpam-6226	299	5	math	math	PROPN
ejpam-6226	299	6	,	,	PUNCT
ejpam-6226	299	7	18	18	NUM
ejpam-6226	299	8	(	(	PUNCT
ejpam-6226	299	9	3	3	NUM
ejpam-6226	299	10	)	)	PUNCT
ejpam-6226	299	11	(	(	PUNCT
ejpam-6226	299	12	2025	2025	NUM
ejpam-6226	299	13	)	)	PUNCT
ejpam-6226	299	14	,	,	PUNCT
ejpam-6226	299	15	6226	6226	NUM
ejpam-6226	299	16	15	15	NUM
ejpam-6226	299	17	of	of	ADP
ejpam-6226	299	18	19	19	NUM
ejpam-6226	299	19	then	then	ADV
ejpam-6226	299	20	g	g	PROPN
ejpam-6226	299	21	and	and	CCONJ
ejpam-6226	299	22	h	h	NOUN
ejpam-6226	299	23	are	be	AUX
ejpam-6226	299	24	two	two	NUM
ejpam-6226	299	25	nmink	nmink	NOUN
ejpam-6226	299	26	-	-	PUNCT
ejpam-6226	299	27	is	be	AUX
ejpam-6226	299	28	of	of	ADP
ejpam-6226	299	29	i.	i.	NOUN
ejpam-6226	299	30	here	here	ADV
ejpam-6226	299	31	tg∪h(0	tg∪h(0	PROPN
ejpam-6226	299	32	)	)	PUNCT
ejpam-6226	299	33	=	=	PUNCT
ejpam-6226	299	34	0.3	0.3	NUM
ejpam-6226	299	35	,	,	PUNCT
ejpam-6226	299	36	but	but	CCONJ
ejpam-6226	299	37	it	it	PRON
ejpam-6226	299	38	is	be	AUX
ejpam-6226	299	39	not	not	PART
ejpam-6226	299	40	greater	great	ADJ
ejpam-6226	299	41	than	than	ADP
ejpam-6226	299	42	or	or	CCONJ
ejpam-6226	299	43	equal	equal	ADJ
ejpam-6226	299	44	to	to	ADP
ejpam-6226	299	45	0.5	0.5	NUM
ejpam-6226	299	46	=	=	NOUN
ejpam-6226	299	47	min{tg∪h((0	min{tg∪h((0	NOUN
ejpam-6226	299	48	•	•	NOUN
ejpam-6226	299	49	(	(	PUNCT
ejpam-6226	299	50	2	2	NUM
ejpam-6226	299	51	•	•	NUM
ejpam-6226	299	52	0	0	NUM
ejpam-6226	299	53	)	)	PUNCT
ejpam-6226	299	54	)	)	PUNCT
ejpam-6226	300	1	•	•	ADP
ejpam-6226	300	2	4	4	NUM
ejpam-6226	300	3	)	)	PUNCT
ejpam-6226	300	4	,	,	PUNCT
ejpam-6226	300	5	tg∪h(4	tg∪h(4	PROPN
ejpam-6226	300	6	)	)	PUNCT
ejpam-6226	300	7	}	}	PUNCT
ejpam-6226	300	8	.	.	PUNCT
ejpam-6226	301	1	similarly	similarly	ADV
ejpam-6226	301	2	,	,	PUNCT
ejpam-6226	301	3	for	for	ADP
ejpam-6226	301	4	ig∪h(0	ig∪h(0	NOUN
ejpam-6226	301	5	)	)	PUNCT
ejpam-6226	301	6	=	=	SYM
ejpam-6226	301	7	0.5	0.5	NUM
ejpam-6226	301	8	,	,	PUNCT
ejpam-6226	301	9	but	but	CCONJ
ejpam-6226	301	10	it	it	PRON
ejpam-6226	301	11	is	be	AUX
ejpam-6226	301	12	not	not	PART
ejpam-6226	301	13	less	less	ADJ
ejpam-6226	301	14	than	than	ADP
ejpam-6226	301	15	or	or	CCONJ
ejpam-6226	301	16	equal	equal	ADJ
ejpam-6226	301	17	to	to	ADP
ejpam-6226	301	18	0.4	0.4	NUM
ejpam-6226	301	19	=	=	SYM
ejpam-6226	301	20	max{ig∪h((0	max{ig∪h((0	NOUN
ejpam-6226	301	21	•	•	NOUN
ejpam-6226	301	22	(	(	PUNCT
ejpam-6226	301	23	2	2	NUM
ejpam-6226	301	24	•	•	NUM
ejpam-6226	301	25	0	0	NUM
ejpam-6226	301	26	)	)	PUNCT
ejpam-6226	301	27	)	)	PUNCT
ejpam-6226	302	1	•	•	ADP
ejpam-6226	302	2	4	4	NUM
ejpam-6226	302	3	)	)	PUNCT
ejpam-6226	302	4	,	,	PUNCT
ejpam-6226	302	5	ig∪h(4	ig∪h(4	PROPN
ejpam-6226	302	6	)	)	PUNCT
ejpam-6226	302	7	}	}	PUNCT
ejpam-6226	302	8	.	.	PUNCT
ejpam-6226	303	1	also	also	ADV
ejpam-6226	303	2	,	,	PUNCT
ejpam-6226	303	3	fg∪h(0	fg∪h(0	PROPN
ejpam-6226	303	4	)	)	PUNCT
ejpam-6226	303	5	=	=	SYM
ejpam-6226	303	6	0.6	0.6	NUM
ejpam-6226	303	7	,	,	PUNCT
ejpam-6226	303	8	but	but	CCONJ
ejpam-6226	303	9	it	it	PRON
ejpam-6226	303	10	is	be	AUX
ejpam-6226	303	11	not	not	PART
ejpam-6226	303	12	less	less	ADJ
ejpam-6226	303	13	than	than	ADP
ejpam-6226	303	14	or	or	CCONJ
ejpam-6226	303	15	equal	equal	ADJ
ejpam-6226	303	16	to	to	ADP
ejpam-6226	303	17	0.5	0.5	NUM
ejpam-6226	303	18	=	=	SYM
ejpam-6226	303	19	max{fg∪h((0	max{fg∪h((0	NOUN
ejpam-6226	303	20	•	•	NOUN
ejpam-6226	303	21	(	(	PUNCT
ejpam-6226	303	22	2	2	NUM
ejpam-6226	303	23	•	•	NUM
ejpam-6226	303	24	0	0	NUM
ejpam-6226	303	25	)	)	PUNCT
ejpam-6226	303	26	)	)	PUNCT
ejpam-6226	303	27	•	•	ADP
ejpam-6226	303	28	4	4	NUM
ejpam-6226	303	29	)	)	PUNCT
ejpam-6226	303	30	,	,	PUNCT
ejpam-6226	303	31	fg∪h(4	fg∪h(4	PROPN
ejpam-6226	303	32	)	)	PUNCT
ejpam-6226	303	33	}	}	PUNCT
ejpam-6226	303	34	.	.	PUNCT
ejpam-6226	304	1	therefore	therefore	ADV
ejpam-6226	304	2	,	,	PUNCT
ejpam-6226	304	3	g	g	PROPN
ejpam-6226	304	4	∪	∪	ADJ
ejpam-6226	304	5	h	h	NOUN
ejpam-6226	304	6	is	be	AUX
ejpam-6226	304	7	not	not	PART
ejpam-6226	304	8	an	an	DET
ejpam-6226	304	9	nmink	nmink	NOUN
ejpam-6226	304	10	-	-	PUNCT
ejpam-6226	304	11	i	i	PRON
ejpam-6226	304	12	of	of	ADP
ejpam-6226	304	13	i.	i.	PROPN
ejpam-6226	304	14	thus	thus	ADV
ejpam-6226	304	15	,	,	PUNCT
ejpam-6226	304	16	the	the	DET
ejpam-6226	304	17	union	union	NOUN
ejpam-6226	304	18	of	of	ADP
ejpam-6226	304	19	nmink	nmink	NOUN
ejpam-6226	304	20	-	-	PUNCT
ejpam-6226	304	21	is	be	AUX
ejpam-6226	304	22	of	of	ADP
ejpam-6226	304	23	an	an	DET
ejpam-6226	304	24	ink	ink	NOUN
ejpam-6226	304	25	-	-	PUNCT
ejpam-6226	304	26	algebra	algebra	NOUN
ejpam-6226	304	27	is	be	AUX
ejpam-6226	304	28	not	not	PART
ejpam-6226	304	29	an	an	DET
ejpam-6226	304	30	nmink	nmink	NOUN
ejpam-6226	304	31	-	-	PUNCT
ejpam-6226	304	32	i.	i.	NOUN
ejpam-6226	304	33	theorem	theorem	NOUN
ejpam-6226	304	34	16	16	NUM
ejpam-6226	304	35	.	.	PUNCT
ejpam-6226	305	1	let	let	VERB
ejpam-6226	305	2	g	g	NOUN
ejpam-6226	305	3	and	and	CCONJ
ejpam-6226	305	4	h	h	NOUN
ejpam-6226	305	5	be	be	VERB
ejpam-6226	305	6	two	two	NUM
ejpam-6226	305	7	nmink	nmink	NOUN
ejpam-6226	305	8	-	-	PUNCT
ejpam-6226	305	9	is	be	AUX
ejpam-6226	305	10	of	of	ADP
ejpam-6226	305	11	an	an	DET
ejpam-6226	305	12	ink	ink	NOUN
ejpam-6226	305	13	-	-	PUNCT
ejpam-6226	305	14	algebra	algebra	NOUN
ejpam-6226	305	15	i.	i.	NOUN
ejpam-6226	305	16	if	if	SCONJ
ejpam-6226	305	17	g	g	PROPN
ejpam-6226	305	18	⊆	⊆	NUM
ejpam-6226	305	19	h	h	NOUN
ejpam-6226	305	20	or	or	CCONJ
ejpam-6226	305	21	h	h	NOUN
ejpam-6226	305	22	⊆	⊆	NUM
ejpam-6226	305	23	g	g	NOUN
ejpam-6226	305	24	,	,	PUNCT
ejpam-6226	305	25	then	then	ADV
ejpam-6226	305	26	g	g	PROPN
ejpam-6226	305	27	∪	∪	PROPN
ejpam-6226	305	28	h	h	NOUN
ejpam-6226	305	29	is	be	AUX
ejpam-6226	305	30	an	an	DET
ejpam-6226	305	31	nmink	nmink	NOUN
ejpam-6226	305	32	-	-	PUNCT
ejpam-6226	305	33	i	i	PRON
ejpam-6226	305	34	of	of	ADP
ejpam-6226	305	35	i.	i.	PROPN
ejpam-6226	305	36	proof	proof	PROPN
ejpam-6226	305	37	.	.	PUNCT
ejpam-6226	306	1	obvious	obvious	ADJ
ejpam-6226	306	2	.	.	PUNCT
ejpam-6226	307	1	theorem	theorem	VERB
ejpam-6226	307	2	17	17	NUM
ejpam-6226	307	3	.	.	PUNCT
ejpam-6226	308	1	let	let	VERB
ejpam-6226	308	2	g	g	PROPN
ejpam-6226	308	3	=	=	SYM
ejpam-6226	308	4	(	(	PUNCT
ejpam-6226	308	5	gt	gt	INTJ
ejpam-6226	308	6	,	,	PUNCT
ejpam-6226	308	7	gi	gi	INTJ
ejpam-6226	308	8	,	,	PUNCT
ejpam-6226	308	9	gf	gf	PROPN
ejpam-6226	308	10	)	)	PUNCT
ejpam-6226	308	11	and	and	CCONJ
ejpam-6226	308	12	h	h	NOUN
ejpam-6226	308	13	=	=	SYM
ejpam-6226	308	14	(	(	PUNCT
ejpam-6226	308	15	ht	ht	INTJ
ejpam-6226	308	16	,	,	PUNCT
ejpam-6226	308	17	hi	hi	INTJ
ejpam-6226	308	18	,	,	PUNCT
ejpam-6226	308	19	hf	hf	INTJ
ejpam-6226	308	20	)	)	PUNCT
ejpam-6226	308	21	be	be	AUX
ejpam-6226	308	22	two	two	NUM
ejpam-6226	308	23	npmink	npmink	NOUN
ejpam-6226	308	24	-	-	PUNCT
ejpam-6226	308	25	is	is	NOUN
ejpam-6226	308	26	of	of	ADP
ejpam-6226	308	27	an	an	DET
ejpam-6226	308	28	inkalgebra	inkalgebra	NOUN
ejpam-6226	308	29	i.	i.	NOUN
ejpam-6226	308	30	then	then	ADV
ejpam-6226	308	31	g	g	PROPN
ejpam-6226	308	32	∩	∩	ADJ
ejpam-6226	308	33	h	h	NOUN
ejpam-6226	308	34	=	=	SYM
ejpam-6226	308	35	(	(	PUNCT
ejpam-6226	308	36	tg∩h	tg∩h	PROPN
ejpam-6226	308	37	,	,	PUNCT
ejpam-6226	308	38	ig∩h	ig∩h	PROPN
ejpam-6226	308	39	,	,	PUNCT
ejpam-6226	308	40	fg∩h	fg∩h	PROPN
ejpam-6226	308	41	)	)	PUNCT
ejpam-6226	308	42	is	be	AUX
ejpam-6226	308	43	an	an	DET
ejpam-6226	308	44	npmink	npmink	NOUN
ejpam-6226	308	45	-	-	PUNCT
ejpam-6226	308	46	i	i	PRON
ejpam-6226	308	47	of	of	ADP
ejpam-6226	308	48	i.	i.	PROPN
ejpam-6226	308	49	proof	proof	PROPN
ejpam-6226	308	50	.	.	PUNCT
ejpam-6226	309	1	the	the	DET
ejpam-6226	309	2	proof	proof	NOUN
ejpam-6226	309	3	is	be	AUX
ejpam-6226	309	4	similar	similar	ADJ
ejpam-6226	309	5	to	to	ADP
ejpam-6226	309	6	theorem	theorem	VERB
ejpam-6226	309	7	15	15	NUM
ejpam-6226	309	8	.	.	PUNCT
ejpam-6226	310	1	note	note	NOUN
ejpam-6226	310	2	:	:	PUNCT
ejpam-6226	310	3	the	the	DET
ejpam-6226	310	4	union	union	NOUN
ejpam-6226	310	5	of	of	ADP
ejpam-6226	310	6	npmink	npmink	PROPN
ejpam-6226	310	7	-	-	PUNCT
ejpam-6226	310	8	is	be	AUX
ejpam-6226	310	9	of	of	ADP
ejpam-6226	310	10	an	an	DET
ejpam-6226	310	11	ink	ink	NOUN
ejpam-6226	310	12	-	-	PUNCT
ejpam-6226	310	13	algebra	algebra	NOUN
ejpam-6226	310	14	need	need	AUX
ejpam-6226	310	15	not	not	PART
ejpam-6226	310	16	be	be	AUX
ejpam-6226	310	17	an	an	DET
ejpam-6226	310	18	npmink	npmink	ADJ
ejpam-6226	310	19	-	-	PUNCT
ejpam-6226	310	20	i.	i.	NOUN
ejpam-6226	310	21	example	example	NOUN
ejpam-6226	310	22	12	12	NUM
ejpam-6226	310	23	.	.	PUNCT
ejpam-6226	311	1	consider	consider	VERB
ejpam-6226	311	2	an	an	DET
ejpam-6226	311	3	ink	ink	NOUN
ejpam-6226	311	4	-	-	PUNCT
ejpam-6226	311	5	algebra	algebra	NOUN
ejpam-6226	311	6	i	i	NOUN
ejpam-6226	311	7	=	=	PUNCT
ejpam-6226	311	8	{	{	PUNCT
ejpam-6226	311	9	0	0	NUM
ejpam-6226	311	10	,	,	PUNCT
ejpam-6226	311	11	2	2	NUM
ejpam-6226	311	12	,	,	PUNCT
ejpam-6226	311	13	4	4	NUM
ejpam-6226	311	14	}	}	PUNCT
ejpam-6226	311	15	defined	define	VERB
ejpam-6226	311	16	in	in	ADP
ejpam-6226	311	17	example	example	NOUN
ejpam-6226	311	18	11	11	NUM
ejpam-6226	311	19	.	.	PUNCT
ejpam-6226	312	1	define	define	VERB
ejpam-6226	312	2	an	an	DET
ejpam-6226	312	3	ns	ns	ADJ
ejpam-6226	312	4	g	g	NOUN
ejpam-6226	312	5	=	=	PUNCT
ejpam-6226	312	6	(	(	PUNCT
ejpam-6226	312	7	gt	gt	INTJ
ejpam-6226	312	8	,	,	PUNCT
ejpam-6226	312	9	gi	gi	INTJ
ejpam-6226	312	10	,	,	PUNCT
ejpam-6226	312	11	gf	gf	PROPN
ejpam-6226	312	12	)	)	PUNCT
ejpam-6226	312	13	of	of	ADP
ejpam-6226	312	14	i	i	PRON
ejpam-6226	312	15	by	by	ADP
ejpam-6226	312	16	0	0	NUM
ejpam-6226	312	17	2	2	NUM
ejpam-6226	312	18	4	4	NUM
ejpam-6226	312	19	gt	gt	PROPN
ejpam-6226	312	20	0.3	0.3	NUM
ejpam-6226	312	21	0.4	0.4	NUM
ejpam-6226	312	22	0.6	0.6	NUM
ejpam-6226	312	23	gi	gi	NOUN
ejpam-6226	312	24	0.5	0.5	NUM
ejpam-6226	312	25	0.4	0.4	NUM
ejpam-6226	312	26	0.4	0.4	NUM
ejpam-6226	312	27	gf	gf	NOUN
ejpam-6226	312	28	0.4	0.4	NUM
ejpam-6226	312	29	0.5	0.5	NUM
ejpam-6226	312	30	0.6	0.6	NUM
ejpam-6226	312	31	define	define	VERB
ejpam-6226	312	32	an	an	DET
ejpam-6226	312	33	ns	ns	ADJ
ejpam-6226	312	34	h	h	NOUN
ejpam-6226	312	35	=	=	PUNCT
ejpam-6226	312	36	(	(	PUNCT
ejpam-6226	312	37	ht	ht	INTJ
ejpam-6226	312	38	,	,	PUNCT
ejpam-6226	312	39	hi	hi	INTJ
ejpam-6226	312	40	,	,	PUNCT
ejpam-6226	312	41	hf	hf	NOUN
ejpam-6226	312	42	)	)	PUNCT
ejpam-6226	312	43	of	of	ADP
ejpam-6226	312	44	i	i	PRON
ejpam-6226	312	45	by	by	ADP
ejpam-6226	312	46	0	0	NUM
ejpam-6226	312	47	2	2	NUM
ejpam-6226	312	48	4	4	NUM
ejpam-6226	312	49	ht	ht	PROPN
ejpam-6226	312	50	0.5	0.5	NUM
ejpam-6226	312	51	0.3	0.3	NUM
ejpam-6226	312	52	0.5	0.5	NUM
ejpam-6226	312	53	hi	hi	NOUN
ejpam-6226	312	54	0.4	0.4	NUM
ejpam-6226	312	55	0.6	0.6	NUM
ejpam-6226	312	56	0.6	0.6	NUM
ejpam-6226	312	57	hf	hf	ADP
ejpam-6226	312	58	0.6	0.6	NUM
ejpam-6226	312	59	0.5	0.5	NUM
ejpam-6226	312	60	0.6	0.6	NUM
ejpam-6226	312	61	then	then	ADV
ejpam-6226	312	62	g	g	PROPN
ejpam-6226	312	63	and	and	CCONJ
ejpam-6226	312	64	h	h	NOUN
ejpam-6226	312	65	are	be	AUX
ejpam-6226	312	66	two	two	NUM
ejpam-6226	312	67	npmink	npmink	NOUN
ejpam-6226	312	68	-	-	PUNCT
ejpam-6226	312	69	is	is	NOUN
ejpam-6226	312	70	of	of	ADP
ejpam-6226	312	71	i.	i.	NOUN
ejpam-6226	312	72	here	here	ADV
ejpam-6226	312	73	tg∪h(0	tg∪h(0	NOUN
ejpam-6226	312	74	•	•	ADP
ejpam-6226	312	75	2	2	NUM
ejpam-6226	312	76	)	)	PUNCT
ejpam-6226	312	77	=	=	SYM
ejpam-6226	312	78	0.3	0.3	NUM
ejpam-6226	312	79	,	,	PUNCT
ejpam-6226	312	80	but	but	CCONJ
ejpam-6226	312	81	it	it	PRON
ejpam-6226	312	82	is	be	AUX
ejpam-6226	312	83	not	not	PART
ejpam-6226	312	84	greater	great	ADJ
ejpam-6226	312	85	than	than	ADP
ejpam-6226	312	86	or	or	CCONJ
ejpam-6226	312	87	equal	equal	ADJ
ejpam-6226	312	88	to	to	ADP
ejpam-6226	312	89	0.4	0.4	NUM
ejpam-6226	312	90	=	=	SYM
ejpam-6226	312	91	min{tg∪h((0	min{tg∪h((0	NOUN
ejpam-6226	312	92	•	•	NOUN
ejpam-6226	312	93	2	2	NUM
ejpam-6226	312	94	)	)	PUNCT
ejpam-6226	312	95	•	•	NUM
ejpam-6226	312	96	4	4	NUM
ejpam-6226	312	97	)	)	PUNCT
ejpam-6226	312	98	,	,	PUNCT
ejpam-6226	312	99	tg∪h(2	tg∪h(2	PROPN
ejpam-6226	312	100	•	•	NOUN
ejpam-6226	312	101	4	4	NUM
ejpam-6226	312	102	)	)	PUNCT
ejpam-6226	312	103	}	}	PUNCT
ejpam-6226	312	104	.	.	PUNCT
ejpam-6226	313	1	similarly	similarly	ADV
ejpam-6226	313	2	,	,	PUNCT
ejpam-6226	313	3	for	for	ADP
ejpam-6226	313	4	ig∪h(0	ig∪h(0	NOUN
ejpam-6226	313	5	•	•	ADP
ejpam-6226	313	6	2	2	NUM
ejpam-6226	313	7	)	)	PUNCT
ejpam-6226	313	8	=	=	NUM
ejpam-6226	313	9	0.5	0.5	NUM
ejpam-6226	313	10	,	,	PUNCT
ejpam-6226	313	11	but	but	CCONJ
ejpam-6226	313	12	it	it	PRON
ejpam-6226	313	13	is	be	AUX
ejpam-6226	313	14	not	not	PART
ejpam-6226	313	15	less	less	ADJ
ejpam-6226	313	16	than	than	ADP
ejpam-6226	313	17	or	or	CCONJ
ejpam-6226	313	18	equal	equal	ADJ
ejpam-6226	313	19	to	to	ADP
ejpam-6226	313	20	0.4	0.4	NUM
ejpam-6226	313	21	=	=	SYM
ejpam-6226	313	22	max{ig∪h((0•2)•4	max{ig∪h((0•2)•4	PROPN
ejpam-6226	313	23	)	)	PUNCT
ejpam-6226	313	24	,	,	PUNCT
ejpam-6226	313	25	ig∪h(2•4	ig∪h(2•4	NOUN
ejpam-6226	313	26	)	)	PUNCT
ejpam-6226	313	27	}	}	PUNCT
ejpam-6226	313	28	.	.	PUNCT
ejpam-6226	314	1	also	also	ADV
ejpam-6226	314	2	,	,	PUNCT
ejpam-6226	314	3	fg∪h(0•2	fg∪h(0•2	ADJ
ejpam-6226	314	4	)	)	PUNCT
ejpam-6226	314	5	=	=	SYM
ejpam-6226	314	6	0.6	0.6	NUM
ejpam-6226	314	7	,	,	PUNCT
ejpam-6226	314	8	but	but	CCONJ
ejpam-6226	314	9	it	it	PRON
ejpam-6226	314	10	is	be	AUX
ejpam-6226	314	11	not	not	PART
ejpam-6226	314	12	less	less	ADJ
ejpam-6226	314	13	than	than	ADP
ejpam-6226	314	14	or	or	CCONJ
ejpam-6226	314	15	equal	equal	ADJ
ejpam-6226	314	16	to	to	ADP
ejpam-6226	314	17	0.5	0.5	NUM
ejpam-6226	314	18	=	=	SYM
ejpam-6226	314	19	max{fg∪h((0	max{fg∪h((0	NOUN
ejpam-6226	314	20	•	•	NOUN
ejpam-6226	314	21	2	2	NUM
ejpam-6226	314	22	)	)	PUNCT
ejpam-6226	314	23	•	•	NUM
ejpam-6226	314	24	4	4	NUM
ejpam-6226	314	25	)	)	PUNCT
ejpam-6226	314	26	,	,	PUNCT
ejpam-6226	314	27	fg∪h(2	fg∪h(2	NOUN
ejpam-6226	314	28	•	•	NOUN
ejpam-6226	314	29	4	4	NUM
ejpam-6226	314	30	)	)	PUNCT
ejpam-6226	314	31	}	}	PUNCT
ejpam-6226	314	32	.	.	PUNCT
ejpam-6226	315	1	therefore	therefore	ADV
ejpam-6226	315	2	,	,	PUNCT
ejpam-6226	315	3	g	g	PROPN
ejpam-6226	315	4	∪	∪	ADJ
ejpam-6226	315	5	h	h	NOUN
ejpam-6226	315	6	is	be	AUX
ejpam-6226	315	7	not	not	PART
ejpam-6226	315	8	an	an	DET
ejpam-6226	315	9	npmink	npmink	NOUN
ejpam-6226	315	10	-	-	PUNCT
ejpam-6226	315	11	i	i	PRON
ejpam-6226	315	12	of	of	ADP
ejpam-6226	315	13	i.	i.	PROPN
ejpam-6226	315	14	thus	thus	ADV
ejpam-6226	315	15	,	,	PUNCT
ejpam-6226	315	16	the	the	DET
ejpam-6226	315	17	union	union	NOUN
ejpam-6226	315	18	of	of	ADP
ejpam-6226	315	19	npmink	npmink	PROPN
ejpam-6226	315	20	-	-	PUNCT
ejpam-6226	315	21	is	is	NOUN
ejpam-6226	315	22	of	of	ADP
ejpam-6226	315	23	ink	ink	NOUN
ejpam-6226	315	24	-	-	PUNCT
ejpam-6226	315	25	algebras	algebras	PROPN
ejpam-6226	315	26	is	be	AUX
ejpam-6226	315	27	not	not	PART
ejpam-6226	315	28	an	an	DET
ejpam-6226	315	29	npmink	npmink	ADJ
ejpam-6226	315	30	-	-	PUNCT
ejpam-6226	315	31	i.	i.	NOUN
ejpam-6226	315	32	theorem	theorem	NOUN
ejpam-6226	315	33	18	18	NUM
ejpam-6226	315	34	.	.	PUNCT
ejpam-6226	316	1	let	let	VERB
ejpam-6226	316	2	g	g	NOUN
ejpam-6226	316	3	and	and	CCONJ
ejpam-6226	316	4	h	h	NOUN
ejpam-6226	316	5	be	be	VERB
ejpam-6226	316	6	two	two	NUM
ejpam-6226	316	7	npmink	npmink	NOUN
ejpam-6226	316	8	-	-	PUNCT
ejpam-6226	316	9	is	be	AUX
ejpam-6226	316	10	of	of	ADP
ejpam-6226	316	11	an	an	DET
ejpam-6226	316	12	ink	ink	NOUN
ejpam-6226	316	13	-	-	PUNCT
ejpam-6226	316	14	algebra	algebra	NOUN
ejpam-6226	316	15	i.	i.	NOUN
ejpam-6226	316	16	if	if	SCONJ
ejpam-6226	316	17	g	g	PROPN
ejpam-6226	316	18	⊆	⊆	NUM
ejpam-6226	316	19	h	h	NOUN
ejpam-6226	316	20	or	or	CCONJ
ejpam-6226	316	21	h	h	NOUN
ejpam-6226	316	22	⊆	⊆	NUM
ejpam-6226	316	23	g	g	NOUN
ejpam-6226	316	24	,	,	PUNCT
ejpam-6226	316	25	then	then	ADV
ejpam-6226	316	26	g	g	PROPN
ejpam-6226	316	27	∪	∪	PROPN
ejpam-6226	316	28	h	h	NOUN
ejpam-6226	316	29	is	be	AUX
ejpam-6226	316	30	an	an	DET
ejpam-6226	316	31	npmink	npmink	NOUN
ejpam-6226	316	32	-	-	PUNCT
ejpam-6226	316	33	i	i	PRON
ejpam-6226	316	34	of	of	ADP
ejpam-6226	316	35	i.	i.	PROPN
ejpam-6226	316	36	proof	proof	PROPN
ejpam-6226	316	37	.	.	PUNCT
ejpam-6226	317	1	obvious	obvious	ADJ
ejpam-6226	317	2	.	.	PUNCT
ejpam-6226	318	1	r.	r.	PROPN
ejpam-6226	318	2	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	318	3	et	et	PROPN
ejpam-6226	318	4	al	al	PROPN
ejpam-6226	318	5	.	.	PUNCT
ejpam-6226	318	6	/	/	SYM
ejpam-6226	318	7	eur	eur	PROPN
ejpam-6226	318	8	.	.	PUNCT
ejpam-6226	319	1	j.	j.	PROPN
ejpam-6226	319	2	pure	pure	PROPN
ejpam-6226	319	3	appl	appl	PROPN
ejpam-6226	319	4	.	.	PROPN
ejpam-6226	319	5	math	math	PROPN
ejpam-6226	319	6	,	,	PUNCT
ejpam-6226	319	7	18	18	NUM
ejpam-6226	319	8	(	(	PUNCT
ejpam-6226	319	9	3	3	NUM
ejpam-6226	319	10	)	)	PUNCT
ejpam-6226	319	11	(	(	PUNCT
ejpam-6226	319	12	2025	2025	NUM
ejpam-6226	319	13	)	)	PUNCT
ejpam-6226	319	14	,	,	PUNCT
ejpam-6226	319	15	6226	6226	NUM
ejpam-6226	319	16	16	16	NUM
ejpam-6226	319	17	of	of	ADP
ejpam-6226	319	18	19	19	NUM
ejpam-6226	319	19	4.2	4.2	NUM
ejpam-6226	319	20	.	.	PUNCT
ejpam-6226	320	1	homomorphism	homomorphism	NOUN
ejpam-6226	320	2	of	of	ADP
ejpam-6226	320	3	neutrosophic	neutrosophic	ADJ
ejpam-6226	320	4	implicative	implicative	ADJ
ejpam-6226	320	5	and	and	CCONJ
ejpam-6226	320	6	positive	positive	ADJ
ejpam-6226	320	7	implicative	implicative	ADJ
ejpam-6226	320	8	ink	ink	NOUN
ejpam-6226	320	9	-	-	PUNCT
ejpam-6226	320	10	ideals	ideal	NOUN
ejpam-6226	320	11	of	of	ADP
ejpam-6226	320	12	ink	ink	NOUN
ejpam-6226	320	13	-	-	PUNCT
ejpam-6226	320	14	algebras	algebras	NOUN
ejpam-6226	320	15	this	this	DET
ejpam-6226	320	16	subsection	subsection	NOUN
ejpam-6226	320	17	is	be	AUX
ejpam-6226	320	18	devoted	devote	VERB
ejpam-6226	320	19	to	to	ADP
ejpam-6226	320	20	the	the	DET
ejpam-6226	320	21	study	study	NOUN
ejpam-6226	320	22	of	of	ADP
ejpam-6226	320	23	the	the	DET
ejpam-6226	320	24	behavior	behavior	NOUN
ejpam-6226	320	25	of	of	ADP
ejpam-6226	320	26	nmink	nmink	NOUN
ejpam-6226	320	27	-	-	PUNCT
ejpam-6226	320	28	is	be	AUX
ejpam-6226	320	29	and	and	CCONJ
ejpam-6226	320	30	npmink	npmink	VERB
ejpam-6226	320	31	-	-	PUNCT
ejpam-6226	320	32	is	be	AUX
ejpam-6226	320	33	under	under	ADP
ejpam-6226	320	34	homomorphisms	homomorphism	NOUN
ejpam-6226	320	35	between	between	ADP
ejpam-6226	320	36	ink	ink	NOUN
ejpam-6226	320	37	-	-	PUNCT
ejpam-6226	320	38	algebras	algebras	PROPN
ejpam-6226	320	39	.	.	PUNCT
ejpam-6226	321	1	specifically	specifically	ADV
ejpam-6226	321	2	,	,	PUNCT
ejpam-6226	321	3	we	we	PRON
ejpam-6226	321	4	investigate	investigate	VERB
ejpam-6226	321	5	whether	whether	SCONJ
ejpam-6226	321	6	the	the	DET
ejpam-6226	321	7	preimage	preimage	NOUN
ejpam-6226	321	8	of	of	ADP
ejpam-6226	321	9	an	an	DET
ejpam-6226	321	10	nmink	nmink	NOUN
ejpam-6226	321	11	-	-	PUNCT
ejpam-6226	321	12	i	i	PRON
ejpam-6226	321	13	or	or	CCONJ
ejpam-6226	321	14	npmink	npmink	VERB
ejpam-6226	321	15	-	-	PUNCT
ejpam-6226	321	16	i	i	PRON
ejpam-6226	321	17	under	under	ADP
ejpam-6226	321	18	a	a	DET
ejpam-6226	321	19	homomorphic	homomorphic	ADJ
ejpam-6226	321	20	mapping	mapping	NOUN
ejpam-6226	321	21	retains	retain	VERB
ejpam-6226	321	22	its	its	PRON
ejpam-6226	321	23	respective	respective	ADJ
ejpam-6226	321	24	neutrosophic	neutrosophic	ADJ
ejpam-6226	321	25	implicative	implicative	ADJ
ejpam-6226	321	26	properties	property	NOUN
ejpam-6226	321	27	.	.	PUNCT
ejpam-6226	322	1	establishing	establish	VERB
ejpam-6226	322	2	such	such	ADJ
ejpam-6226	322	3	preservation	preservation	NOUN
ejpam-6226	322	4	results	result	NOUN
ejpam-6226	322	5	is	be	AUX
ejpam-6226	322	6	essential	essential	ADJ
ejpam-6226	322	7	for	for	ADP
ejpam-6226	322	8	ensuring	ensure	VERB
ejpam-6226	322	9	that	that	SCONJ
ejpam-6226	322	10	these	these	DET
ejpam-6226	322	11	ideal	ideal	ADJ
ejpam-6226	322	12	structures	structure	NOUN
ejpam-6226	322	13	are	be	AUX
ejpam-6226	322	14	robust	robust	ADJ
ejpam-6226	322	15	under	under	ADP
ejpam-6226	322	16	algebraic	algebraic	ADJ
ejpam-6226	322	17	transformations	transformation	NOUN
ejpam-6226	322	18	,	,	PUNCT
ejpam-6226	322	19	thus	thus	ADV
ejpam-6226	322	20	reinforcing	reinforce	VERB
ejpam-6226	322	21	their	their	PRON
ejpam-6226	322	22	theoretical	theoretical	ADJ
ejpam-6226	322	23	and	and	CCONJ
ejpam-6226	322	24	practical	practical	ADJ
ejpam-6226	322	25	applicability	applicability	NOUN
ejpam-6226	322	26	.	.	PUNCT
ejpam-6226	323	1	the	the	DET
ejpam-6226	323	2	theorems	theorem	NOUN
ejpam-6226	323	3	presented	present	VERB
ejpam-6226	323	4	in	in	ADP
ejpam-6226	323	5	this	this	DET
ejpam-6226	323	6	section	section	NOUN
ejpam-6226	323	7	confirm	confirm	VERB
ejpam-6226	323	8	that	that	SCONJ
ejpam-6226	323	9	both	both	CCONJ
ejpam-6226	323	10	nmink	nmink	NOUN
ejpam-6226	323	11	-	-	PUNCT
ejpam-6226	323	12	i	i	PRON
ejpam-6226	323	13	and	and	CCONJ
ejpam-6226	323	14	npmink	npmink	ADJ
ejpam-6226	323	15	-	-	PUNCT
ejpam-6226	323	16	i	i	PRON
ejpam-6226	323	17	are	be	AUX
ejpam-6226	323	18	preserved	preserve	VERB
ejpam-6226	323	19	under	under	ADP
ejpam-6226	323	20	homomorphic	homomorphic	ADJ
ejpam-6226	323	21	pre	pre	NOUN
ejpam-6226	323	22	-	-	NOUN
ejpam-6226	323	23	images	image	NOUN
ejpam-6226	323	24	,	,	PUNCT
ejpam-6226	323	25	further	far	ADV
ejpam-6226	323	26	highlighting	highlight	VERB
ejpam-6226	323	27	the	the	DET
ejpam-6226	323	28	structural	structural	ADJ
ejpam-6226	323	29	soundness	soundness	NOUN
ejpam-6226	323	30	of	of	ADP
ejpam-6226	323	31	these	these	DET
ejpam-6226	323	32	generalized	generalized	ADJ
ejpam-6226	323	33	ideals	ideal	NOUN
ejpam-6226	323	34	.	.	PUNCT
ejpam-6226	324	1	definition	definition	NOUN
ejpam-6226	324	2	22	22	NUM
ejpam-6226	324	3	.	.	PUNCT
ejpam-6226	325	1	[	[	X
ejpam-6226	325	2	6	6	NUM
ejpam-6226	325	3	]	]	PUNCT
ejpam-6226	325	4	let	let	VERB
ejpam-6226	325	5	κ	κ	NOUN
ejpam-6226	325	6	:	:	PUNCT
ejpam-6226	325	7	i	i	PRON
ejpam-6226	325	8	→	→	PUNCT
ejpam-6226	325	9	ĭ	ĭ	NOUN
ejpam-6226	325	10	be	be	AUX
ejpam-6226	325	11	a	a	DET
ejpam-6226	325	12	homomorphism	homomorphism	NOUN
ejpam-6226	325	13	of	of	ADP
ejpam-6226	325	14	ink	ink	NOUN
ejpam-6226	325	15	-	-	PUNCT
ejpam-6226	325	16	algebras	algebras	PROPN
ejpam-6226	325	17	and	and	CCONJ
ejpam-6226	325	18	g	g	NOUN
ejpam-6226	325	19	=	=	SYM
ejpam-6226	325	20	(	(	PUNCT
ejpam-6226	325	21	gt	gt	INTJ
ejpam-6226	325	22	,	,	PUNCT
ejpam-6226	325	23	gi	gi	INTJ
ejpam-6226	325	24	,	,	PUNCT
ejpam-6226	325	25	gf	gf	PROPN
ejpam-6226	325	26	)	)	PUNCT
ejpam-6226	325	27	be	be	AUX
ejpam-6226	325	28	an	an	DET
ejpam-6226	325	29	ns	ns	NOUN
ejpam-6226	325	30	in	in	ADP
ejpam-6226	325	31	ĭ.	ĭ.	PROPN
ejpam-6226	325	32	then	then	ADV
ejpam-6226	325	33	the	the	DET
ejpam-6226	325	34	ns	ns	PROPN
ejpam-6226	325	35	g[κ	g[κ	PROPN
ejpam-6226	325	36	]	]	X
ejpam-6226	325	37	=	=	SYM
ejpam-6226	325	38	(	(	PUNCT
ejpam-6226	325	39	gt	gt	PROPN
ejpam-6226	326	1	[	[	X
ejpam-6226	326	2	κ	κ	X
ejpam-6226	326	3	]	]	X
ejpam-6226	326	4	,	,	PUNCT
ejpam-6226	326	5	gi	gi	X
ejpam-6226	327	1	[	[	X
ejpam-6226	327	2	κ	κ	X
ejpam-6226	327	3	]	]	X
ejpam-6226	327	4	,	,	PUNCT
ejpam-6226	327	5	gf	gf	X
ejpam-6226	328	1	[	[	X
ejpam-6226	328	2	κ	κ	X
ejpam-6226	328	3	]	]	X
ejpam-6226	328	4	)	)	PUNCT
ejpam-6226	328	5	in	in	ADP
ejpam-6226	328	6	i	i	PRON
ejpam-6226	328	7	is	be	AUX
ejpam-6226	328	8	defined	define	VERB
ejpam-6226	328	9	by	by	ADP
ejpam-6226	328	10	gt	gt	PROPN
ejpam-6226	329	1	[	[	X
ejpam-6226	329	2	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	329	3	)	)	PUNCT
ejpam-6226	329	4	=	=	SYM
ejpam-6226	329	5	gt	gt	PROPN
ejpam-6226	329	6	(	(	PUNCT
ejpam-6226	329	7	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	329	8	)	)	PUNCT
ejpam-6226	329	9	)	)	PUNCT
ejpam-6226	329	10	,	,	PUNCT
ejpam-6226	329	11	gi	gi	VERB
ejpam-6226	329	12	[	[	X
ejpam-6226	329	13	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	329	14	)	)	PUNCT
ejpam-6226	329	15	=	=	SYM
ejpam-6226	330	1	gi(κ(ϵ	gi(κ(ϵ	NOUN
ejpam-6226	330	2	)	)	PUNCT
ejpam-6226	330	3	)	)	PUNCT
ejpam-6226	330	4	,	,	PUNCT
ejpam-6226	330	5	and	and	CCONJ
ejpam-6226	330	6	gf	gf	X
ejpam-6226	331	1	[	[	X
ejpam-6226	331	2	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	331	3	)	)	PUNCT
ejpam-6226	332	1	=	=	SYM
ejpam-6226	332	2	gf	gf	X
ejpam-6226	332	3	(	(	PUNCT
ejpam-6226	332	4	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	332	5	)	)	PUNCT
ejpam-6226	332	6	)	)	PUNCT
ejpam-6226	332	7	for	for	ADP
ejpam-6226	332	8	every	every	DET
ejpam-6226	332	9	ϵ	ϵ	PROPN
ejpam-6226	332	10	∈	∈	PROPN
ejpam-6226	332	11	i	i	PRON
ejpam-6226	332	12	,	,	PUNCT
ejpam-6226	332	13	is	be	AUX
ejpam-6226	332	14	called	call	VERB
ejpam-6226	332	15	the	the	DET
ejpam-6226	332	16	preimage	preimage	NOUN
ejpam-6226	332	17	of	of	ADP
ejpam-6226	332	18	g	g	PROPN
ejpam-6226	332	19	under	under	ADP
ejpam-6226	332	20	κ	κ	PROPN
ejpam-6226	332	21	.	.	PUNCT
ejpam-6226	333	1	theorem	theorem	PROPN
ejpam-6226	333	2	19	19	NUM
ejpam-6226	333	3	.	.	PUNCT
ejpam-6226	334	1	a	a	DET
ejpam-6226	334	2	homomorphic	homomorphic	ADJ
ejpam-6226	334	3	pre	pre	NOUN
ejpam-6226	334	4	-	-	NOUN
ejpam-6226	334	5	image	image	NOUN
ejpam-6226	334	6	of	of	ADP
ejpam-6226	334	7	an	an	DET
ejpam-6226	334	8	nmink	nmink	NOUN
ejpam-6226	334	9	-	-	PUNCT
ejpam-6226	334	10	i	i	PRON
ejpam-6226	334	11	of	of	ADP
ejpam-6226	334	12	an	an	DET
ejpam-6226	334	13	ink	ink	NOUN
ejpam-6226	334	14	-	-	PUNCT
ejpam-6226	334	15	algebra	algebra	NOUN
ejpam-6226	334	16	is	be	AUX
ejpam-6226	334	17	an	an	DET
ejpam-6226	334	18	nminki	nminki	NOUN
ejpam-6226	334	19	.	.	PUNCT
ejpam-6226	335	1	proof	proof	NOUN
ejpam-6226	335	2	.	.	PUNCT
ejpam-6226	336	1	let	let	VERB
ejpam-6226	336	2	κ	κ	NOUN
ejpam-6226	336	3	:	:	PUNCT
ejpam-6226	336	4	i	i	PRON
ejpam-6226	336	5	→	→	PUNCT
ejpam-6226	336	6	ĭ	ĭ	NOUN
ejpam-6226	336	7	be	be	AUX
ejpam-6226	336	8	a	a	DET
ejpam-6226	336	9	homomorphism	homomorphism	NOUN
ejpam-6226	336	10	of	of	ADP
ejpam-6226	336	11	ink	ink	NOUN
ejpam-6226	336	12	-	-	PUNCT
ejpam-6226	336	13	algebras	algebras	NOUN
ejpam-6226	336	14	.	.	PUNCT
ejpam-6226	337	1	if	if	SCONJ
ejpam-6226	337	2	g	g	PROPN
ejpam-6226	337	3	=	=	SYM
ejpam-6226	337	4	(	(	PUNCT
ejpam-6226	337	5	gt	gt	INTJ
ejpam-6226	337	6	,	,	PUNCT
ejpam-6226	337	7	gi	gi	INTJ
ejpam-6226	337	8	,	,	PUNCT
ejpam-6226	337	9	gf	gf	PROPN
ejpam-6226	337	10	)	)	PUNCT
ejpam-6226	337	11	is	be	AUX
ejpam-6226	337	12	an	an	DET
ejpam-6226	337	13	nmink	nmink	NOUN
ejpam-6226	337	14	-	-	PUNCT
ejpam-6226	337	15	i	i	PRON
ejpam-6226	337	16	of	of	ADP
ejpam-6226	337	17	ĭ	ĭ	PROPN
ejpam-6226	337	18	,	,	PUNCT
ejpam-6226	337	19	then	then	ADV
ejpam-6226	337	20	gt	gt	PROPN
ejpam-6226	338	1	[	[	X
ejpam-6226	338	2	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	338	3	)	)	PUNCT
ejpam-6226	339	1	=	=	SYM
ejpam-6226	339	2	gt	gt	PROPN
ejpam-6226	339	3	(	(	PUNCT
ejpam-6226	339	4	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	339	5	)	)	PUNCT
ejpam-6226	339	6	)	)	PUNCT
ejpam-6226	339	7	≥	≥	PROPN
ejpam-6226	340	1	gt	gt	INTJ
ejpam-6226	340	2	(	(	PUNCT
ejpam-6226	340	3	0	0	NUM
ejpam-6226	340	4	)	)	PUNCT
ejpam-6226	340	5	=	=	SYM
ejpam-6226	340	6	gt	gt	PROPN
ejpam-6226	340	7	(	(	PUNCT
ejpam-6226	340	8	κ(0	κ(0	PROPN
ejpam-6226	340	9	)	)	PUNCT
ejpam-6226	340	10	)	)	PUNCT
ejpam-6226	341	1	=	=	PUNCT
ejpam-6226	341	2	gt	gt	PROPN
ejpam-6226	342	1	[	[	X
ejpam-6226	342	2	κ](0	κ](0	NOUN
ejpam-6226	342	3	)	)	PUNCT
ejpam-6226	342	4	,	,	PUNCT
ejpam-6226	342	5	gi	gi	X
ejpam-6226	342	6	[	[	X
ejpam-6226	342	7	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	342	8	)	)	PUNCT
ejpam-6226	343	1	=	=	PUNCT
ejpam-6226	343	2	gi(κ(ϵ	gi(κ(ϵ	X
ejpam-6226	343	3	)	)	PUNCT
ejpam-6226	343	4	)	)	PUNCT
ejpam-6226	344	1	≤	≤	NOUN
ejpam-6226	345	1	gi(0	gi(0	NOUN
ejpam-6226	345	2	)	)	PUNCT
ejpam-6226	345	3	=	=	SYM
ejpam-6226	345	4	gigi(κ(0	gigi(κ(0	NOUN
ejpam-6226	345	5	)	)	PUNCT
ejpam-6226	345	6	)	)	PUNCT
ejpam-6226	346	1	=	=	PUNCT
ejpam-6226	346	2	gi	gi	X
ejpam-6226	346	3	[	[	X
ejpam-6226	346	4	κ](0	κ](0	NOUN
ejpam-6226	346	5	)	)	PUNCT
ejpam-6226	346	6	,	,	PUNCT
ejpam-6226	346	7	gf	gf	X
ejpam-6226	347	1	[	[	X
ejpam-6226	347	2	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	347	3	)	)	PUNCT
ejpam-6226	348	1	=	=	SYM
ejpam-6226	348	2	gf	gf	X
ejpam-6226	348	3	(	(	PUNCT
ejpam-6226	348	4	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	348	5	)	)	PUNCT
ejpam-6226	348	6	)	)	PUNCT
ejpam-6226	348	7	≤	≤	NUM
ejpam-6226	348	8	gf	gf	X
ejpam-6226	348	9	(	(	PUNCT
ejpam-6226	348	10	0	0	NUM
ejpam-6226	348	11	)	)	PUNCT
ejpam-6226	348	12	=	=	SYM
ejpam-6226	348	13	gf	gf	X
ejpam-6226	348	14	(	(	PUNCT
ejpam-6226	348	15	κ(0	κ(0	PROPN
ejpam-6226	348	16	)	)	PUNCT
ejpam-6226	348	17	)	)	PUNCT
ejpam-6226	348	18	=	=	PUNCT
ejpam-6226	348	19	gf	gf	X
ejpam-6226	348	20	[	[	X
ejpam-6226	348	21	κ](0),∀ϵ	κ](0),∀ϵ	PROPN
ejpam-6226	348	22	∈	∈	PROPN
ejpam-6226	348	23	i.	i.	NOUN
ejpam-6226	348	24	let	let	VERB
ejpam-6226	348	25	ϵ	ϵ	NUM
ejpam-6226	348	26	,	,	PUNCT
ejpam-6226	348	27	ξ	ξ	PROPN
ejpam-6226	348	28	,	,	PUNCT
ejpam-6226	348	29	ς	ς	PROPN
ejpam-6226	348	30	∈	∈	PROPN
ejpam-6226	348	31	i.	i.	NOUN
ejpam-6226	348	32	then	then	ADV
ejpam-6226	348	33	min{gt	min{gt	VERB
ejpam-6226	349	1	[	[	X
ejpam-6226	349	2	κ]((ϵ	κ]((ϵ	INTJ
ejpam-6226	349	3	•	•	NOUN
ejpam-6226	349	4	(	(	PUNCT
ejpam-6226	349	5	ξ	ξ	PROPN
ejpam-6226	349	6	•	•	NUM
ejpam-6226	349	7	ϵ	ϵ	NOUN
ejpam-6226	349	8	)	)	PUNCT
ejpam-6226	349	9	)	)	PUNCT
ejpam-6226	349	10	•	•	ADP
ejpam-6226	349	11	ς	ς	PROPN
ejpam-6226	349	12	)	)	PUNCT
ejpam-6226	349	13	,	,	PUNCT
ejpam-6226	349	14	gt	gt	PROPN
ejpam-6226	350	1	[	[	X
ejpam-6226	350	2	κ](ς	κ](ς	NOUN
ejpam-6226	350	3	)	)	PUNCT
ejpam-6226	350	4	}	}	PUNCT
ejpam-6226	351	1	=	=	SYM
ejpam-6226	351	2	min{gt	min{gt	PRON
ejpam-6226	351	3	(	(	PUNCT
ejpam-6226	351	4	κ((ϵ	κ((ϵ	NOUN
ejpam-6226	351	5	•	•	NOUN
ejpam-6226	351	6	(	(	PUNCT
ejpam-6226	351	7	ξ	ξ	NOUN
ejpam-6226	351	8	•	•	NUM
ejpam-6226	351	9	ϵ	ϵ	NOUN
ejpam-6226	351	10	)	)	PUNCT
ejpam-6226	351	11	)	)	PUNCT
ejpam-6226	351	12	•	•	NUM
ejpam-6226	351	13	ς	ς	PROPN
ejpam-6226	351	14	)	)	PUNCT
ejpam-6226	351	15	)	)	PUNCT
ejpam-6226	351	16	,	,	PUNCT
ejpam-6226	351	17	gt	gt	PROPN
ejpam-6226	351	18	(	(	PUNCT
ejpam-6226	351	19	κ(ς	κ(ς	PROPN
ejpam-6226	351	20	)	)	PUNCT
ejpam-6226	351	21	)	)	PUNCT
ejpam-6226	351	22	}	}	PUNCT
ejpam-6226	352	1	=	=	SYM
ejpam-6226	352	2	min{gt	min{gt	NOUN
ejpam-6226	352	3	(	(	PUNCT
ejpam-6226	352	4	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	352	5	•	•	NUM
ejpam-6226	352	6	ς	ς	PROPN
ejpam-6226	352	7	)	)	PUNCT
ejpam-6226	352	8	)	)	PUNCT
ejpam-6226	352	9	,	,	PUNCT
ejpam-6226	352	10	gt	gt	PROPN
ejpam-6226	352	11	(	(	PUNCT
ejpam-6226	352	12	κ(ς	κ(ς	PROPN
ejpam-6226	352	13	)	)	PUNCT
ejpam-6226	352	14	)	)	PUNCT
ejpam-6226	352	15	}	}	PUNCT
ejpam-6226	352	16	=	=	SYM
ejpam-6226	352	17	gt	gt	PROPN
ejpam-6226	352	18	(	(	PUNCT
ejpam-6226	352	19	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	352	20	)	)	PUNCT
ejpam-6226	352	21	)	)	PUNCT
ejpam-6226	353	1	=	=	PUNCT
ejpam-6226	353	2	gt	gt	PROPN
ejpam-6226	354	1	[	[	X
ejpam-6226	354	2	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	354	3	)	)	PUNCT
ejpam-6226	354	4	,	,	PUNCT
ejpam-6226	354	5	max{gi	max{gi	NOUN
ejpam-6226	355	1	[	[	X
ejpam-6226	355	2	κ]((ϵ	κ]((ϵ	INTJ
ejpam-6226	355	3	•	•	NOUN
ejpam-6226	355	4	(	(	PUNCT
ejpam-6226	355	5	ξ	ξ	PROPN
ejpam-6226	355	6	•	•	NUM
ejpam-6226	355	7	ϵ	ϵ	NOUN
ejpam-6226	355	8	)	)	PUNCT
ejpam-6226	355	9	)	)	PUNCT
ejpam-6226	355	10	•	•	ADP
ejpam-6226	355	11	ς	ς	NOUN
ejpam-6226	355	12	)	)	PUNCT
ejpam-6226	355	13	,	,	PUNCT
ejpam-6226	355	14	gi	gi	VERB
ejpam-6226	355	15	[	[	X
ejpam-6226	355	16	κ](ς	κ](ς	NOUN
ejpam-6226	355	17	)	)	PUNCT
ejpam-6226	355	18	}	}	PUNCT
ejpam-6226	356	1	=	=	PUNCT
ejpam-6226	356	2	max{gi(κ((ϵ	max{gi(κ((ϵ	NOUN
ejpam-6226	357	1	•	•	NOUN
ejpam-6226	357	2	(	(	PUNCT
ejpam-6226	357	3	ξ	ξ	NOUN
ejpam-6226	357	4	•	•	NUM
ejpam-6226	357	5	ϵ	ϵ	NOUN
ejpam-6226	357	6	)	)	PUNCT
ejpam-6226	357	7	)	)	PUNCT
ejpam-6226	357	8	•	•	NUM
ejpam-6226	357	9	ς	ς	PROPN
ejpam-6226	357	10	)	)	PUNCT
ejpam-6226	357	11	)	)	PUNCT
ejpam-6226	357	12	,	,	PUNCT
ejpam-6226	357	13	gi(κ(ς	gi(κ(ς	NOUN
ejpam-6226	357	14	)	)	PUNCT
ejpam-6226	357	15	)	)	PUNCT
ejpam-6226	357	16	}	}	PUNCT
ejpam-6226	357	17	=	=	PUNCT
ejpam-6226	357	18	max{gi(κ(ϵ	max{gi(κ(ϵ	PROPN
ejpam-6226	357	19	•	•	NOUN
ejpam-6226	357	20	ς	ς	NOUN
ejpam-6226	357	21	)	)	PUNCT
ejpam-6226	357	22	)	)	PUNCT
ejpam-6226	357	23	,	,	PUNCT
ejpam-6226	357	24	gi(κ(ς	gi(κ(ς	NOUN
ejpam-6226	357	25	)	)	PUNCT
ejpam-6226	357	26	)	)	PUNCT
ejpam-6226	357	27	}	}	PUNCT
ejpam-6226	357	28	=	=	SYM
ejpam-6226	357	29	gi(κ(ϵ	gi(κ(ϵ	X
ejpam-6226	357	30	)	)	PUNCT
ejpam-6226	357	31	)	)	PUNCT
ejpam-6226	358	1	=	=	PUNCT
ejpam-6226	358	2	gi	gi	NOUN
ejpam-6226	359	1	[	[	X
ejpam-6226	359	2	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	359	3	)	)	PUNCT
ejpam-6226	359	4	,	,	PUNCT
ejpam-6226	359	5	max{gf	max{gf	X
ejpam-6226	360	1	[	[	X
ejpam-6226	360	2	κ]((ϵ	κ]((ϵ	INTJ
ejpam-6226	360	3	•	•	NOUN
ejpam-6226	360	4	(	(	PUNCT
ejpam-6226	360	5	ξ	ξ	PROPN
ejpam-6226	360	6	•	•	NUM
ejpam-6226	360	7	ϵ	ϵ	NOUN
ejpam-6226	360	8	)	)	PUNCT
ejpam-6226	360	9	)	)	PUNCT
ejpam-6226	360	10	•	•	ADP
ejpam-6226	360	11	ς	ς	NOUN
ejpam-6226	360	12	)	)	PUNCT
ejpam-6226	360	13	,	,	PUNCT
ejpam-6226	360	14	gf	gf	X
ejpam-6226	361	1	[	[	X
ejpam-6226	361	2	κ](ς	κ](ς	NOUN
ejpam-6226	361	3	)	)	PUNCT
ejpam-6226	361	4	}	}	PUNCT
ejpam-6226	362	1	=	=	SYM
ejpam-6226	362	2	max{gf	max{gf	X
ejpam-6226	362	3	(	(	PUNCT
ejpam-6226	362	4	κ((ϵ	κ((ϵ	NOUN
ejpam-6226	362	5	•	•	NOUN
ejpam-6226	362	6	(	(	PUNCT
ejpam-6226	362	7	ξ	ξ	NOUN
ejpam-6226	362	8	•	•	NUM
ejpam-6226	362	9	ϵ	ϵ	NOUN
ejpam-6226	362	10	)	)	PUNCT
ejpam-6226	362	11	)	)	PUNCT
ejpam-6226	362	12	•	•	NUM
ejpam-6226	362	13	ς	ς	PROPN
ejpam-6226	362	14	)	)	PUNCT
ejpam-6226	362	15	)	)	PUNCT
ejpam-6226	362	16	,	,	PUNCT
ejpam-6226	362	17	gf	gf	X
ejpam-6226	362	18	(	(	PUNCT
ejpam-6226	362	19	κ(ς	κ(ς	PROPN
ejpam-6226	362	20	)	)	PUNCT
ejpam-6226	362	21	)	)	PUNCT
ejpam-6226	362	22	}	}	PUNCT
ejpam-6226	363	1	=	=	SYM
ejpam-6226	363	2	max{gf	max{gf	X
ejpam-6226	363	3	(	(	PUNCT
ejpam-6226	363	4	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	363	5	•	•	NUM
ejpam-6226	363	6	ς	ς	PROPN
ejpam-6226	363	7	)	)	PUNCT
ejpam-6226	363	8	)	)	PUNCT
ejpam-6226	363	9	,	,	PUNCT
ejpam-6226	363	10	gf	gf	X
ejpam-6226	363	11	(	(	PUNCT
ejpam-6226	363	12	κ(ς	κ(ς	PROPN
ejpam-6226	363	13	)	)	PUNCT
ejpam-6226	363	14	)	)	PUNCT
ejpam-6226	363	15	}	}	PUNCT
ejpam-6226	363	16	=	=	SYM
ejpam-6226	363	17	gf	gf	X
ejpam-6226	363	18	(	(	PUNCT
ejpam-6226	363	19	κ(ϵ	κ(ϵ	PROPN
ejpam-6226	363	20	)	)	PUNCT
ejpam-6226	363	21	)	)	PUNCT
ejpam-6226	364	1	=	=	PUNCT
ejpam-6226	364	2	gf	gf	X
ejpam-6226	365	1	[	[	X
ejpam-6226	365	2	κ](ϵ	κ](ϵ	NOUN
ejpam-6226	365	3	)	)	PUNCT
ejpam-6226	365	4	.	.	PUNCT
ejpam-6226	366	1	hence	hence	ADV
ejpam-6226	366	2	,	,	PUNCT
ejpam-6226	366	3	g[κ	g[κ	PROPN
ejpam-6226	366	4	]	]	X
ejpam-6226	366	5	is	be	AUX
ejpam-6226	366	6	an	an	DET
ejpam-6226	366	7	nmink	nmink	NOUN
ejpam-6226	366	8	-	-	PUNCT
ejpam-6226	366	9	i	i	PRON
ejpam-6226	366	10	of	of	ADP
ejpam-6226	366	11	i.	i.	PROPN
ejpam-6226	366	12	r.	r.	PROPN
ejpam-6226	366	13	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	366	14	et	et	PROPN
ejpam-6226	366	15	al	al	PROPN
ejpam-6226	366	16	.	.	PUNCT
ejpam-6226	366	17	/	/	SYM
ejpam-6226	366	18	eur	eur	PROPN
ejpam-6226	366	19	.	.	PUNCT
ejpam-6226	367	1	j.	j.	PROPN
ejpam-6226	367	2	pure	pure	PROPN
ejpam-6226	367	3	appl	appl	PROPN
ejpam-6226	367	4	.	.	PROPN
ejpam-6226	367	5	math	math	PROPN
ejpam-6226	367	6	,	,	PUNCT
ejpam-6226	367	7	18	18	NUM
ejpam-6226	367	8	(	(	PUNCT
ejpam-6226	367	9	3	3	NUM
ejpam-6226	367	10	)	)	PUNCT
ejpam-6226	367	11	(	(	PUNCT
ejpam-6226	367	12	2025	2025	NUM
ejpam-6226	367	13	)	)	PUNCT
ejpam-6226	367	14	,	,	PUNCT
ejpam-6226	367	15	6226	6226	NUM
ejpam-6226	367	16	17	17	NUM
ejpam-6226	367	17	of	of	ADP
ejpam-6226	367	18	19	19	NUM
ejpam-6226	367	19	theorem	theorem	NOUN
ejpam-6226	367	20	20	20	NUM
ejpam-6226	367	21	.	.	PUNCT
ejpam-6226	368	1	a	a	DET
ejpam-6226	368	2	homomorphic	homomorphic	ADJ
ejpam-6226	368	3	pre	pre	NOUN
ejpam-6226	368	4	-	-	NOUN
ejpam-6226	368	5	image	image	NOUN
ejpam-6226	368	6	of	of	ADP
ejpam-6226	368	7	an	an	DET
ejpam-6226	368	8	npmink	npmink	NOUN
ejpam-6226	368	9	-	-	PUNCT
ejpam-6226	368	10	i	i	PRON
ejpam-6226	368	11	of	of	ADP
ejpam-6226	368	12	ink	ink	NOUN
ejpam-6226	368	13	-	-	PUNCT
ejpam-6226	368	14	algebras	algebras	PROPN
ejpam-6226	368	15	is	be	AUX
ejpam-6226	368	16	an	an	DET
ejpam-6226	368	17	npminki	npminki	NOUN
ejpam-6226	368	18	.	.	PUNCT
ejpam-6226	369	1	proof	proof	NOUN
ejpam-6226	369	2	.	.	PUNCT
ejpam-6226	370	1	the	the	DET
ejpam-6226	370	2	proof	proof	NOUN
ejpam-6226	370	3	is	be	AUX
ejpam-6226	370	4	similar	similar	ADJ
ejpam-6226	370	5	to	to	ADP
ejpam-6226	370	6	theorem	theorem	VERB
ejpam-6226	370	7	19	19	NUM
ejpam-6226	370	8	.	.	NOUN
ejpam-6226	370	9	5	5	NUM
ejpam-6226	370	10	.	.	X
ejpam-6226	370	11	conclusion	conclusion	NOUN
ejpam-6226	370	12	this	this	DET
ejpam-6226	370	13	study	study	NOUN
ejpam-6226	370	14	introduces	introduce	NOUN
ejpam-6226	370	15	and	and	CCONJ
ejpam-6226	370	16	formalizes	formalize	VERB
ejpam-6226	370	17	the	the	DET
ejpam-6226	370	18	concepts	concept	NOUN
ejpam-6226	370	19	of	of	ADP
ejpam-6226	370	20	mink	mink	NOUN
ejpam-6226	370	21	-	-	PUNCT
ejpam-6226	370	22	is	be	AUX
ejpam-6226	370	23	and	and	CCONJ
ejpam-6226	370	24	pmink	pmink	NOUN
ejpam-6226	370	25	-	-	PUNCT
ejpam-6226	370	26	is	be	AUX
ejpam-6226	370	27	within	within	ADP
ejpam-6226	370	28	the	the	DET
ejpam-6226	370	29	structure	structure	NOUN
ejpam-6226	370	30	of	of	ADP
ejpam-6226	370	31	ink	ink	NOUN
ejpam-6226	370	32	-	-	PUNCT
ejpam-6226	370	33	algebras	algebra	NOUN
ejpam-6226	370	34	,	,	PUNCT
ejpam-6226	370	35	and	and	CCONJ
ejpam-6226	370	36	extends	extend	VERB
ejpam-6226	370	37	these	these	DET
ejpam-6226	370	38	notions	notion	NOUN
ejpam-6226	370	39	to	to	ADP
ejpam-6226	370	40	fuzzy	fuzzy	ADJ
ejpam-6226	370	41	and	and	CCONJ
ejpam-6226	370	42	neutrosophic	neutrosophic	ADJ
ejpam-6226	370	43	contexts	contexts	NOUN
ejpam-6226	370	44	.	.	PUNCT
ejpam-6226	371	1	the	the	DET
ejpam-6226	371	2	resulting	result	VERB
ejpam-6226	371	3	classes	class	NOUN
ejpam-6226	371	4	of	of	ADP
ejpam-6226	371	5	fmink	fmink	NOUN
ejpam-6226	371	6	-	-	PUNCT
ejpam-6226	371	7	is	be	AUX
ejpam-6226	371	8	,	,	PUNCT
ejpam-6226	371	9	fpmink	fpmink	NOUN
ejpam-6226	371	10	-	-	PUNCT
ejpam-6226	371	11	is	be	AUX
ejpam-6226	371	12	,	,	PUNCT
ejpam-6226	371	13	nmink	nmink	NOUN
ejpam-6226	371	14	-	-	PUNCT
ejpam-6226	371	15	is	be	AUX
ejpam-6226	371	16	,	,	PUNCT
ejpam-6226	371	17	and	and	CCONJ
ejpam-6226	371	18	npmink	npmink	NOUN
ejpam-6226	371	19	-	-	PUNCT
ejpam-6226	371	20	is	be	AUX
ejpam-6226	371	21	are	be	AUX
ejpam-6226	371	22	investigated	investigate	VERB
ejpam-6226	371	23	in	in	ADP
ejpam-6226	371	24	terms	term	NOUN
ejpam-6226	371	25	of	of	ADP
ejpam-6226	371	26	their	their	PRON
ejpam-6226	371	27	structural	structural	ADJ
ejpam-6226	371	28	properties	property	NOUN
ejpam-6226	371	29	,	,	PUNCT
ejpam-6226	371	30	including	include	VERB
ejpam-6226	371	31	closure	closure	NOUN
ejpam-6226	371	32	under	under	ADP
ejpam-6226	371	33	intersection	intersection	NOUN
ejpam-6226	371	34	and	and	CCONJ
ejpam-6226	371	35	behavior	behavior	NOUN
ejpam-6226	371	36	under	under	ADP
ejpam-6226	371	37	homomorphic	homomorphic	ADJ
ejpam-6226	371	38	pre	pre	NOUN
ejpam-6226	371	39	-	-	NOUN
ejpam-6226	371	40	images	image	NOUN
ejpam-6226	371	41	.	.	PUNCT
ejpam-6226	372	1	it	it	PRON
ejpam-6226	372	2	is	be	AUX
ejpam-6226	372	3	shown	show	VERB
ejpam-6226	372	4	that	that	SCONJ
ejpam-6226	372	5	while	while	SCONJ
ejpam-6226	372	6	intersection	intersection	NOUN
ejpam-6226	372	7	preserves	preserve	VERB
ejpam-6226	372	8	the	the	DET
ejpam-6226	372	9	implicative	implicative	ADJ
ejpam-6226	372	10	nature	nature	NOUN
ejpam-6226	372	11	of	of	ADP
ejpam-6226	372	12	these	these	DET
ejpam-6226	372	13	ideals	ideal	NOUN
ejpam-6226	372	14	,	,	PUNCT
ejpam-6226	372	15	union	union	NOUN
ejpam-6226	372	16	does	do	AUX
ejpam-6226	372	17	not	not	PART
ejpam-6226	372	18	necessarily	necessarily	ADV
ejpam-6226	372	19	do	do	VERB
ejpam-6226	372	20	so	so	ADV
ejpam-6226	372	21	.	.	PUNCT
ejpam-6226	373	1	these	these	DET
ejpam-6226	373	2	findings	finding	NOUN
ejpam-6226	373	3	enhance	enhance	VERB
ejpam-6226	373	4	the	the	DET
ejpam-6226	373	5	theoretical	theoretical	ADJ
ejpam-6226	373	6	foundation	foundation	NOUN
ejpam-6226	373	7	of	of	ADP
ejpam-6226	373	8	ink	ink	NOUN
ejpam-6226	373	9	-	-	PUNCT
ejpam-6226	373	10	algebras	algebra	NOUN
ejpam-6226	373	11	and	and	CCONJ
ejpam-6226	373	12	open	open	ADJ
ejpam-6226	373	13	pathways	pathway	NOUN
ejpam-6226	373	14	for	for	ADP
ejpam-6226	373	15	their	their	PRON
ejpam-6226	373	16	application	application	NOUN
ejpam-6226	373	17	in	in	ADP
ejpam-6226	373	18	domains	domain	NOUN
ejpam-6226	373	19	that	that	PRON
ejpam-6226	373	20	require	require	VERB
ejpam-6226	373	21	reasoning	reasoning	NOUN
ejpam-6226	373	22	under	under	ADP
ejpam-6226	373	23	uncertainty	uncertainty	NOUN
ejpam-6226	373	24	,	,	PUNCT
ejpam-6226	373	25	such	such	ADJ
ejpam-6226	373	26	as	as	ADP
ejpam-6226	373	27	decision	decision	NOUN
ejpam-6226	373	28	support	support	NOUN
ejpam-6226	373	29	systems	system	NOUN
ejpam-6226	373	30	and	and	CCONJ
ejpam-6226	373	31	artificial	artificial	ADJ
ejpam-6226	373	32	intelligence	intelligence	NOUN
ejpam-6226	373	33	.	.	PUNCT
ejpam-6226	374	1	future	future	ADJ
ejpam-6226	374	2	research	research	NOUN
ejpam-6226	374	3	may	may	AUX
ejpam-6226	374	4	focus	focus	VERB
ejpam-6226	374	5	on	on	ADP
ejpam-6226	374	6	the	the	DET
ejpam-6226	374	7	practical	practical	ADJ
ejpam-6226	374	8	application	application	NOUN
ejpam-6226	374	9	of	of	ADP
ejpam-6226	374	10	these	these	DET
ejpam-6226	374	11	ideals	ideal	NOUN
ejpam-6226	374	12	in	in	ADP
ejpam-6226	374	13	areas	area	NOUN
ejpam-6226	374	14	such	such	ADJ
ejpam-6226	374	15	as	as	ADP
ejpam-6226	374	16	medical	medical	ADJ
ejpam-6226	374	17	diagnostics	diagnostic	NOUN
ejpam-6226	374	18	and	and	CCONJ
ejpam-6226	374	19	intelligent	intelligent	ADJ
ejpam-6226	374	20	systems	system	NOUN
ejpam-6226	374	21	,	,	PUNCT
ejpam-6226	374	22	where	where	SCONJ
ejpam-6226	374	23	managing	manage	VERB
ejpam-6226	374	24	ambiguity	ambiguity	NOUN
ejpam-6226	374	25	is	be	AUX
ejpam-6226	374	26	essential	essential	ADJ
ejpam-6226	374	27	.	.	PUNCT
ejpam-6226	375	1	moreover	moreover	ADV
ejpam-6226	375	2	,	,	PUNCT
ejpam-6226	375	3	generalizing	generalize	VERB
ejpam-6226	375	4	these	these	DET
ejpam-6226	375	5	concepts	concept	NOUN
ejpam-6226	375	6	to	to	ADP
ejpam-6226	375	7	other	other	ADJ
ejpam-6226	375	8	algebraic	algebraic	ADJ
ejpam-6226	375	9	structures	structure	NOUN
ejpam-6226	375	10	and	and	CCONJ
ejpam-6226	375	11	developing	develop	VERB
ejpam-6226	375	12	computational	computational	ADJ
ejpam-6226	375	13	frameworks	framework	NOUN
ejpam-6226	375	14	or	or	CCONJ
ejpam-6226	375	15	algorithms	algorithm	NOUN
ejpam-6226	375	16	based	base	VERB
ejpam-6226	375	17	on	on	ADP
ejpam-6226	375	18	their	their	PRON
ejpam-6226	375	19	properties	property	NOUN
ejpam-6226	375	20	could	could	AUX
ejpam-6226	375	21	further	far	ADV
ejpam-6226	375	22	support	support	VERB
ejpam-6226	375	23	complex	complex	ADJ
ejpam-6226	375	24	decision	decision	NOUN
ejpam-6226	375	25	-	-	PUNCT
ejpam-6226	375	26	making	make	VERB
ejpam-6226	375	27	processes	process	NOUN
ejpam-6226	375	28	in	in	ADP
ejpam-6226	375	29	real	real	ADJ
ejpam-6226	375	30	-	-	PUNCT
ejpam-6226	375	31	time	time	NOUN
ejpam-6226	375	32	environments	environment	NOUN
ejpam-6226	375	33	.	.	PUNCT
ejpam-6226	376	1	in	in	ADP
ejpam-6226	376	2	particular	particular	ADJ
ejpam-6226	376	3	,	,	PUNCT
ejpam-6226	376	4	the	the	DET
ejpam-6226	376	5	exploration	exploration	NOUN
ejpam-6226	376	6	of	of	ADP
ejpam-6226	376	7	neutrosophic	neutrosophic	ADJ
ejpam-6226	376	8	hyperstructures	hyperstructure	NOUN
ejpam-6226	376	9	,	,	PUNCT
ejpam-6226	376	10	as	as	SCONJ
ejpam-6226	376	11	discussed	discuss	VERB
ejpam-6226	376	12	by	by	ADP
ejpam-6226	376	13	alsubie	alsubie	NOUN
ejpam-6226	376	14	and	and	CCONJ
ejpam-6226	376	15	al	al	PROPN
ejpam-6226	376	16	-	-	PROPN
ejpam-6226	376	17	masarwah	masarwah	PROPN
ejpam-6226	376	18	[	[	X
ejpam-6226	376	19	27	27	NUM
ejpam-6226	376	20	]	]	PUNCT
ejpam-6226	376	21	,	,	PUNCT
ejpam-6226	376	22	offers	offer	VERB
ejpam-6226	376	23	a	a	DET
ejpam-6226	376	24	compelling	compelling	ADJ
ejpam-6226	376	25	direction	direction	NOUN
ejpam-6226	376	26	for	for	ADP
ejpam-6226	376	27	extending	extend	VERB
ejpam-6226	376	28	the	the	DET
ejpam-6226	376	29	present	present	ADJ
ejpam-6226	376	30	work	work	NOUN
ejpam-6226	376	31	to	to	ADP
ejpam-6226	376	32	more	more	ADJ
ejpam-6226	376	33	generalized	generalized	ADJ
ejpam-6226	376	34	systems	system	NOUN
ejpam-6226	376	35	such	such	ADJ
ejpam-6226	376	36	as	as	ADP
ejpam-6226	376	37	hyper	hyper	ADJ
ejpam-6226	376	38	bck	bck	NOUN
ejpam-6226	376	39	-	-	PUNCT
ejpam-6226	376	40	algebras	algebras	PROPN
ejpam-6226	376	41	.	.	PUNCT
ejpam-6226	377	1	furthermore	furthermore	ADV
ejpam-6226	377	2	,	,	PUNCT
ejpam-6226	377	3	the	the	DET
ejpam-6226	377	4	integration	integration	NOUN
ejpam-6226	377	5	of	of	ADP
ejpam-6226	377	6	fuzzy	fuzzy	ADJ
ejpam-6226	377	7	soft	soft	ADJ
ejpam-6226	377	8	computing	computing	NOUN
ejpam-6226	377	9	paradigms	paradigm	NOUN
ejpam-6226	377	10	,	,	PUNCT
ejpam-6226	377	11	such	such	ADJ
ejpam-6226	377	12	as	as	ADP
ejpam-6226	377	13	fuzzy	fuzzy	ADJ
ejpam-6226	377	14	soft	soft	ADJ
ejpam-6226	377	15	graphs	graph	NOUN
ejpam-6226	377	16	[	[	X
ejpam-6226	377	17	28	28	NUM
ejpam-6226	377	18	]	]	PUNCT
ejpam-6226	377	19	,	,	PUNCT
ejpam-6226	377	20	may	may	AUX
ejpam-6226	377	21	provide	provide	VERB
ejpam-6226	377	22	enriched	enrich	VERB
ejpam-6226	377	23	algebraic	algebraic	ADJ
ejpam-6226	377	24	modeling	modeling	NOUN
ejpam-6226	377	25	tools	tool	NOUN
ejpam-6226	377	26	for	for	ADP
ejpam-6226	377	27	handling	handle	VERB
ejpam-6226	377	28	complex	complex	ADJ
ejpam-6226	377	29	uncertainty	uncertainty	NOUN
ejpam-6226	377	30	and	and	CCONJ
ejpam-6226	377	31	flexible	flexible	ADJ
ejpam-6226	377	32	information	information	NOUN
ejpam-6226	377	33	structures	structure	NOUN
ejpam-6226	377	34	in	in	ADP
ejpam-6226	377	35	abstract	abstract	ADJ
ejpam-6226	377	36	systems	system	NOUN
ejpam-6226	377	37	.	.	PUNCT
ejpam-6226	378	1	acknowledgements	acknowledgement	NOUN
ejpam-6226	378	2	this	this	DET
ejpam-6226	378	3	research	research	NOUN
ejpam-6226	378	4	was	be	AUX
ejpam-6226	378	5	supported	support	VERB
ejpam-6226	378	6	by	by	ADP
ejpam-6226	378	7	the	the	DET
ejpam-6226	378	8	university	university	NOUN
ejpam-6226	378	9	of	of	ADP
ejpam-6226	378	10	phayao	phayao	NOUN
ejpam-6226	378	11	and	and	CCONJ
ejpam-6226	378	12	the	the	DET
ejpam-6226	378	13	thailand	thailand	PROPN
ejpam-6226	378	14	science	science	PROPN
ejpam-6226	378	15	research	research	PROPN
ejpam-6226	378	16	and	and	CCONJ
ejpam-6226	378	17	innovation	innovation	NOUN
ejpam-6226	378	18	fund	fund	NOUN
ejpam-6226	378	19	(	(	PUNCT
ejpam-6226	378	20	fundamental	fundamental	ADJ
ejpam-6226	378	21	fund	fund	NOUN
ejpam-6226	378	22	2025	2025	NUM
ejpam-6226	378	23	,	,	PUNCT
ejpam-6226	378	24	grant	grant	VERB
ejpam-6226	378	25	no	no	NOUN
ejpam-6226	378	26	.	.	PROPN
ejpam-6226	379	1	5027/2567	5027/2567	NUM
ejpam-6226	379	2	)	)	PUNCT
ejpam-6226	379	3	.	.	PUNCT
ejpam-6226	380	1	references	reference	NOUN
ejpam-6226	380	2	[	[	X
ejpam-6226	380	3	1	1	NUM
ejpam-6226	380	4	]	]	PUNCT
ejpam-6226	380	5	k.	k.	PROPN
ejpam-6226	380	6	iséki	iséki	PROPN
ejpam-6226	380	7	.	.	PROPN
ejpam-6226	381	1	on	on	ADP
ejpam-6226	381	2	bci	bci	NOUN
ejpam-6226	381	3	-	-	PUNCT
ejpam-6226	381	4	algebras	algebra	NOUN
ejpam-6226	381	5	.	.	PUNCT
ejpam-6226	382	1	mathematics	mathematic	NOUN
ejpam-6226	382	2	seminar	seminar	NOUN
ejpam-6226	382	3	notes	note	NOUN
ejpam-6226	382	4	(	(	PUNCT
ejpam-6226	382	5	kobe	kobe	PROPN
ejpam-6226	382	6	university	university	PROPN
ejpam-6226	382	7	)	)	PUNCT
ejpam-6226	382	8	,	,	PUNCT
ejpam-6226	382	9	8(1):125	8(1):125	NUM
ejpam-6226	382	10	–	–	PUNCT
ejpam-6226	382	11	130	130	NUM
ejpam-6226	382	12	,	,	PUNCT
ejpam-6226	382	13	1980	1980	NUM
ejpam-6226	382	14	.	.	PUNCT
ejpam-6226	383	1	[	[	X
ejpam-6226	383	2	2	2	NUM
ejpam-6226	383	3	]	]	PUNCT
ejpam-6226	383	4	k.	k.	PROPN
ejpam-6226	383	5	iséki	iséki	PROPN
ejpam-6226	383	6	and	and	CCONJ
ejpam-6226	383	7	s.	s.	PROPN
ejpam-6226	383	8	tanaka	tanaka	PROPN
ejpam-6226	383	9	.	.	PUNCT
ejpam-6226	384	1	an	an	DET
ejpam-6226	384	2	introduction	introduction	NOUN
ejpam-6226	384	3	to	to	ADP
ejpam-6226	384	4	the	the	DET
ejpam-6226	384	5	theory	theory	NOUN
ejpam-6226	384	6	of	of	ADP
ejpam-6226	384	7	bck	bck	PROPN
ejpam-6226	384	8	-	-	PUNCT
ejpam-6226	384	9	algebras	algebras	PROPN
ejpam-6226	384	10	.	.	PUNCT
ejpam-6226	385	1	mathematica	mathematica	PROPN
ejpam-6226	385	2	japonica	japonica	PROPN
ejpam-6226	385	3	,	,	PUNCT
ejpam-6226	385	4	23(1):1–25	23(1):1–25	NUM
ejpam-6226	385	5	,	,	PUNCT
ejpam-6226	385	6	1978	1978	NUM
ejpam-6226	385	7	.	.	PUNCT
ejpam-6226	386	1	[	[	X
ejpam-6226	386	2	3	3	X
ejpam-6226	386	3	]	]	X
ejpam-6226	386	4	m.	m.	NOUN
ejpam-6226	386	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	386	6	and	and	CCONJ
ejpam-6226	386	7	k.	k.	PROPN
ejpam-6226	386	8	indhira	indhira	PROPN
ejpam-6226	386	9	.	.	PUNCT
ejpam-6226	387	1	on	on	ADP
ejpam-6226	387	2	intuitionistic	intuitionistic	ADJ
ejpam-6226	387	3	fuzzy	fuzzy	ADJ
ejpam-6226	387	4	ink	ink	NOUN
ejpam-6226	387	5	-	-	PUNCT
ejpam-6226	387	6	ideals	ideal	NOUN
ejpam-6226	387	7	of	of	ADP
ejpam-6226	387	8	ink	ink	NOUN
ejpam-6226	387	9	-	-	PUNCT
ejpam-6226	387	10	algebras	algebras	PROPN
ejpam-6226	387	11	.	.	PUNCT
ejpam-6226	388	1	iop	iop	PROPN
ejpam-6226	388	2	conference	conference	PROPN
ejpam-6226	388	3	series	series	PROPN
ejpam-6226	388	4	:	:	PUNCT
ejpam-6226	388	5	materials	material	NOUN
ejpam-6226	388	6	science	science	NOUN
ejpam-6226	388	7	and	and	CCONJ
ejpam-6226	388	8	engineering	engineering	NOUN
ejpam-6226	388	9	,	,	PUNCT
ejpam-6226	388	10	263:042142	263:042142	NUM
ejpam-6226	388	11	,	,	PUNCT
ejpam-6226	388	12	2017	2017	NUM
ejpam-6226	388	13	.	.	PUNCT
ejpam-6226	389	1	[	[	X
ejpam-6226	389	2	4	4	NUM
ejpam-6226	389	3	]	]	X
ejpam-6226	389	4	m.	m.	NOUN
ejpam-6226	389	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	389	6	,	,	PUNCT
ejpam-6226	389	7	k.	k.	PROPN
ejpam-6226	389	8	indhira	indhira	PROPN
ejpam-6226	389	9	,	,	PUNCT
ejpam-6226	389	10	v.	v.	ADP
ejpam-6226	389	11	m.	m.	NOUN
ejpam-6226	389	12	chandrasekaran	chandrasekaran	VERB
ejpam-6226	389	13	,	,	PUNCT
ejpam-6226	389	14	and	and	CCONJ
ejpam-6226	389	15	k.	k.	PROPN
ejpam-6226	389	16	jacob	jacob	PROPN
ejpam-6226	389	17	.	.	PROPN
ejpam-6226	390	1	interval	interval	NOUN
ejpam-6226	390	2	-	-	PUNCT
ejpam-6226	390	3	valued	value	VERB
ejpam-6226	390	4	fuzzy	fuzzy	ADJ
ejpam-6226	390	5	subalgebra	subalgebra	NOUN
ejpam-6226	390	6	and	and	CCONJ
ejpam-6226	390	7	fuzzy	fuzzy	ADJ
ejpam-6226	390	8	ink	ink	NOUN
ejpam-6226	390	9	-	-	PUNCT
ejpam-6226	390	10	ideal	ideal	NOUN
ejpam-6226	390	11	in	in	ADP
ejpam-6226	390	12	ink	ink	NOUN
ejpam-6226	390	13	-	-	PUNCT
ejpam-6226	390	14	algebra	algebra	NOUN
ejpam-6226	390	15	,	,	PUNCT
ejpam-6226	390	16	advances	advance	NOUN
ejpam-6226	390	17	in	in	ADP
ejpam-6226	390	18	algebra	algebra	NOUN
ejpam-6226	390	19	and	and	CCONJ
ejpam-6226	390	20	analysis	analysis	NOUN
ejpam-6226	390	21	.	.	PUNCT
ejpam-6226	391	1	trends	trend	NOUN
ejpam-6226	391	2	in	in	ADP
ejpam-6226	391	3	mathematics	mathematic	NOUN
ejpam-6226	391	4	.	.	PUNCT
ejpam-6226	392	1	birkhäuser	birkhäuser	NOUN
ejpam-6226	392	2	,	,	PUNCT
ejpam-6226	392	3	cham	cham	NOUN
ejpam-6226	392	4	,	,	PUNCT
ejpam-6226	392	5	2018	2018	NUM
ejpam-6226	392	6	.	.	PUNCT
ejpam-6226	393	1	r.	r.	PROPN
ejpam-6226	393	2	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	393	3	et	et	PROPN
ejpam-6226	393	4	al	al	PROPN
ejpam-6226	393	5	.	.	PUNCT
ejpam-6226	393	6	/	/	SYM
ejpam-6226	393	7	eur	eur	PROPN
ejpam-6226	393	8	.	.	PUNCT
ejpam-6226	394	1	j.	j.	PROPN
ejpam-6226	394	2	pure	pure	PROPN
ejpam-6226	394	3	appl	appl	PROPN
ejpam-6226	394	4	.	.	PROPN
ejpam-6226	394	5	math	math	PROPN
ejpam-6226	394	6	,	,	PUNCT
ejpam-6226	394	7	18	18	NUM
ejpam-6226	394	8	(	(	PUNCT
ejpam-6226	394	9	3	3	NUM
ejpam-6226	394	10	)	)	PUNCT
ejpam-6226	394	11	(	(	PUNCT
ejpam-6226	394	12	2025	2025	NUM
ejpam-6226	394	13	)	)	PUNCT
ejpam-6226	394	14	,	,	PUNCT
ejpam-6226	394	15	6226	6226	NUM
ejpam-6226	394	16	18	18	NUM
ejpam-6226	394	17	of	of	ADP
ejpam-6226	394	18	19	19	NUM
ejpam-6226	394	19	[	[	SYM
ejpam-6226	394	20	5	5	NUM
ejpam-6226	394	21	]	]	PUNCT
ejpam-6226	394	22	r.	r.	NOUN
ejpam-6226	394	23	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	394	24	,	,	PUNCT
ejpam-6226	394	25	e.	e.	PROPN
ejpam-6226	394	26	tamma	tamma	PROPN
ejpam-6226	394	27	,	,	PUNCT
ejpam-6226	394	28	and	and	CCONJ
ejpam-6226	394	29	c.	c.	PROPN
ejpam-6226	394	30	jana	jana	PROPN
ejpam-6226	394	31	.	.	PUNCT
ejpam-6226	395	1	bipolar	bipolar	ADJ
ejpam-6226	395	2	fuzzy	fuzzy	ADJ
ejpam-6226	395	3	ink	ink	NOUN
ejpam-6226	395	4	-	-	PUNCT
ejpam-6226	395	5	subalgebras	subalgebras	NOUN
ejpam-6226	395	6	of	of	ADP
ejpam-6226	395	7	ink	ink	NOUN
ejpam-6226	395	8	-	-	PUNCT
ejpam-6226	395	9	algebras	algebras	PROPN
ejpam-6226	395	10	.	.	PUNCT
ejpam-6226	396	1	aims	aim	VERB
ejpam-6226	396	2	mathematics	mathematic	NOUN
ejpam-6226	396	3	,	,	PUNCT
ejpam-6226	396	4	9(10):27593–27606	9(10):27593–27606	NUM
ejpam-6226	396	5	,	,	PUNCT
ejpam-6226	396	6	2024	2024	NUM
ejpam-6226	396	7	.	.	PUNCT
ejpam-6226	397	1	[	[	X
ejpam-6226	397	2	6	6	NUM
ejpam-6226	397	3	]	]	PUNCT
ejpam-6226	397	4	r.	r.	PROPN
ejpam-6226	397	5	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	397	6	,	,	PUNCT
ejpam-6226	397	7	e.	e.	PROPN
ejpam-6226	397	8	tamma	tamma	PROPN
ejpam-6226	397	9	,	,	PUNCT
ejpam-6226	397	10	v.	v.	PROPN
ejpam-6226	397	11	kalyani	kalyani	PROPN
ejpam-6226	397	12	uppuluri	uppuluri	PROPN
ejpam-6226	397	13	,	,	PUNCT
ejpam-6226	397	14	and	and	CCONJ
ejpam-6226	397	15	a.	a.	NOUN
ejpam-6226	397	16	iampan	iampan	PROPN
ejpam-6226	397	17	.	.	PUNCT
ejpam-6226	398	1	homomorphisms	homomorphism	NOUN
ejpam-6226	398	2	and	and	CCONJ
ejpam-6226	398	3	anti	anti	ADJ
ejpam-6226	398	4	-	-	ADJ
ejpam-6226	398	5	homomorphisms	homomorphism	NOUN
ejpam-6226	398	6	of	of	ADP
ejpam-6226	398	7	neutrosophic	neutrosophic	ADJ
ejpam-6226	398	8	ink	ink	NOUN
ejpam-6226	398	9	-	-	PUNCT
ejpam-6226	398	10	algebras	algebras	PROPN
ejpam-6226	398	11	.	.	PUNCT
ejpam-6226	399	1	international	international	ADJ
ejpam-6226	399	2	journal	journal	PROPN
ejpam-6226	399	3	of	of	ADP
ejpam-6226	399	4	neutrosophic	neutrosophic	ADJ
ejpam-6226	399	5	science	science	NOUN
ejpam-6226	399	6	,	,	PUNCT
ejpam-6226	399	7	23(1):335–340	23(1):335–340	PROPN
ejpam-6226	399	8	,	,	PUNCT
ejpam-6226	399	9	2024	2024	NUM
ejpam-6226	399	10	.	.	PUNCT
ejpam-6226	400	1	[	[	X
ejpam-6226	400	2	7	7	X
ejpam-6226	400	3	]	]	PUNCT
ejpam-6226	400	4	a.	a.	PROPN
ejpam-6226	400	5	al	al	PROPN
ejpam-6226	400	6	-	-	PUNCT
ejpam-6226	400	7	masarwah	masarwah	PROPN
ejpam-6226	400	8	,	,	PUNCT
ejpam-6226	400	9	m.	m.	NOUN
ejpam-6226	400	10	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	400	11	,	,	PUNCT
ejpam-6226	400	12	k.	k.	PROPN
ejpam-6226	400	13	alnefaie	alnefaie	PROPN
ejpam-6226	400	14	,	,	PUNCT
ejpam-6226	400	15	and	and	CCONJ
ejpam-6226	400	16	m.	m.	NOUN
ejpam-6226	400	17	rajeshwari	rajeshwari	PROPN
ejpam-6226	400	18	.	.	PUNCT
ejpam-6226	401	1	fermatean	fermatean	PROPN
ejpam-6226	401	2	neutrosophic	neutrosophic	PROPN
ejpam-6226	401	3	ink	ink	NOUN
ejpam-6226	401	4	-	-	PUNCT
ejpam-6226	401	5	algebras	algebras	PROPN
ejpam-6226	401	6	.	.	PUNCT
ejpam-6226	402	1	european	european	PROPN
ejpam-6226	402	2	journal	journal	PROPN
ejpam-6226	402	3	of	of	ADP
ejpam-6226	402	4	pure	pure	ADJ
ejpam-6226	402	5	and	and	CCONJ
ejpam-6226	402	6	applied	applied	ADJ
ejpam-6226	402	7	mathematics	mathematic	NOUN
ejpam-6226	402	8	,	,	PUNCT
ejpam-6226	402	9	17(2):1113–1128	17(2):1113–1128	NUM
ejpam-6226	402	10	,	,	PUNCT
ejpam-6226	402	11	2024	2024	NUM
ejpam-6226	402	12	.	.	PUNCT
ejpam-6226	403	1	[	[	X
ejpam-6226	403	2	8	8	NUM
ejpam-6226	403	3	]	]	X
ejpam-6226	403	4	w.	w.	PROPN
ejpam-6226	403	5	f.	f.	PROPN
ejpam-6226	403	6	al	al	PROPN
ejpam-6226	403	7	-	-	PUNCT
ejpam-6226	403	8	omeri	omeri	ADJ
ejpam-6226	403	9	,	,	PUNCT
ejpam-6226	403	10	m.	m.	NOUN
ejpam-6226	403	11	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	403	12	,	,	PUNCT
ejpam-6226	403	13	and	and	CCONJ
ejpam-6226	403	14	m.	m.	NOUN
ejpam-6226	403	15	rajeshwari	rajeshwari	PROPN
ejpam-6226	403	16	.	.	PUNCT
ejpam-6226	404	1	translation	translation	NOUN
ejpam-6226	404	2	of	of	ADP
ejpam-6226	404	3	neutrosophic	neutrosophic	ADJ
ejpam-6226	404	4	ink	ink	NOUN
ejpam-6226	404	5	-	-	PUNCT
ejpam-6226	404	6	algebras	algebras	PROPN
ejpam-6226	404	7	.	.	PUNCT
ejpam-6226	404	8	neutrosophic	neutrosophic	ADJ
ejpam-6226	404	9	sets	set	NOUN
ejpam-6226	404	10	and	and	CCONJ
ejpam-6226	404	11	systems	system	NOUN
ejpam-6226	404	12	,	,	PUNCT
ejpam-6226	404	13	66:119–135	66:119–135	PROPN
ejpam-6226	404	14	,	,	PUNCT
ejpam-6226	404	15	2024	2024	NUM
ejpam-6226	404	16	.	.	PUNCT
ejpam-6226	405	1	[	[	X
ejpam-6226	405	2	9	9	NUM
ejpam-6226	405	3	]	]	PUNCT
ejpam-6226	405	4	m.	m.	NOUN
ejpam-6226	405	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	405	6	,	,	PUNCT
ejpam-6226	405	7	k.	k.	PROPN
ejpam-6226	405	8	indhira	indhira	PROPN
ejpam-6226	405	9	,	,	PUNCT
ejpam-6226	405	10	and	and	CCONJ
ejpam-6226	405	11	v.	v.	ADP
ejpam-6226	405	12	m.	m.	NOUN
ejpam-6226	405	13	chandrasekaran	chandrasekaran	VERB
ejpam-6226	405	14	.	.	PUNCT
ejpam-6226	406	1	direct	direct	ADJ
ejpam-6226	406	2	product	product	NOUN
ejpam-6226	406	3	of	of	ADP
ejpam-6226	406	4	neutrosophic	neutrosophic	ADJ
ejpam-6226	406	5	ink	ink	NOUN
ejpam-6226	406	6	-	-	PUNCT
ejpam-6226	406	7	algebras	algebras	PROPN
ejpam-6226	406	8	.	.	PUNCT
ejpam-6226	406	9	neutrosophic	neutrosophic	ADJ
ejpam-6226	406	10	sets	set	NOUN
ejpam-6226	406	11	and	and	CCONJ
ejpam-6226	406	12	systems	system	NOUN
ejpam-6226	406	13	,	,	PUNCT
ejpam-6226	406	14	38:227–234	38:227–234	NUM
ejpam-6226	406	15	,	,	PUNCT
ejpam-6226	406	16	2020	2020	NUM
ejpam-6226	406	17	.	.	PUNCT
ejpam-6226	407	1	[	[	X
ejpam-6226	407	2	10	10	NUM
ejpam-6226	407	3	]	]	X
ejpam-6226	407	4	l.	l.	PROPN
ejpam-6226	407	5	a.	a.	PROPN
ejpam-6226	407	6	zadeh	zadeh	PROPN
ejpam-6226	407	7	.	.	PUNCT
ejpam-6226	407	8	fuzzy	fuzzy	ADJ
ejpam-6226	407	9	sets	set	NOUN
ejpam-6226	407	10	.	.	PUNCT
ejpam-6226	408	1	information	information	NOUN
ejpam-6226	408	2	and	and	CCONJ
ejpam-6226	408	3	control	control	NOUN
ejpam-6226	408	4	,	,	PUNCT
ejpam-6226	408	5	8(3):338–353	8(3):338–353	NUM
ejpam-6226	408	6	,	,	PUNCT
ejpam-6226	408	7	1965	1965	NUM
ejpam-6226	408	8	.	.	PUNCT
ejpam-6226	409	1	[	[	X
ejpam-6226	409	2	11	11	NUM
ejpam-6226	409	3	]	]	X
ejpam-6226	409	4	y.	y.	PROPN
ejpam-6226	409	5	b.	b.	PROPN
ejpam-6226	409	6	jun	jun	PROPN
ejpam-6226	409	7	,	,	PUNCT
ejpam-6226	409	8	e.	e.	PROPN
ejpam-6226	409	9	h.	h.	PROPN
ejpam-6226	409	10	roh	roh	PROPN
ejpam-6226	409	11	,	,	PUNCT
ejpam-6226	409	12	and	and	CCONJ
ejpam-6226	409	13	s.	s.	PROPN
ejpam-6226	409	14	m.	m.	PROPN
ejpam-6226	409	15	mostafa	mostafa	PROPN
ejpam-6226	409	16	.	.	PUNCT
ejpam-6226	410	1	on	on	ADP
ejpam-6226	410	2	fuzzy	fuzzy	ADJ
ejpam-6226	410	3	implicative	implicative	ADJ
ejpam-6226	410	4	ideals	ideal	NOUN
ejpam-6226	410	5	of	of	ADP
ejpam-6226	410	6	bck	bck	NOUN
ejpam-6226	410	7	-	-	PUNCT
ejpam-6226	410	8	algebras	algebras	PROPN
ejpam-6226	410	9	.	.	PUNCT
ejpam-6226	411	1	soochow	soochow	PROPN
ejpam-6226	411	2	journal	journal	PROPN
ejpam-6226	411	3	of	of	ADP
ejpam-6226	411	4	mathematics	mathematic	NOUN
ejpam-6226	411	5	,	,	PUNCT
ejpam-6226	411	6	25(1):57–70	25(1):57–70	NUM
ejpam-6226	411	7	,	,	PUNCT
ejpam-6226	411	8	1999	1999	NUM
ejpam-6226	411	9	.	.	PUNCT
ejpam-6226	412	1	[	[	X
ejpam-6226	412	2	12	12	NUM
ejpam-6226	412	3	]	]	PUNCT
ejpam-6226	412	4	a.	a.	NOUN
ejpam-6226	412	5	paad	paad	NOUN
ejpam-6226	412	6	.	.	PUNCT
ejpam-6226	413	1	on	on	ADP
ejpam-6226	413	2	fuzzy	fuzzy	ADJ
ejpam-6226	413	3	implicative	implicative	ADJ
ejpam-6226	413	4	ideals	ideal	NOUN
ejpam-6226	413	5	in	in	ADP
ejpam-6226	413	6	bl	bl	NOUN
ejpam-6226	413	7	-	-	PUNCT
ejpam-6226	413	8	algebras	algebras	PROPN
ejpam-6226	413	9	.	.	PUNCT
ejpam-6226	414	1	journal	journal	PROPN
ejpam-6226	414	2	of	of	ADP
ejpam-6226	414	3	algebraic	algebraic	PROPN
ejpam-6226	414	4	hyperstructures	hyperstructure	NOUN
ejpam-6226	414	5	and	and	CCONJ
ejpam-6226	414	6	logical	logical	ADJ
ejpam-6226	414	7	algebras	algebra	NOUN
ejpam-6226	414	8	,	,	PUNCT
ejpam-6226	414	9	1(4):83–94	1(4):83–94	NUM
ejpam-6226	414	10	,	,	PUNCT
ejpam-6226	414	11	2020	2020	NUM
ejpam-6226	414	12	.	.	PUNCT
ejpam-6226	415	1	[	[	X
ejpam-6226	415	2	13	13	NUM
ejpam-6226	415	3	]	]	PUNCT
ejpam-6226	415	4	s.	s.	PROPN
ejpam-6226	415	5	sowmiya	sowmiya	PROPN
ejpam-6226	415	6	and	and	CCONJ
ejpam-6226	415	7	p.	p.	NOUN
ejpam-6226	415	8	jeyalakshmi	jeyalakshmi	PROPN
ejpam-6226	415	9	.	.	PUNCT
ejpam-6226	416	1	on	on	ADP
ejpam-6226	416	2	fuzzy	fuzzy	ADJ
ejpam-6226	416	3	implicative	implicative	ADJ
ejpam-6226	416	4	ideals	ideal	NOUN
ejpam-6226	416	5	in	in	ADP
ejpam-6226	416	6	z	z	PROPN
ejpam-6226	416	7	-	-	PUNCT
ejpam-6226	416	8	algebras	algebras	X
ejpam-6226	416	9	.	.	PUNCT
ejpam-6226	416	10	advances	advance	NOUN
ejpam-6226	416	11	and	and	CCONJ
ejpam-6226	416	12	applications	application	NOUN
ejpam-6226	416	13	in	in	ADP
ejpam-6226	416	14	mathematical	mathematical	ADJ
ejpam-6226	416	15	sciences	science	NOUN
ejpam-6226	416	16	,	,	PUNCT
ejpam-6226	416	17	21(10):5911–5922	21(10):5911–5922	NUM
ejpam-6226	416	18	,	,	PUNCT
ejpam-6226	416	19	2022	2022	NUM
ejpam-6226	416	20	.	.	PUNCT
ejpam-6226	417	1	[	[	X
ejpam-6226	417	2	14	14	NUM
ejpam-6226	417	3	]	]	PUNCT
ejpam-6226	417	4	k.	k.	PROPN
ejpam-6226	417	5	t.	t.	PROPN
ejpam-6226	417	6	atanassov	atanassov	PROPN
ejpam-6226	417	7	.	.	PUNCT
ejpam-6226	418	1	intuitionistic	intuitionistic	ADJ
ejpam-6226	418	2	fuzzy	fuzzy	ADJ
ejpam-6226	418	3	sets	set	NOUN
ejpam-6226	418	4	.	.	PUNCT
ejpam-6226	419	1	fuzzy	fuzzy	ADJ
ejpam-6226	419	2	sets	set	NOUN
ejpam-6226	419	3	and	and	CCONJ
ejpam-6226	419	4	systems	system	NOUN
ejpam-6226	419	5	,	,	PUNCT
ejpam-6226	419	6	20(1):87–96	20(1):87–96	NUM
ejpam-6226	419	7	,	,	PUNCT
ejpam-6226	419	8	1986	1986	NUM
ejpam-6226	419	9	.	.	PUNCT
ejpam-6226	420	1	[	[	X
ejpam-6226	420	2	15	15	NUM
ejpam-6226	420	3	]	]	X
ejpam-6226	420	4	b.	b.	PROPN
ejpam-6226	420	5	satyanarayana	satyanarayana	PROPN
ejpam-6226	420	6	,	,	PUNCT
ejpam-6226	420	7	l.	l.	PROPN
ejpam-6226	420	8	krishna	krishna	PROPN
ejpam-6226	420	9	,	,	PUNCT
ejpam-6226	420	10	and	and	CCONJ
ejpam-6226	420	11	r.	r.	PROPN
ejpam-6226	420	12	d.	d.	PROPN
ejpam-6226	420	13	prasad	prasad	PROPN
ejpam-6226	420	14	.	.	PUNCT
ejpam-6226	421	1	on	on	ADP
ejpam-6226	421	2	intuitionistic	intuitionistic	ADJ
ejpam-6226	421	3	fuzzy	fuzzy	ADJ
ejpam-6226	421	4	implicative	implicative	ADJ
ejpam-6226	421	5	hyper	hyper	ADJ
ejpam-6226	421	6	bck	bck	NOUN
ejpam-6226	421	7	-	-	PUNCT
ejpam-6226	421	8	ideals	ideal	NOUN
ejpam-6226	421	9	of	of	ADP
ejpam-6226	421	10	hyper	hyper	ADJ
ejpam-6226	421	11	bck	bck	NOUN
ejpam-6226	421	12	-	-	PUNCT
ejpam-6226	421	13	algebras	algebras	PROPN
ejpam-6226	421	14	.	.	PUNCT
ejpam-6226	422	1	international	international	ADJ
ejpam-6226	422	2	journal	journal	PROPN
ejpam-6226	422	3	of	of	ADP
ejpam-6226	422	4	mathematics	mathematics	PROPN
ejpam-6226	422	5	and	and	CCONJ
ejpam-6226	422	6	statistics	statistic	NOUN
ejpam-6226	422	7	invention	invention	NOUN
ejpam-6226	422	8	,	,	PUNCT
ejpam-6226	422	9	2(2):77–85	2(2):77–85	NUM
ejpam-6226	422	10	,	,	PUNCT
ejpam-6226	422	11	2014	2014	NUM
ejpam-6226	422	12	.	.	PUNCT
ejpam-6226	423	1	[	[	X
ejpam-6226	423	2	16	16	NUM
ejpam-6226	423	3	]	]	PUNCT
ejpam-6226	423	4	r.	r.	PROPN
ejpam-6226	423	5	d.	d.	PROPN
ejpam-6226	423	6	prasad	prasad	PROPN
ejpam-6226	423	7	,	,	PUNCT
ejpam-6226	423	8	l.	l.	PROPN
ejpam-6226	423	9	krishna	krishna	PROPN
ejpam-6226	423	10	,	,	PUNCT
ejpam-6226	423	11	and	and	CCONJ
ejpam-6226	423	12	b.	b.	PROPN
ejpam-6226	423	13	satyanarayana	satyanarayana	PROPN
ejpam-6226	423	14	.	.	PUNCT
ejpam-6226	424	1	on	on	ADP
ejpam-6226	424	2	interval	interval	NOUN
ejpam-6226	424	3	-	-	PUNCT
ejpam-6226	424	4	valued	value	VERB
ejpam-6226	424	5	intuitionistic	intuitionistic	ADJ
ejpam-6226	424	6	fuzzy	fuzzy	ADJ
ejpam-6226	424	7	(	(	PUNCT
ejpam-6226	424	8	implicative	implicative	ADJ
ejpam-6226	424	9	and	and	CCONJ
ejpam-6226	424	10	commutative	commutative	ADJ
ejpam-6226	424	11	)	)	PUNCT
ejpam-6226	424	12	ideals	ideal	NOUN
ejpam-6226	424	13	of	of	ADP
ejpam-6226	424	14	bck	bck	NOUN
ejpam-6226	424	15	-	-	PUNCT
ejpam-6226	424	16	algebra	algebra	NOUN
ejpam-6226	424	17	.	.	PUNCT
ejpam-6226	425	1	advances	advance	NOUN
ejpam-6226	425	2	in	in	ADP
ejpam-6226	425	3	fuzzy	fuzzy	ADJ
ejpam-6226	425	4	mathematics	mathematic	NOUN
ejpam-6226	425	5	,	,	PUNCT
ejpam-6226	425	6	12(3):371–380	12(3):371–380	PROPN
ejpam-6226	425	7	,	,	PUNCT
ejpam-6226	425	8	2017	2017	NUM
ejpam-6226	425	9	.	.	PUNCT
ejpam-6226	426	1	[	[	X
ejpam-6226	426	2	17	17	NUM
ejpam-6226	426	3	]	]	X
ejpam-6226	426	4	b.	b.	PROPN
ejpam-6226	426	5	satyanarayana	satyanarayana	PROPN
ejpam-6226	426	6	,	,	PUNCT
ejpam-6226	426	7	v.	v.	PROPN
ejpam-6226	426	8	j.	j.	PROPN
ejpam-6226	426	9	sree	sree	PROPN
ejpam-6226	426	10	,	,	PUNCT
ejpam-6226	426	11	r.	r.	PROPN
ejpam-6226	426	12	d.	d.	PROPN
ejpam-6226	426	13	prasad	prasad	PROPN
ejpam-6226	426	14	,	,	PUNCT
ejpam-6226	426	15	and	and	CCONJ
ejpam-6226	426	16	u.	u.	PROPN
ejpam-6226	426	17	b.	b.	PROPN
ejpam-6226	426	18	madhavi	madhavi	PROPN
ejpam-6226	426	19	.	.	PUNCT
ejpam-6226	427	1	derivations	derivation	NOUN
ejpam-6226	427	2	of	of	ADP
ejpam-6226	427	3	intuitionistic	intuitionistic	ADJ
ejpam-6226	427	4	fuzzy	fuzzy	ADJ
ejpam-6226	427	5	implicative	implicative	ADJ
ejpam-6226	427	6	ideals	ideal	NOUN
ejpam-6226	427	7	of	of	ADP
ejpam-6226	427	8	bck	bck	NOUN
ejpam-6226	427	9	-	-	PUNCT
ejpam-6226	427	10	algebra	algebra	NOUN
ejpam-6226	427	11	.	.	PUNCT
ejpam-6226	428	1	advances	advance	NOUN
ejpam-6226	428	2	and	and	CCONJ
ejpam-6226	428	3	applications	application	NOUN
ejpam-6226	428	4	in	in	ADP
ejpam-6226	428	5	mathematical	mathematical	ADJ
ejpam-6226	428	6	sciences	science	NOUN
ejpam-6226	428	7	,	,	PUNCT
ejpam-6226	428	8	20(6):1147–1166	20(6):1147–1166	NUM
ejpam-6226	428	9	,	,	PUNCT
ejpam-6226	428	10	2021	2021	NUM
ejpam-6226	428	11	.	.	PUNCT
ejpam-6226	429	1	[	[	X
ejpam-6226	429	2	18	18	NUM
ejpam-6226	429	3	]	]	X
ejpam-6226	429	4	r.	r.	PROPN
ejpam-6226	429	5	rasuli	rasuli	PROPN
ejpam-6226	429	6	.	.	PUNCT
ejpam-6226	430	1	intuitionistic	intuitionistic	ADJ
ejpam-6226	430	2	fuzzy	fuzzy	ADJ
ejpam-6226	430	3	bci	bci	NOUN
ejpam-6226	430	4	-	-	PUNCT
ejpam-6226	430	5	algebras	algebras	X
ejpam-6226	430	6	(	(	PUNCT
ejpam-6226	430	7	implicative	implicative	ADJ
ejpam-6226	430	8	ideals	ideal	NOUN
ejpam-6226	430	9	,	,	PUNCT
ejpam-6226	430	10	closed	close	VERB
ejpam-6226	430	11	implicative	implicative	ADJ
ejpam-6226	430	12	ideals	ideal	NOUN
ejpam-6226	430	13	,	,	PUNCT
ejpam-6226	430	14	commutative	commutative	ADJ
ejpam-6226	430	15	ideals	ideal	NOUN
ejpam-6226	430	16	)	)	PUNCT
ejpam-6226	430	17	under	under	ADP
ejpam-6226	430	18	norms	norm	NOUN
ejpam-6226	430	19	.	.	PUNCT
ejpam-6226	431	1	mathematical	mathematical	ADJ
ejpam-6226	431	2	analysis	analysis	NOUN
ejpam-6226	431	3	and	and	CCONJ
ejpam-6226	431	4	its	its	PRON
ejpam-6226	431	5	contemporary	contemporary	ADJ
ejpam-6226	431	6	applications	application	NOUN
ejpam-6226	431	7	,	,	PUNCT
ejpam-6226	431	8	4(3):17–34	4(3):17–34	NUM
ejpam-6226	431	9	,	,	PUNCT
ejpam-6226	431	10	2022	2022	NUM
ejpam-6226	431	11	.	.	PUNCT
ejpam-6226	432	1	[	[	X
ejpam-6226	432	2	19	19	NUM
ejpam-6226	432	3	]	]	X
ejpam-6226	432	4	f.	f.	PROPN
ejpam-6226	432	5	smarandache	smarandache	PROPN
ejpam-6226	432	6	.	.	PUNCT
ejpam-6226	433	1	a	a	DET
ejpam-6226	433	2	unifying	unifying	ADJ
ejpam-6226	433	3	field	field	NOUN
ejpam-6226	433	4	in	in	ADP
ejpam-6226	433	5	logics	logic	NOUN
ejpam-6226	433	6	:	:	PUNCT
ejpam-6226	433	7	neutrosophic	neutrosophic	ADJ
ejpam-6226	433	8	logic	logic	NOUN
ejpam-6226	433	9	,	,	PUNCT
ejpam-6226	433	10	neutrosophy	neutrosophy	NOUN
ejpam-6226	433	11	,	,	PUNCT
ejpam-6226	433	12	neutrosophic	neutrosophic	ADJ
ejpam-6226	433	13	set	set	NOUN
ejpam-6226	433	14	,	,	PUNCT
ejpam-6226	433	15	neutrosophic	neutrosophic	ADJ
ejpam-6226	433	16	probability	probability	NOUN
ejpam-6226	433	17	.	.	PUNCT
ejpam-6226	434	1	american	american	PROPN
ejpam-6226	434	2	research	research	PROPN
ejpam-6226	434	3	press	press	PROPN
ejpam-6226	434	4	,	,	PUNCT
ejpam-6226	434	5	rehoboth	rehoboth	PROPN
ejpam-6226	434	6	,	,	PUNCT
ejpam-6226	434	7	new	new	PROPN
ejpam-6226	434	8	mexico	mexico	PROPN
ejpam-6226	434	9	,	,	PUNCT
ejpam-6226	434	10	1999	1999	NUM
ejpam-6226	434	11	.	.	PUNCT
ejpam-6226	435	1	[	[	X
ejpam-6226	435	2	20	20	NUM
ejpam-6226	435	3	]	]	X
ejpam-6226	435	4	y.	y.	PROPN
ejpam-6226	435	5	b.	b.	PROPN
ejpam-6226	435	6	jun	jun	PROPN
ejpam-6226	435	7	and	and	CCONJ
ejpam-6226	435	8	e.	e.	PROPN
ejpam-6226	435	9	h.	h.	PROPN
ejpam-6226	435	10	roh	roh	PROPN
ejpam-6226	435	11	.	.	PUNCT
ejpam-6226	436	1	mbj	mbj	PROPN
ejpam-6226	436	2	-	-	PUNCT
ejpam-6226	436	3	neutrosophic	neutrosophic	ADJ
ejpam-6226	436	4	ideals	ideal	NOUN
ejpam-6226	436	5	of	of	ADP
ejpam-6226	436	6	bck	bck	PROPN
ejpam-6226	436	7	/	/	SYM
ejpam-6226	436	8	bci	bci	NOUN
ejpam-6226	436	9	-	-	PUNCT
ejpam-6226	436	10	algebras	algebras	X
ejpam-6226	436	11	.	.	PUNCT
ejpam-6226	437	1	open	open	ADJ
ejpam-6226	437	2	mathematics	mathematic	NOUN
ejpam-6226	437	3	,	,	PUNCT
ejpam-6226	437	4	17(1):588–601	17(1):588–601	NUM
ejpam-6226	437	5	,	,	PUNCT
ejpam-6226	437	6	2019	2019	NUM
ejpam-6226	437	7	.	.	PUNCT
ejpam-6226	438	1	[	[	X
ejpam-6226	438	2	21	21	NUM
ejpam-6226	438	3	]	]	X
ejpam-6226	438	4	r.	r.	PROPN
ejpam-6226	438	5	a.	a.	PROPN
ejpam-6226	438	6	borzooei	borzooei	PROPN
ejpam-6226	438	7	,	,	PUNCT
ejpam-6226	438	8	m.	m.	NOUN
ejpam-6226	438	9	m.	m.	PROPN
ejpam-6226	438	10	takallo	takallo	PROPN
ejpam-6226	438	11	,	,	PUNCT
ejpam-6226	438	12	f.	f.	PROPN
ejpam-6226	438	13	smarandache	smarandache	PROPN
ejpam-6226	438	14	,	,	PUNCT
ejpam-6226	438	15	and	and	CCONJ
ejpam-6226	438	16	y.	y.	PROPN
ejpam-6226	438	17	b.	b.	PROPN
ejpam-6226	438	18	jun	jun	PROPN
ejpam-6226	438	19	.	.	PROPN
ejpam-6226	438	20	positive	positive	ADJ
ejpam-6226	438	21	implicative	implicative	ADJ
ejpam-6226	438	22	bmbj	bmbj	ADJ
ejpam-6226	438	23	-	-	PUNCT
ejpam-6226	438	24	neutrosophic	neutrosophic	ADJ
ejpam-6226	438	25	ideals	ideal	NOUN
ejpam-6226	438	26	in	in	ADP
ejpam-6226	438	27	bck	bck	NOUN
ejpam-6226	438	28	-	-	PUNCT
ejpam-6226	438	29	algebras	algebras	PROPN
ejpam-6226	438	30	.	.	PUNCT
ejpam-6226	438	31	neutrosophic	neutrosophic	ADJ
ejpam-6226	438	32	sets	set	NOUN
ejpam-6226	438	33	and	and	CCONJ
ejpam-6226	438	34	systems	system	NOUN
ejpam-6226	438	35	,	,	PUNCT
ejpam-6226	438	36	23:126	23:126	NUM
ejpam-6226	438	37	–	–	PUNCT
ejpam-6226	438	38	141	141	NUM
ejpam-6226	438	39	,	,	PUNCT
ejpam-6226	438	40	2018	2018	NUM
ejpam-6226	438	41	.	.	PUNCT
ejpam-6226	439	1	[	[	X
ejpam-6226	439	2	22	22	NUM
ejpam-6226	439	3	]	]	PUNCT
ejpam-6226	439	4	h.	h.	PROPN
ejpam-6226	439	5	bordbar	bordbar	PROPN
ejpam-6226	439	6	,	,	PUNCT
ejpam-6226	439	7	x.	x.	PROPN
ejpam-6226	439	8	l.	l.	PROPN
ejpam-6226	439	9	xin	xin	PROPN
ejpam-6226	439	10	,	,	PUNCT
ejpam-6226	439	11	r.	r.	PROPN
ejpam-6226	439	12	a.	a.	PROPN
ejpam-6226	439	13	borzooei	borzooei	PROPN
ejpam-6226	439	14	,	,	PUNCT
ejpam-6226	439	15	and	and	CCONJ
ejpam-6226	439	16	y.	y.	PROPN
ejpam-6226	439	17	b.	b.	PROPN
ejpam-6226	440	1	jun	jun	PROPN
ejpam-6226	440	2	.	.	PROPN
ejpam-6226	441	1	positive	positive	ADJ
ejpam-6226	441	2	implicative	implicative	ADJ
ejpam-6226	441	3	ideals	ideal	NOUN
ejpam-6226	441	4	of	of	ADP
ejpam-6226	441	5	bck	bck	NOUN
ejpam-6226	441	6	-	-	PUNCT
ejpam-6226	441	7	algebras	algebras	PROPN
ejpam-6226	441	8	based	base	VERB
ejpam-6226	441	9	on	on	ADP
ejpam-6226	441	10	neutrosophic	neutrosophic	ADJ
ejpam-6226	441	11	sets	set	NOUN
ejpam-6226	441	12	and	and	CCONJ
ejpam-6226	441	13	falling	fall	VERB
ejpam-6226	441	14	shadows	shadow	NOUN
ejpam-6226	441	15	.	.	PUNCT
ejpam-6226	442	1	neutrosophic	neutrosophic	ADJ
ejpam-6226	442	2	sets	set	NOUN
ejpam-6226	442	3	and	and	CCONJ
ejpam-6226	442	4	systems	system	NOUN
ejpam-6226	442	5	,	,	PUNCT
ejpam-6226	442	6	48:9–30	48:9–30	NUM
ejpam-6226	442	7	,	,	PUNCT
ejpam-6226	442	8	2022	2022	NUM
ejpam-6226	442	9	.	.	PUNCT
ejpam-6226	443	1	r.	r.	PROPN
ejpam-6226	443	2	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6226	443	3	et	et	PROPN
ejpam-6226	443	4	al	al	PROPN
ejpam-6226	443	5	.	.	PUNCT
ejpam-6226	443	6	/	/	SYM
ejpam-6226	443	7	eur	eur	PROPN
ejpam-6226	443	8	.	.	PUNCT
ejpam-6226	444	1	j.	j.	PROPN
ejpam-6226	444	2	pure	pure	PROPN
ejpam-6226	444	3	appl	appl	PROPN
ejpam-6226	444	4	.	.	PROPN
ejpam-6226	444	5	math	math	PROPN
ejpam-6226	444	6	,	,	PUNCT
ejpam-6226	444	7	18	18	NUM
ejpam-6226	444	8	(	(	PUNCT
ejpam-6226	444	9	3	3	NUM
ejpam-6226	444	10	)	)	PUNCT
ejpam-6226	444	11	(	(	PUNCT
ejpam-6226	444	12	2025	2025	NUM
ejpam-6226	444	13	)	)	PUNCT
ejpam-6226	444	14	,	,	PUNCT
ejpam-6226	444	15	6226	6226	NUM
ejpam-6226	444	16	19	19	NUM
ejpam-6226	444	17	of	of	ADP
ejpam-6226	444	18	19	19	NUM
ejpam-6226	445	1	[	[	SYM
ejpam-6226	445	2	23	23	NUM
ejpam-6226	445	3	]	]	PUNCT
ejpam-6226	445	4	b.	b.	PROPN
ejpam-6226	445	5	satyanarayana	satyanarayana	PROPN
ejpam-6226	445	6	and	and	CCONJ
ejpam-6226	445	7	s.	s.	PROPN
ejpam-6226	445	8	baji	baji	PROPN
ejpam-6226	445	9	.	.	PUNCT
ejpam-6226	446	1	positive	positive	ADJ
ejpam-6226	446	2	implicative	implicative	ADJ
ejpam-6226	446	3	,	,	PUNCT
ejpam-6226	446	4	implicative	implicative	ADJ
ejpam-6226	446	5	,	,	PUNCT
ejpam-6226	446	6	and	and	CCONJ
ejpam-6226	446	7	commutative	commutative	ADJ
ejpam-6226	446	8	sbneutrosophic	sbneutrosophic	ADJ
ejpam-6226	446	9	ideals	ideal	NOUN
ejpam-6226	446	10	in	in	ADP
ejpam-6226	446	11	bck	bck	PROPN
ejpam-6226	446	12	/	/	SYM
ejpam-6226	446	13	bci	bci	NOUN
ejpam-6226	446	14	-	-	PUNCT
ejpam-6226	446	15	algebras	algebra	NOUN
ejpam-6226	446	16	.	.	PUNCT
ejpam-6226	447	1	iaeng	iaeng	PROPN
ejpam-6226	447	2	international	international	PROPN
ejpam-6226	447	3	journal	journal	PROPN
ejpam-6226	447	4	of	of	ADP
ejpam-6226	447	5	applied	apply	VERB
ejpam-6226	447	6	mathematics	mathematic	NOUN
ejpam-6226	447	7	,	,	PUNCT
ejpam-6226	447	8	54(5):815–830	54(5):815–830	PROPN
ejpam-6226	447	9	,	,	PUNCT
ejpam-6226	447	10	2024	2024	NUM
ejpam-6226	447	11	.	.	PUNCT
ejpam-6226	448	1	[	[	X
ejpam-6226	448	2	24	24	NUM
ejpam-6226	448	3	]	]	PUNCT
ejpam-6226	448	4	m.	m.	NOUN
ejpam-6226	448	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	448	6	,	,	PUNCT
ejpam-6226	448	7	k.	k.	PROPN
ejpam-6226	448	8	indhira	indhira	PROPN
ejpam-6226	448	9	,	,	PUNCT
ejpam-6226	448	10	and	and	CCONJ
ejpam-6226	448	11	v.	v.	ADP
ejpam-6226	448	12	m.	m.	NOUN
ejpam-6226	448	13	chandrasekaran	chandrasekaran	VERB
ejpam-6226	448	14	.	.	PUNCT
ejpam-6226	449	1	introduction	introduction	NOUN
ejpam-6226	449	2	on	on	ADP
ejpam-6226	449	3	inkalgebras	inkalgebra	NOUN
ejpam-6226	449	4	.	.	PUNCT
ejpam-6226	450	1	international	international	ADJ
ejpam-6226	450	2	journal	journal	NOUN
ejpam-6226	450	3	of	of	ADP
ejpam-6226	450	4	pure	pure	ADJ
ejpam-6226	450	5	and	and	CCONJ
ejpam-6226	450	6	applied	applied	ADJ
ejpam-6226	450	7	mathematics	mathematic	NOUN
ejpam-6226	450	8	,	,	PUNCT
ejpam-6226	450	9	115(9):1–10	115(9):1–10	NUM
ejpam-6226	450	10	,	,	PUNCT
ejpam-6226	450	11	2017	2017	NUM
ejpam-6226	450	12	.	.	PUNCT
ejpam-6226	451	1	[	[	X
ejpam-6226	451	2	25	25	NUM
ejpam-6226	451	3	]	]	PUNCT
ejpam-6226	451	4	m.	m.	NOUN
ejpam-6226	451	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	451	6	,	,	PUNCT
ejpam-6226	451	7	k.	k.	PROPN
ejpam-6226	451	8	indhira	indhira	PROPN
ejpam-6226	451	9	,	,	PUNCT
ejpam-6226	451	10	and	and	CCONJ
ejpam-6226	451	11	v.	v.	ADP
ejpam-6226	451	12	m.	m.	NOUN
ejpam-6226	451	13	chandrasekaran	chandrasekaran	VERB
ejpam-6226	451	14	.	.	PUNCT
ejpam-6226	452	1	fuzzy	fuzzy	ADJ
ejpam-6226	452	2	subalgebras	subalgebra	NOUN
ejpam-6226	452	3	and	and	CCONJ
ejpam-6226	452	4	fuzzy	fuzzy	ADJ
ejpam-6226	452	5	k	k	NOUN
ejpam-6226	452	6	-	-	NOUN
ejpam-6226	452	7	ideals	ideal	NOUN
ejpam-6226	452	8	in	in	ADP
ejpam-6226	452	9	ink	ink	NOUN
ejpam-6226	452	10	-	-	PUNCT
ejpam-6226	452	11	algebras	algebras	PROPN
ejpam-6226	452	12	.	.	PUNCT
ejpam-6226	453	1	international	international	ADJ
ejpam-6226	453	2	journal	journal	PROPN
ejpam-6226	453	3	of	of	ADP
ejpam-6226	453	4	pure	pure	ADJ
ejpam-6226	453	5	and	and	CCONJ
ejpam-6226	453	6	applied	applied	ADJ
ejpam-6226	453	7	mathematics	mathematic	NOUN
ejpam-6226	453	8	,	,	PUNCT
ejpam-6226	453	9	113(6):47–55	113(6):47–55	NUM
ejpam-6226	453	10	,	,	PUNCT
ejpam-6226	453	11	2017	2017	NUM
ejpam-6226	453	12	.	.	PUNCT
ejpam-6226	454	1	[	[	X
ejpam-6226	454	2	26	26	NUM
ejpam-6226	454	3	]	]	PUNCT
ejpam-6226	454	4	m.	m.	NOUN
ejpam-6226	454	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6226	454	6	,	,	PUNCT
ejpam-6226	454	7	k.	k.	PROPN
ejpam-6226	454	8	indhira	indhira	PROPN
ejpam-6226	454	9	,	,	PUNCT
ejpam-6226	454	10	and	and	CCONJ
ejpam-6226	454	11	v.	v.	ADP
ejpam-6226	454	12	m.	m.	NOUN
ejpam-6226	454	13	chandrasekaran	chandrasekaran	VERB
ejpam-6226	454	14	.	.	PUNCT
ejpam-6226	455	1	neutrosophic	neutrosophic	PROPN
ejpam-6226	455	2	set	set	VERB
ejpam-6226	455	3	in	in	ADP
ejpam-6226	455	4	inkalgebra	inkalgebra	NOUN
ejpam-6226	455	5	.	.	PUNCT
ejpam-6226	456	1	advances	advance	NOUN
ejpam-6226	456	2	in	in	ADP
ejpam-6226	456	3	mathematics	mathematic	NOUN
ejpam-6226	456	4	:	:	PUNCT
ejpam-6226	456	5	scientific	scientific	ADJ
ejpam-6226	456	6	journal	journal	NOUN
ejpam-6226	456	7	,	,	PUNCT
ejpam-6226	456	8	9(7):4345–4352	9(7):4345–4352	NUM
ejpam-6226	456	9	,	,	PUNCT
ejpam-6226	456	10	2020	2020	NUM
ejpam-6226	456	11	.	.	PUNCT
ejpam-6226	457	1	[	[	X
ejpam-6226	457	2	27	27	NUM
ejpam-6226	457	3	]	]	PUNCT
ejpam-6226	457	4	a.	a.	NOUN
ejpam-6226	457	5	alsubie	alsubie	PROPN
ejpam-6226	457	6	and	and	CCONJ
ejpam-6226	457	7	a.	a.	PROPN
ejpam-6226	457	8	al	al	PROPN
ejpam-6226	457	9	-	-	PROPN
ejpam-6226	457	10	masarwah	masarwah	PROPN
ejpam-6226	457	11	.	.	PUNCT
ejpam-6226	458	1	mbj	mbj	PROPN
ejpam-6226	458	2	-	-	PUNCT
ejpam-6226	458	3	neutrosophic	neutrosophic	ADJ
ejpam-6226	458	4	hyper	hyper	ADJ
ejpam-6226	458	5	bck	bck	NOUN
ejpam-6226	458	6	-	-	PUNCT
ejpam-6226	458	7	ideals	ideal	NOUN
ejpam-6226	458	8	in	in	ADP
ejpam-6226	458	9	hyper	hyper	NOUN
ejpam-6226	458	10	bckalgebras	bckalgebra	NOUN
ejpam-6226	458	11	.	.	PUNCT
ejpam-6226	459	1	aims	aim	VERB
ejpam-6226	459	2	mathematics	mathematic	NOUN
ejpam-6226	459	3	,	,	PUNCT
ejpam-6226	459	4	6(6):6107–6121	6(6):6107–6121	PROPN
ejpam-6226	459	5	,	,	PUNCT
ejpam-6226	459	6	2021	2021	NUM
ejpam-6226	459	7	.	.	PUNCT
ejpam-6226	460	1	[	[	X
ejpam-6226	460	2	28	28	NUM
ejpam-6226	460	3	]	]	X
ejpam-6226	460	4	a.	a.	PROPN
ejpam-6226	460	5	al	al	PROPN
ejpam-6226	460	6	-	-	PROPN
ejpam-6226	460	7	masarwah	masarwah	PROPN
ejpam-6226	460	8	and	and	CCONJ
ejpam-6226	460	9	m.	m.	PROPN
ejpam-6226	460	10	a.	a.	PROPN
ejpam-6226	460	11	qamar	qamar	PROPN
ejpam-6226	460	12	.	.	PUNCT
ejpam-6226	461	1	certain	certain	ADJ
ejpam-6226	461	2	types	type	NOUN
ejpam-6226	461	3	of	of	ADP
ejpam-6226	461	4	fuzzy	fuzzy	ADJ
ejpam-6226	461	5	soft	soft	ADJ
ejpam-6226	461	6	graphs	graph	NOUN
ejpam-6226	461	7	.	.	PUNCT
ejpam-6226	462	1	new	new	ADJ
ejpam-6226	462	2	mathematics	mathematic	NOUN
ejpam-6226	462	3	and	and	CCONJ
ejpam-6226	462	4	natural	natural	ADJ
ejpam-6226	462	5	computation	computation	NOUN
ejpam-6226	462	6	,	,	PUNCT
ejpam-6226	462	7	14(2):145–156	14(2):145–156	NUM
ejpam-6226	462	8	,	,	PUNCT
ejpam-6226	462	9	2018	2018	NUM
ejpam-6226	462	10	.	.	PUNCT