id	sid	tid	token	lemma	pos
ejpam-2332	1	1	compile	compile	NOUN
ejpam-2332	1	2	/	/	SYM
ejpam-2332	1	3	output.dvi	output.dvi	NOUN
ejpam-2332	1	4	european	european	ADJ
ejpam-2332	1	5	journal	journal	NOUN
ejpam-2332	1	6	of	of	ADP
ejpam-2332	1	7	pure	pure	ADJ
ejpam-2332	1	8	and	and	CCONJ
ejpam-2332	1	9	applied	apply	VERB
ejpam-2332	1	10	mathematics	mathematic	NOUN
ejpam-2332	1	11	vol	vol	NOUN
ejpam-2332	1	12	.	.	PROPN
ejpam-2332	1	13	8	8	NUM
ejpam-2332	1	14	,	,	PUNCT
ejpam-2332	1	15	no	no	INTJ
ejpam-2332	1	16	.	.	NOUN
ejpam-2332	1	17	2	2	NUM
ejpam-2332	1	18	,	,	PUNCT
ejpam-2332	1	19	2015	2015	NUM
ejpam-2332	1	20	,	,	PUNCT
ejpam-2332	1	21	153	153	NUM
ejpam-2332	1	22	-	-	SYM
ejpam-2332	1	23	171	171	NUM
ejpam-2332	1	24	issn	issn	PROPN
ejpam-2332	1	25	1307	1307	NUM
ejpam-2332	1	26	-	-	SYM
ejpam-2332	1	27	5543	5543	NUM
ejpam-2332	1	28	–	–	PUNCT
ejpam-2332	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2332	1	30	solving	solve	VERB
ejpam-2332	1	31	bi	bi	ADJ
ejpam-2332	1	32	-	-	ADJ
ejpam-2332	1	33	matrix	matrix	NOUN
ejpam-2332	1	34	games	game	NOUN
ejpam-2332	1	35	with	with	ADP
ejpam-2332	1	36	pay	pay	NOUN
ejpam-2332	1	37	-	-	PUNCT
ejpam-2332	1	38	offs	off	NOUN
ejpam-2332	1	39	of	of	ADP
ejpam-2332	1	40	triangular	triangular	NOUN
ejpam-2332	1	41	intuitionistic	intuitionistic	ADJ
ejpam-2332	1	42	fuzzy	fuzzy	ADJ
ejpam-2332	1	43	numbers	number	NOUN
ejpam-2332	1	44	mijanur	mijanur	VERB
ejpam-2332	1	45	rahaman	rahaman	NOUN
ejpam-2332	1	46	seikh1∗	seikh1∗	PROPN
ejpam-2332	1	47	,	,	PUNCT
ejpam-2332	1	48	prasun	prasun	PROPN
ejpam-2332	1	49	kumar	kumar	PROPN
ejpam-2332	1	50	nayak	nayak	PROPN
ejpam-2332	1	51	2	2	NUM
ejpam-2332	1	52	,	,	PUNCT
ejpam-2332	1	53	madhumangal	madhumangal	ADJ
ejpam-2332	1	54	pal	pal	ADJ
ejpam-2332	1	55	3	3	NUM
ejpam-2332	1	56	1	1	NUM
ejpam-2332	1	57	department	department	NOUN
ejpam-2332	1	58	of	of	ADP
ejpam-2332	1	59	mathematics	mathematic	NOUN
ejpam-2332	1	60	,	,	PUNCT
ejpam-2332	1	61	kazi	kazi	PROPN
ejpam-2332	1	62	nazrul	nazrul	PROPN
ejpam-2332	1	63	university	university	PROPN
ejpam-2332	1	64	,	,	PUNCT
ejpam-2332	1	65	asansol-713	asansol-713	NOUN
ejpam-2332	1	66	303	303	NUM
ejpam-2332	1	67	,	,	PUNCT
ejpam-2332	1	68	india	india	PROPN
ejpam-2332	1	69	2	2	NUM
ejpam-2332	1	70	department	department	NOUN
ejpam-2332	1	71	of	of	ADP
ejpam-2332	1	72	mathematics	mathematic	NOUN
ejpam-2332	1	73	,	,	PUNCT
ejpam-2332	1	74	midnapore	midnapore	ADJ
ejpam-2332	1	75	college	college	NOUN
ejpam-2332	1	76	,	,	PUNCT
ejpam-2332	1	77	midnapore-721	midnapore-721	ADJ
ejpam-2332	1	78	101	101	NUM
ejpam-2332	1	79	,	,	PUNCT
ejpam-2332	1	80	india	india	PROPN
ejpam-2332	1	81	3	3	PROPN
ejpam-2332	1	82	department	department	NOUN
ejpam-2332	1	83	of	of	ADP
ejpam-2332	1	84	applied	apply	VERB
ejpam-2332	1	85	mathematics	mathematic	NOUN
ejpam-2332	1	86	with	with	ADP
ejpam-2332	1	87	oceanology	oceanology	NOUN
ejpam-2332	1	88	and	and	CCONJ
ejpam-2332	1	89	computer	computer	NOUN
ejpam-2332	1	90	programming	programming	NOUN
ejpam-2332	1	91	,	,	PUNCT
ejpam-2332	1	92	vidyasagar	vidyasagar	NOUN
ejpam-2332	1	93	university	university	NOUN
ejpam-2332	1	94	,	,	PUNCT
ejpam-2332	1	95	midnapore-721	midnapore-721	ADJ
ejpam-2332	1	96	102	102	NUM
ejpam-2332	1	97	,	,	PUNCT
ejpam-2332	1	98	india	india	PROPN
ejpam-2332	1	99	abstract	abstract	NOUN
ejpam-2332	1	100	.	.	PUNCT
ejpam-2332	2	1	this	this	DET
ejpam-2332	2	2	paper	paper	NOUN
ejpam-2332	2	3	presents	present	VERB
ejpam-2332	2	4	a	a	DET
ejpam-2332	2	5	solution	solution	NOUN
ejpam-2332	2	6	methodology	methodology	NOUN
ejpam-2332	2	7	for	for	ADP
ejpam-2332	2	8	bi	bi	ADJ
ejpam-2332	2	9	-	-	ADJ
ejpam-2332	2	10	matrix	matrix	NOUN
ejpam-2332	2	11	games	game	NOUN
ejpam-2332	2	12	in	in	ADP
ejpam-2332	2	13	which	which	PRON
ejpam-2332	2	14	pay	pay	VERB
ejpam-2332	2	15	-	-	PUNCT
ejpam-2332	2	16	off	off	ADP
ejpam-2332	2	17	matrices	matrix	NOUN
ejpam-2332	2	18	are	be	AUX
ejpam-2332	2	19	represented	represent	VERB
ejpam-2332	2	20	by	by	ADP
ejpam-2332	2	21	triangular	triangular	NOUN
ejpam-2332	2	22	intuitionistic	intuitionistic	ADJ
ejpam-2332	2	23	fuzzy	fuzzy	ADJ
ejpam-2332	2	24	numbers	number	NOUN
ejpam-2332	2	25	(	(	PUNCT
ejpam-2332	2	26	tifns	tifns	NOUN
ejpam-2332	2	27	)	)	PUNCT
ejpam-2332	2	28	.	.	PUNCT
ejpam-2332	3	1	in	in	ADP
ejpam-2332	3	2	this	this	DET
ejpam-2332	3	3	methodology	methodology	NOUN
ejpam-2332	3	4	,	,	PUNCT
ejpam-2332	3	5	a	a	DET
ejpam-2332	3	6	new	new	ADJ
ejpam-2332	3	7	ranking	ranking	NOUN
ejpam-2332	3	8	function	function	NOUN
ejpam-2332	3	9	is	be	AUX
ejpam-2332	3	10	defined	define	VERB
ejpam-2332	3	11	to	to	PART
ejpam-2332	3	12	defuzzify	defuzzify	VERB
ejpam-2332	3	13	the	the	DET
ejpam-2332	3	14	tifns	tifns	NOUN
ejpam-2332	3	15	.	.	PUNCT
ejpam-2332	4	1	a	a	DET
ejpam-2332	4	2	non	non	ADJ
ejpam-2332	4	3	-	-	ADJ
ejpam-2332	4	4	linear	linear	ADJ
ejpam-2332	4	5	intuitionistic	intuitionistic	ADJ
ejpam-2332	4	6	fuzzy	fuzzy	ADJ
ejpam-2332	4	7	(	(	PUNCT
ejpam-2332	4	8	i	i	NOUN
ejpam-2332	4	9	-	-	PUNCT
ejpam-2332	4	10	fuzzy	fuzzy	ADJ
ejpam-2332	4	11	)	)	PUNCT
ejpam-2332	4	12	programming	programming	NOUN
ejpam-2332	4	13	problem	problem	NOUN
ejpam-2332	4	14	is	be	AUX
ejpam-2332	4	15	constructed	construct	VERB
ejpam-2332	4	16	to	to	PART
ejpam-2332	4	17	conceptualize	conceptualize	VERB
ejpam-2332	4	18	the	the	DET
ejpam-2332	4	19	term	term	NOUN
ejpam-2332	4	20	equilibrium	equilibrium	NOUN
ejpam-2332	4	21	solution	solution	NOUN
ejpam-2332	4	22	for	for	ADP
ejpam-2332	4	23	such	such	ADJ
ejpam-2332	4	24	type	type	NOUN
ejpam-2332	4	25	of	of	ADP
ejpam-2332	4	26	bi	bi	ADJ
ejpam-2332	4	27	-	-	ADJ
ejpam-2332	4	28	matrix	matrix	NOUN
ejpam-2332	4	29	games	game	NOUN
ejpam-2332	4	30	.	.	PUNCT
ejpam-2332	5	1	it	it	PRON
ejpam-2332	5	2	is	be	AUX
ejpam-2332	5	3	shown	show	VERB
ejpam-2332	5	4	that	that	SCONJ
ejpam-2332	5	5	this	this	DET
ejpam-2332	5	6	non	non	ADJ
ejpam-2332	5	7	-	-	ADJ
ejpam-2332	5	8	linear	linear	ADJ
ejpam-2332	5	9	i	i	ADJ
ejpam-2332	5	10	-	-	PUNCT
ejpam-2332	5	11	fuzzy	fuzzy	ADJ
ejpam-2332	5	12	programming	programming	NOUN
ejpam-2332	5	13	problem	problem	NOUN
ejpam-2332	5	14	is	be	AUX
ejpam-2332	5	15	a	a	DET
ejpam-2332	5	16	generalization	generalization	NOUN
ejpam-2332	5	17	of	of	ADP
ejpam-2332	5	18	fuzzy	fuzzy	ADJ
ejpam-2332	5	19	non	non	ADJ
ejpam-2332	5	20	-	-	ADJ
ejpam-2332	5	21	linear	linear	ADJ
ejpam-2332	5	22	programming	programming	NOUN
ejpam-2332	5	23	problem	problem	NOUN
ejpam-2332	5	24	.	.	PUNCT
ejpam-2332	6	1	finally	finally	ADV
ejpam-2332	6	2	,	,	PUNCT
ejpam-2332	6	3	based	base	VERB
ejpam-2332	6	4	on	on	ADP
ejpam-2332	6	5	the	the	DET
ejpam-2332	6	6	ranking	ranking	NOUN
ejpam-2332	6	7	function	function	NOUN
ejpam-2332	6	8	the	the	DET
ejpam-2332	6	9	problem	problem	NOUN
ejpam-2332	6	10	is	be	AUX
ejpam-2332	6	11	transformed	transform	VERB
ejpam-2332	6	12	into	into	ADP
ejpam-2332	6	13	a	a	DET
ejpam-2332	6	14	crisp	crisp	ADJ
ejpam-2332	6	15	non	non	ADJ
ejpam-2332	6	16	-	-	ADJ
ejpam-2332	6	17	linear	linear	ADJ
ejpam-2332	6	18	programming	programming	NOUN
ejpam-2332	6	19	problem	problem	NOUN
ejpam-2332	6	20	which	which	PRON
ejpam-2332	6	21	can	can	AUX
ejpam-2332	6	22	be	be	AUX
ejpam-2332	6	23	solved	solve	VERB
ejpam-2332	6	24	to	to	PART
ejpam-2332	6	25	obtain	obtain	VERB
ejpam-2332	6	26	the	the	DET
ejpam-2332	6	27	equilibrium	equilibrium	NOUN
ejpam-2332	6	28	solution	solution	NOUN
ejpam-2332	6	29	for	for	ADP
ejpam-2332	6	30	each	each	DET
ejpam-2332	6	31	player	player	NOUN
ejpam-2332	6	32	.	.	PUNCT
ejpam-2332	7	1	numerical	numerical	PROPN
ejpam-2332	7	2	simulation	simulation	PROPN
ejpam-2332	7	3	is	be	AUX
ejpam-2332	7	4	provided	provide	VERB
ejpam-2332	7	5	to	to	PART
ejpam-2332	7	6	show	show	VERB
ejpam-2332	7	7	the	the	DET
ejpam-2332	7	8	validity	validity	NOUN
ejpam-2332	7	9	and	and	CCONJ
ejpam-2332	7	10	applicability	applicability	NOUN
ejpam-2332	7	11	of	of	ADP
ejpam-2332	7	12	this	this	DET
ejpam-2332	7	13	methodology	methodology	NOUN
ejpam-2332	7	14	.	.	PUNCT
ejpam-2332	8	1	2010	2010	NUM
ejpam-2332	8	2	mathematics	mathematic	NOUN
ejpam-2332	8	3	subject	subject	NOUN
ejpam-2332	8	4	classifications	classification	NOUN
ejpam-2332	8	5	:	:	PUNCT
ejpam-2332	8	6	91a05	91a05	NUM
ejpam-2332	8	7	,	,	PUNCT
ejpam-2332	8	8	91a80	91a80	NUM
ejpam-2332	8	9	key	key	ADJ
ejpam-2332	8	10	words	word	NOUN
ejpam-2332	8	11	and	and	CCONJ
ejpam-2332	8	12	phrases	phrase	NOUN
ejpam-2332	8	13	:	:	PUNCT
ejpam-2332	8	14	bi	bi	ADJ
ejpam-2332	8	15	-	-	ADJ
ejpam-2332	8	16	matrix	matrix	NOUN
ejpam-2332	8	17	game	game	NOUN
ejpam-2332	8	18	,	,	PUNCT
ejpam-2332	8	19	triangular	triangular	NOUN
ejpam-2332	8	20	intuitionistic	intuitionistic	ADJ
ejpam-2332	8	21	fuzzy	fuzzy	ADJ
ejpam-2332	8	22	numbers	number	NOUN
ejpam-2332	8	23	,	,	PUNCT
ejpam-2332	8	24	mathematical	mathematical	ADJ
ejpam-2332	8	25	programming	programming	NOUN
ejpam-2332	8	26	,	,	PUNCT
ejpam-2332	8	27	ranking	rank	VERB
ejpam-2332	8	28	function	function	NOUN
ejpam-2332	8	29	.	.	PUNCT
ejpam-2332	9	1	1	1	X
ejpam-2332	9	2	.	.	X
ejpam-2332	9	3	introduction	introduction	NOUN
ejpam-2332	9	4	game	game	NOUN
ejpam-2332	9	5	theory	theory	NOUN
ejpam-2332	9	6	is	be	AUX
ejpam-2332	9	7	a	a	DET
ejpam-2332	9	8	formal	formal	ADJ
ejpam-2332	9	9	way	way	NOUN
ejpam-2332	9	10	to	to	PART
ejpam-2332	9	11	analyze	analyze	VERB
ejpam-2332	9	12	conflict	conflict	NOUN
ejpam-2332	9	13	of	of	ADP
ejpam-2332	9	14	interest	interest	NOUN
ejpam-2332	9	15	among	among	ADP
ejpam-2332	9	16	rational	rational	ADJ
ejpam-2332	9	17	agents	agent	NOUN
ejpam-2332	9	18	.	.	PUNCT
ejpam-2332	10	1	bimatrix	bimatrix	NOUN
ejpam-2332	10	2	game	game	NOUN
ejpam-2332	10	3	is	be	AUX
ejpam-2332	10	4	a	a	DET
ejpam-2332	10	5	two	two	NUM
ejpam-2332	10	6	players	player	NOUN
ejpam-2332	10	7	non	non	ADJ
ejpam-2332	10	8	-	-	ADJ
ejpam-2332	10	9	zero	zero	NUM
ejpam-2332	10	10	sum	sum	NOUN
ejpam-2332	10	11	game	game	NOUN
ejpam-2332	10	12	which	which	PRON
ejpam-2332	10	13	have	have	AUX
ejpam-2332	10	14	been	be	AUX
ejpam-2332	10	15	successfully	successfully	ADV
ejpam-2332	10	16	applied	apply	VERB
ejpam-2332	10	17	in	in	ADP
ejpam-2332	10	18	different	different	ADJ
ejpam-2332	10	19	areas	area	NOUN
ejpam-2332	10	20	such	such	ADJ
ejpam-2332	10	21	as	as	ADP
ejpam-2332	10	22	competition	competition	NOUN
ejpam-2332	10	23	,	,	PUNCT
ejpam-2332	10	24	voting	voting	NOUN
ejpam-2332	10	25	,	,	PUNCT
ejpam-2332	10	26	artificial	artificial	ADJ
ejpam-2332	10	27	intelligence	intelligence	NOUN
ejpam-2332	10	28	etc	etc	X
ejpam-2332	10	29	.	.	X
ejpam-2332	10	30	in	in	ADP
ejpam-2332	10	31	traditional	traditional	ADJ
ejpam-2332	10	32	bi	bi	ADJ
ejpam-2332	10	33	-	-	ADJ
ejpam-2332	10	34	matrix	matrix	NOUN
ejpam-2332	10	35	games	game	NOUN
ejpam-2332	10	36	it	it	PRON
ejpam-2332	10	37	assume	assume	VERB
ejpam-2332	10	38	that	that	SCONJ
ejpam-2332	10	39	the	the	DET
ejpam-2332	10	40	pay	pay	VERB
ejpam-2332	10	41	-	-	PUNCT
ejpam-2332	10	42	off	off	ADP
ejpam-2332	10	43	values	value	NOUN
ejpam-2332	10	44	are	be	AUX
ejpam-2332	10	45	known	know	VERB
ejpam-2332	10	46	exactly	exactly	ADV
ejpam-2332	10	47	by	by	ADP
ejpam-2332	10	48	the	the	DET
ejpam-2332	10	49	players	player	NOUN
ejpam-2332	10	50	.	.	PUNCT
ejpam-2332	11	1	but	but	CCONJ
ejpam-2332	11	2	,	,	PUNCT
ejpam-2332	11	3	in	in	ADP
ejpam-2332	11	4	real	real	ADJ
ejpam-2332	11	5	situations	situation	NOUN
ejpam-2332	11	6	,	,	PUNCT
ejpam-2332	11	7	it	it	PRON
ejpam-2332	11	8	often	often	ADV
ejpam-2332	11	9	happens	happen	VERB
ejpam-2332	11	10	that	that	SCONJ
ejpam-2332	11	11	the	the	DET
ejpam-2332	11	12	players	player	NOUN
ejpam-2332	11	13	are	be	AUX
ejpam-2332	11	14	not	not	PART
ejpam-2332	11	15	able	able	ADJ
ejpam-2332	11	16	to	to	PART
ejpam-2332	11	17	evaluate	evaluate	VERB
ejpam-2332	11	18	exactly	exactly	ADV
ejpam-2332	11	19	the	the	DET
ejpam-2332	11	20	pay	pay	VERB
ejpam-2332	11	21	-	-	PUNCT
ejpam-2332	11	22	off	off	ADP
ejpam-2332	11	23	values	value	NOUN
ejpam-2332	11	24	due	due	ADP
ejpam-2332	11	25	to	to	ADP
ejpam-2332	11	26	imprecision	imprecision	NOUN
ejpam-2332	11	27	and	and	CCONJ
ejpam-2332	11	28	unavailability	unavailability	NOUN
ejpam-2332	11	29	of	of	ADP
ejpam-2332	11	30	information	information	NOUN
ejpam-2332	11	31	.	.	PUNCT
ejpam-2332	12	1	in	in	ADP
ejpam-2332	12	2	such	such	ADJ
ejpam-2332	12	3	situations	situation	NOUN
ejpam-2332	12	4	,	,	PUNCT
ejpam-2332	12	5	the	the	DET
ejpam-2332	12	6	fuzzy	fuzzy	ADJ
ejpam-2332	12	7	set	set	NOUN
ejpam-2332	12	8	theory	theory	NOUN
ejpam-2332	12	9	(	(	PUNCT
ejpam-2332	12	10	zadeh	zadeh	PROPN
ejpam-2332	12	11	[	[	X
ejpam-2332	12	12	36	36	NUM
ejpam-2332	12	13	]	]	PUNCT
ejpam-2332	12	14	)	)	PUNCT
ejpam-2332	12	15	is	be	AUX
ejpam-2332	12	16	used	use	VERB
ejpam-2332	12	17	and	and	CCONJ
ejpam-2332	12	18	has	have	AUX
ejpam-2332	12	19	achieved	achieve	VERB
ejpam-2332	12	20	a	a	DET
ejpam-2332	12	21	great	great	ADJ
ejpam-2332	12	22	success	success	NOUN
ejpam-2332	12	23	(	(	PUNCT
ejpam-2332	12	24	bector	bector	NOUN
ejpam-2332	12	25	and	and	CCONJ
ejpam-2332	12	26	chandra	chandra	PROPN
ejpam-2332	13	1	[	[	X
ejpam-2332	13	2	4	4	NUM
ejpam-2332	13	3	]	]	PUNCT
ejpam-2332	13	4	,	,	PUNCT
ejpam-2332	13	5	vijay	vijay	NOUN
ejpam-2332	13	6	et	et	PROPN
ejpam-2332	13	7	al	al	PROPN
ejpam-2332	13	8	.	.	PUNCT
ejpam-2332	14	1	[	[	X
ejpam-2332	14	2	33	33	NUM
ejpam-2332	14	3	,	,	PUNCT
ejpam-2332	14	4	34	34	NUM
ejpam-2332	14	5	]	]	PUNCT
ejpam-2332	14	6	,	,	PUNCT
ejpam-2332	14	7	li	li	PROPN
ejpam-2332	15	1	[	[	X
ejpam-2332	15	2	9	9	NUM
ejpam-2332	15	3	,	,	PUNCT
ejpam-2332	15	4	10	10	NUM
ejpam-2332	15	5	]	]	PUNCT
ejpam-2332	15	6	,	,	PUNCT
ejpam-2332	15	7	cevikel	cevikel	NOUN
ejpam-2332	15	8	and	and	CCONJ
ejpam-2332	15	9	ahlatcioglu	ahlatcioglu	NOUN
ejpam-2332	16	1	[	[	X
ejpam-2332	16	2	5	5	NUM
ejpam-2332	16	3	]	]	PUNCT
ejpam-2332	16	4	,	,	PUNCT
ejpam-2332	16	5	kocken	kocken	VERB
ejpam-2332	16	6	et	et	PROPN
ejpam-2332	16	7	al	al	PROPN
ejpam-2332	16	8	.	.	PUNCT
ejpam-2332	17	1	[	[	X
ejpam-2332	17	2	7	7	NUM
ejpam-2332	17	3	]	]	PUNCT
ejpam-2332	17	4	,	,	PUNCT
ejpam-2332	17	5	seikh	seikh	PROPN
ejpam-2332	17	6	et	et	PROPN
ejpam-2332	17	7	al	al	PROPN
ejpam-2332	17	8	.	.	PUNCT
ejpam-2332	18	1	[	[	X
ejpam-2332	18	2	29	29	NUM
ejpam-2332	18	3	]	]	PUNCT
ejpam-2332	18	4	)	)	PUNCT
ejpam-2332	18	5	.	.	PUNCT
ejpam-2332	19	1	in	in	ADP
ejpam-2332	19	2	recent	recent	ADJ
ejpam-2332	19	3	past	past	NOUN
ejpam-2332	19	4	,	,	PUNCT
ejpam-2332	19	5	various	various	ADJ
ejpam-2332	19	6	attempt	attempt	NOUN
ejpam-2332	19	7	have	have	AUX
ejpam-2332	19	8	been	be	AUX
ejpam-2332	19	9	made	make	VERB
ejpam-2332	19	10	in	in	ADP
ejpam-2332	19	11	fuzzy	fuzzy	ADJ
ejpam-2332	19	12	bi	bi	ADJ
ejpam-2332	19	13	-	-	ADJ
ejpam-2332	19	14	matrix	matrix	NOUN
ejpam-2332	19	15	game	game	NOUN
ejpam-2332	19	16	theory	theory	NOUN
ejpam-2332	19	17	namely	namely	ADV
ejpam-2332	19	18	(	(	PUNCT
ejpam-2332	19	19	nishizaki	nishizaki	ADJ
ejpam-2332	19	20	and	and	CCONJ
ejpam-2332	19	21	∗corresponding	∗corresponde	VERB
ejpam-2332	19	22	author	author	NOUN
ejpam-2332	19	23	.	.	PUNCT
ejpam-2332	20	1	email	email	NOUN
ejpam-2332	20	2	addresses	address	NOUN
ejpam-2332	20	3	:	:	PUNCT
ejpam-2332	21	1	mrseikh@ymail.com	mrseikh@ymail.com	X
ejpam-2332	21	2	(	(	PUNCT
ejpam-2332	21	3	m.	m.	NOUN
ejpam-2332	21	4	seikh	seikh	PROPN
ejpam-2332	21	5	)	)	PUNCT
ejpam-2332	21	6	,	,	PUNCT
ejpam-2332	21	7	nayak_prasun@rediffmail.com	nayak_prasun@rediffmail.com	X
ejpam-2332	21	8	(	(	PUNCT
ejpam-2332	21	9	p.	p.	PROPN
ejpam-2332	21	10	nayak	nayak	PROPN
ejpam-2332	21	11	)	)	PUNCT
ejpam-2332	21	12	,	,	PUNCT
ejpam-2332	21	13	mmpalvu@gmail.com	mmpalvu@gmail.com	X
ejpam-2332	21	14	(	(	PUNCT
ejpam-2332	21	15	m.	m.	NOUN
ejpam-2332	21	16	pal	pal	NOUN
ejpam-2332	21	17	)	)	PUNCT
ejpam-2332	21	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2332	22	1	153	153	NUM
ejpam-2332	22	2	c	c	NOUN
ejpam-2332	22	3	©	©	PROPN
ejpam-2332	22	4	2015	2015	NUM
ejpam-2332	22	5	ejpam	ejpam	VERB
ejpam-2332	22	6	all	all	DET
ejpam-2332	22	7	rights	right	NOUN
ejpam-2332	22	8	reserved	reserve	VERB
ejpam-2332	22	9	.	.	PUNCT
ejpam-2332	23	1	m.	m.	NOUN
ejpam-2332	23	2	seikh	seikh	PROPN
ejpam-2332	23	3	,	,	PUNCT
ejpam-2332	23	4	p.	p.	PROPN
ejpam-2332	23	5	nayak	nayak	PROPN
ejpam-2332	23	6	,	,	PUNCT
ejpam-2332	23	7	m.	m.	NOUN
ejpam-2332	23	8	pal	pal	PROPN
ejpam-2332	23	9	/	/	SYM
ejpam-2332	23	10	eur	eur	PROPN
ejpam-2332	23	11	.	.	PUNCT
ejpam-2332	24	1	j.	j.	PROPN
ejpam-2332	24	2	pure	pure	PROPN
ejpam-2332	24	3	appl	appl	PROPN
ejpam-2332	24	4	.	.	PROPN
ejpam-2332	24	5	math	math	PROPN
ejpam-2332	24	6	,	,	PUNCT
ejpam-2332	24	7	8	8	NUM
ejpam-2332	24	8	(	(	PUNCT
ejpam-2332	24	9	2015	2015	NUM
ejpam-2332	24	10	)	)	PUNCT
ejpam-2332	24	11	,	,	PUNCT
ejpam-2332	24	12	153	153	NUM
ejpam-2332	24	13	-	-	SYM
ejpam-2332	24	14	171	171	NUM
ejpam-2332	24	15	154	154	NUM
ejpam-2332	24	16	sakawa	sakawa	NOUN
ejpam-2332	25	1	[	[	X
ejpam-2332	25	2	21	21	NUM
ejpam-2332	25	3	,	,	PUNCT
ejpam-2332	25	4	22	22	NUM
ejpam-2332	25	5	]	]	PUNCT
ejpam-2332	25	6	,	,	PUNCT
ejpam-2332	25	7	sakawa	sakawa	NOUN
ejpam-2332	25	8	and	and	CCONJ
ejpam-2332	25	9	nishizaki	nishizaki	ADV
ejpam-2332	25	10	[	[	X
ejpam-2332	25	11	24	24	NUM
ejpam-2332	25	12	]	]	PUNCT
ejpam-2332	25	13	,	,	PUNCT
ejpam-2332	25	14	maeda	maeda	PROPN
ejpam-2332	25	15	[	[	X
ejpam-2332	25	16	13	13	NUM
ejpam-2332	25	17	]	]	PUNCT
ejpam-2332	25	18	,	,	PUNCT
ejpam-2332	25	19	vidyottama	vidyottama	PROPN
ejpam-2332	25	20	et	et	PROPN
ejpam-2332	25	21	al	al	PROPN
ejpam-2332	25	22	.	.	PUNCT
ejpam-2332	26	1	[	[	X
ejpam-2332	26	2	32	32	NUM
ejpam-2332	26	3	]	]	PUNCT
ejpam-2332	26	4	,	,	PUNCT
ejpam-2332	26	5	nayak	nayak	NOUN
ejpam-2332	26	6	and	and	CCONJ
ejpam-2332	26	7	pal	pal	ADJ
ejpam-2332	26	8	[	[	X
ejpam-2332	26	9	18	18	NUM
ejpam-2332	26	10	]	]	NUM
ejpam-2332	26	11	)	)	PUNCT
ejpam-2332	26	12	.	.	PUNCT
ejpam-2332	27	1	however	however	ADV
ejpam-2332	27	2	,	,	PUNCT
ejpam-2332	27	3	fuzzy	fuzzy	ADJ
ejpam-2332	27	4	set	set	NOUN
ejpam-2332	27	5	uses	use	VERB
ejpam-2332	27	6	only	only	ADV
ejpam-2332	27	7	a	a	DET
ejpam-2332	27	8	membership	membership	NOUN
ejpam-2332	27	9	degree	degree	NOUN
ejpam-2332	27	10	to	to	PART
ejpam-2332	27	11	describe	describe	VERB
ejpam-2332	27	12	the	the	DET
ejpam-2332	27	13	degree	degree	NOUN
ejpam-2332	27	14	of	of	ADP
ejpam-2332	27	15	belongingness	belongingness	NOUN
ejpam-2332	27	16	.	.	PUNCT
ejpam-2332	28	1	the	the	DET
ejpam-2332	28	2	non	non	ADJ
ejpam-2332	28	3	-	-	ADJ
ejpam-2332	28	4	membership	membership	ADJ
ejpam-2332	28	5	degree	degree	NOUN
ejpam-2332	28	6	is	be	AUX
ejpam-2332	28	7	just	just	ADV
ejpam-2332	28	8	automatically	automatically	ADV
ejpam-2332	28	9	equal	equal	ADJ
ejpam-2332	28	10	to	to	ADP
ejpam-2332	28	11	the	the	DET
ejpam-2332	28	12	complement	complement	NOUN
ejpam-2332	28	13	to	to	ADP
ejpam-2332	28	14	1	1	NUM
ejpam-2332	28	15	.	.	PUNCT
ejpam-2332	29	1	but	but	CCONJ
ejpam-2332	29	2	,	,	PUNCT
ejpam-2332	29	3	in	in	ADP
ejpam-2332	29	4	some	some	DET
ejpam-2332	29	5	real	real	ADJ
ejpam-2332	29	6	situations	situation	NOUN
ejpam-2332	29	7	,	,	PUNCT
ejpam-2332	29	8	players	player	NOUN
ejpam-2332	29	9	/	/	SYM
ejpam-2332	29	10	decision	decision	NOUN
ejpam-2332	29	11	makers(dms	makers(dm	NOUN
ejpam-2332	29	12	)	)	PUNCT
ejpam-2332	29	13	could	could	AUX
ejpam-2332	29	14	only	only	ADV
ejpam-2332	29	15	know	know	VERB
ejpam-2332	29	16	the	the	DET
ejpam-2332	29	17	pay	pay	NOUN
ejpam-2332	29	18	-	-	PUNCT
ejpam-2332	29	19	offs	off	NOUN
ejpam-2332	29	20	approximately	approximately	ADV
ejpam-2332	29	21	with	with	ADP
ejpam-2332	29	22	some	some	DET
ejpam-2332	29	23	imprecise	imprecise	ADJ
ejpam-2332	29	24	degree	degree	NOUN
ejpam-2332	29	25	.	.	PUNCT
ejpam-2332	30	1	in	in	ADP
ejpam-2332	30	2	other	other	ADJ
ejpam-2332	30	3	words	word	NOUN
ejpam-2332	30	4	,	,	PUNCT
ejpam-2332	30	5	players	player	NOUN
ejpam-2332	30	6	/	/	SYM
ejpam-2332	30	7	dms	dms	PROPN
ejpam-2332	30	8	may	may	AUX
ejpam-2332	30	9	have	have	VERB
ejpam-2332	30	10	some	some	DET
ejpam-2332	30	11	hesitation	hesitation	NOUN
ejpam-2332	30	12	degree	degree	NOUN
ejpam-2332	30	13	about	about	ADP
ejpam-2332	30	14	the	the	DET
ejpam-2332	30	15	approximate	approximate	ADJ
ejpam-2332	30	16	pay	pay	NOUN
ejpam-2332	30	17	-	-	PUNCT
ejpam-2332	30	18	offs	off	NOUN
ejpam-2332	30	19	.	.	PUNCT
ejpam-2332	31	1	therefore	therefore	ADV
ejpam-2332	31	2	,	,	PUNCT
ejpam-2332	31	3	the	the	DET
ejpam-2332	31	4	fuzzy	fuzzy	ADJ
ejpam-2332	31	5	set	set	NOUN
ejpam-2332	31	6	has	have	VERB
ejpam-2332	31	7	no	no	DET
ejpam-2332	31	8	means	mean	NOUN
ejpam-2332	31	9	to	to	PART
ejpam-2332	31	10	incorporate	incorporate	VERB
ejpam-2332	31	11	the	the	DET
ejpam-2332	31	12	hesitation	hesitation	NOUN
ejpam-2332	31	13	degree	degree	NOUN
ejpam-2332	31	14	.	.	PUNCT
ejpam-2332	32	1	intuitionistic	intuitionistic	ADJ
ejpam-2332	32	2	fuzzy	fuzzy	ADJ
ejpam-2332	32	3	set	set	NOUN
ejpam-2332	32	4	(	(	PUNCT
ejpam-2332	32	5	ifs	ifs	PROPN
ejpam-2332	32	6	)	)	PUNCT
ejpam-2332	32	7	,	,	PUNCT
ejpam-2332	32	8	introduced	introduce	VERB
ejpam-2332	32	9	by	by	ADP
ejpam-2332	32	10	atanassov	atanassov	NOUN
ejpam-2332	32	11	[	[	X
ejpam-2332	32	12	2	2	NUM
ejpam-2332	32	13	,	,	PUNCT
ejpam-2332	32	14	3	3	NUM
ejpam-2332	32	15	]	]	PUNCT
ejpam-2332	32	16	has	have	AUX
ejpam-2332	32	17	been	be	AUX
ejpam-2332	32	18	found	find	VERB
ejpam-2332	32	19	to	to	PART
ejpam-2332	32	20	be	be	AUX
ejpam-2332	32	21	well	well	ADV
ejpam-2332	32	22	suited	suited	ADJ
ejpam-2332	32	23	than	than	ADP
ejpam-2332	32	24	the	the	DET
ejpam-2332	32	25	fuzzy	fuzzy	ADJ
ejpam-2332	32	26	set	set	NOUN
ejpam-2332	32	27	to	to	PART
ejpam-2332	32	28	express	express	VERB
ejpam-2332	32	29	and	and	CCONJ
ejpam-2332	32	30	describe	describe	VERB
ejpam-2332	32	31	information	information	NOUN
ejpam-2332	32	32	under	under	ADP
ejpam-2332	32	33	uncertainty	uncertainty	NOUN
ejpam-2332	32	34	.	.	PUNCT
ejpam-2332	33	1	the	the	DET
ejpam-2332	33	2	ifs	ifs	PROPN
ejpam-2332	33	3	is	be	AUX
ejpam-2332	33	4	characterized	characterize	VERB
ejpam-2332	33	5	by	by	ADP
ejpam-2332	33	6	two	two	NUM
ejpam-2332	33	7	functions	function	NOUN
ejpam-2332	33	8	expressing	express	VERB
ejpam-2332	33	9	the	the	DET
ejpam-2332	33	10	degree	degree	NOUN
ejpam-2332	33	11	of	of	ADP
ejpam-2332	33	12	membership	membership	NOUN
ejpam-2332	33	13	and	and	CCONJ
ejpam-2332	33	14	the	the	DET
ejpam-2332	33	15	degree	degree	NOUN
ejpam-2332	33	16	of	of	ADP
ejpam-2332	33	17	nonmembership	nonmembership	NOUN
ejpam-2332	33	18	respectively	respectively	ADV
ejpam-2332	33	19	,	,	PUNCT
ejpam-2332	33	20	so	so	SCONJ
ejpam-2332	33	21	that	that	SCONJ
ejpam-2332	33	22	the	the	DET
ejpam-2332	33	23	sum	sum	NOUN
ejpam-2332	33	24	of	of	ADP
ejpam-2332	33	25	both	both	DET
ejpam-2332	33	26	values	value	NOUN
ejpam-2332	33	27	is	be	AUX
ejpam-2332	33	28	less	less	ADJ
ejpam-2332	33	29	than	than	ADP
ejpam-2332	33	30	or	or	CCONJ
ejpam-2332	33	31	equal	equal	ADJ
ejpam-2332	33	32	to	to	ADP
ejpam-2332	33	33	1	1	NUM
ejpam-2332	33	34	.	.	PUNCT
ejpam-2332	34	1	the	the	DET
ejpam-2332	34	2	hesitation	hesitation	NOUN
ejpam-2332	34	3	degree	degree	NOUN
ejpam-2332	34	4	is	be	AUX
ejpam-2332	34	5	equal	equal	ADJ
ejpam-2332	34	6	to	to	ADP
ejpam-2332	34	7	1	1	NUM
ejpam-2332	34	8	minus	minus	ADP
ejpam-2332	34	9	the	the	DET
ejpam-2332	34	10	degree	degree	NOUN
ejpam-2332	34	11	of	of	ADP
ejpam-2332	34	12	membership	membership	NOUN
ejpam-2332	34	13	and	and	CCONJ
ejpam-2332	34	14	the	the	DET
ejpam-2332	34	15	degree	degree	NOUN
ejpam-2332	34	16	of	of	ADP
ejpam-2332	34	17	non	non	ADJ
ejpam-2332	34	18	-	-	NOUN
ejpam-2332	34	19	membership	membership	NOUN
ejpam-2332	34	20	.	.	PUNCT
ejpam-2332	35	1	therefore	therefore	ADV
ejpam-2332	35	2	,	,	PUNCT
ejpam-2332	35	3	the	the	DET
ejpam-2332	35	4	concept	concept	NOUN
ejpam-2332	35	5	of	of	ADP
ejpam-2332	35	6	an	an	DET
ejpam-2332	35	7	ifs	ifs	PROPN
ejpam-2332	35	8	can	can	AUX
ejpam-2332	35	9	be	be	AUX
ejpam-2332	35	10	seen	see	VERB
ejpam-2332	35	11	in	in	ADP
ejpam-2332	35	12	the	the	DET
ejpam-2332	35	13	literature	literature	NOUN
ejpam-2332	35	14	(	(	PUNCT
ejpam-2332	35	15	nan	nan	PROPN
ejpam-2332	35	16	et	et	PROPN
ejpam-2332	35	17	al	al	PROPN
ejpam-2332	35	18	.	.	PUNCT
ejpam-2332	36	1	[	[	X
ejpam-2332	36	2	15	15	NUM
ejpam-2332	36	3	,	,	PUNCT
ejpam-2332	36	4	16	16	NUM
ejpam-2332	36	5	]	]	PUNCT
ejpam-2332	36	6	,	,	PUNCT
ejpam-2332	36	7	seikh	seikh	PROPN
ejpam-2332	36	8	et	et	PROPN
ejpam-2332	36	9	al	al	PROPN
ejpam-2332	36	10	.	.	PUNCT
ejpam-2332	37	1	[	[	X
ejpam-2332	37	2	28	28	NUM
ejpam-2332	37	3	,	,	PUNCT
ejpam-2332	37	4	30	30	NUM
ejpam-2332	37	5	,	,	PUNCT
ejpam-2332	37	6	31	31	NUM
ejpam-2332	37	7	]	]	PUNCT
ejpam-2332	37	8	,	,	PUNCT
ejpam-2332	37	9	aggarwal	aggarwal	NOUN
ejpam-2332	37	10	et	et	NOUN
ejpam-2332	37	11	al	al	PROPN
ejpam-2332	37	12	.	.	PUNCT
ejpam-2332	38	1	[	[	X
ejpam-2332	38	2	1	1	NUM
ejpam-2332	38	3	]	]	PUNCT
ejpam-2332	38	4	)	)	PUNCT
ejpam-2332	38	5	as	as	ADP
ejpam-2332	38	6	an	an	DET
ejpam-2332	38	7	alternative	alternative	ADJ
ejpam-2332	38	8	approach	approach	NOUN
ejpam-2332	38	9	to	to	PART
ejpam-2332	38	10	define	define	VERB
ejpam-2332	38	11	a	a	DET
ejpam-2332	38	12	fuzzy	fuzzy	ADJ
ejpam-2332	38	13	set	set	NOUN
ejpam-2332	38	14	in	in	ADP
ejpam-2332	38	15	cases	case	NOUN
ejpam-2332	38	16	where	where	SCONJ
ejpam-2332	38	17	available	available	ADJ
ejpam-2332	38	18	information	information	NOUN
ejpam-2332	38	19	is	be	AUX
ejpam-2332	38	20	not	not	PART
ejpam-2332	38	21	sufficient	sufficient	ADJ
ejpam-2332	38	22	.	.	PUNCT
ejpam-2332	39	1	however	however	ADV
ejpam-2332	39	2	,	,	PUNCT
ejpam-2332	39	3	there	there	PRON
ejpam-2332	39	4	exist	exist	VERB
ejpam-2332	39	5	less	less	ADJ
ejpam-2332	39	6	investigation	investigation	NOUN
ejpam-2332	39	7	on	on	ADP
ejpam-2332	39	8	application	application	NOUN
ejpam-2332	39	9	of	of	ADP
ejpam-2332	39	10	ifs	ifs	PROPN
ejpam-2332	39	11	in	in	ADP
ejpam-2332	39	12	bi	bi	ADJ
ejpam-2332	39	13	-	-	ADJ
ejpam-2332	39	14	matrix	matrix	NOUN
ejpam-2332	39	15	games	game	NOUN
ejpam-2332	39	16	.	.	PUNCT
ejpam-2332	40	1	intuitionistic	intuitionistic	ADJ
ejpam-2332	40	2	fuzziness	fuzziness	NOUN
ejpam-2332	40	3	in	in	ADP
ejpam-2332	40	4	bi	bi	ADJ
ejpam-2332	40	5	-	-	ADJ
ejpam-2332	40	6	matrix	matrix	NOUN
ejpam-2332	40	7	games	game	NOUN
ejpam-2332	40	8	can	can	AUX
ejpam-2332	40	9	appear	appear	VERB
ejpam-2332	40	10	in	in	ADP
ejpam-2332	40	11	so	so	ADV
ejpam-2332	40	12	many	many	ADJ
ejpam-2332	40	13	ways	way	NOUN
ejpam-2332	40	14	,	,	PUNCT
ejpam-2332	40	15	but	but	CCONJ
ejpam-2332	40	16	two	two	NUM
ejpam-2332	40	17	cases	case	NOUN
ejpam-2332	40	18	of	of	ADP
ejpam-2332	40	19	fuzziness	fuzziness	NOUN
ejpam-2332	40	20	seem	seem	VERB
ejpam-2332	40	21	to	to	PART
ejpam-2332	40	22	be	be	AUX
ejpam-2332	40	23	very	very	ADV
ejpam-2332	40	24	natural	natural	ADJ
ejpam-2332	40	25	.	.	PUNCT
ejpam-2332	41	1	these	these	PRON
ejpam-2332	41	2	being	be	AUX
ejpam-2332	41	3	the	the	DET
ejpam-2332	41	4	one	one	NOUN
ejpam-2332	41	5	in	in	ADP
ejpam-2332	41	6	which	which	PRON
ejpam-2332	41	7	dms	dms	PROPN
ejpam-2332	41	8	have	have	VERB
ejpam-2332	41	9	if	if	SCONJ
ejpam-2332	41	10	goals	goal	NOUN
ejpam-2332	41	11	and	and	CCONJ
ejpam-2332	41	12	the	the	DET
ejpam-2332	41	13	other	other	ADJ
ejpam-2332	41	14	in	in	ADP
ejpam-2332	41	15	which	which	PRON
ejpam-2332	41	16	the	the	DET
ejpam-2332	41	17	elements	element	NOUN
ejpam-2332	41	18	of	of	ADP
ejpam-2332	41	19	the	the	DET
ejpam-2332	41	20	pay	pay	VERB
ejpam-2332	41	21	-	-	PUNCT
ejpam-2332	41	22	off	off	ADP
ejpam-2332	41	23	matrices	matrix	NOUN
ejpam-2332	41	24	are	be	AUX
ejpam-2332	41	25	given	give	VERB
ejpam-2332	41	26	by	by	ADP
ejpam-2332	41	27	intuitionistic	intuitionistic	ADJ
ejpam-2332	41	28	fuzzy	fuzzy	ADJ
ejpam-2332	41	29	numbers	number	NOUN
ejpam-2332	41	30	(	(	PUNCT
ejpam-2332	41	31	li	li	X
ejpam-2332	41	32	[	[	X
ejpam-2332	41	33	8	8	NUM
ejpam-2332	41	34	]	]	PUNCT
ejpam-2332	41	35	,	,	PUNCT
ejpam-2332	41	36	seikh	seikh	PROPN
ejpam-2332	41	37	et	et	PROPN
ejpam-2332	41	38	al	al	PROPN
ejpam-2332	41	39	.	.	PUNCT
ejpam-2332	42	1	[	[	X
ejpam-2332	42	2	25	25	NUM
ejpam-2332	42	3	,	,	PUNCT
ejpam-2332	42	4	27	27	NUM
ejpam-2332	42	5	]	]	PUNCT
ejpam-2332	42	6	)	)	PUNCT
ejpam-2332	42	7	.	.	PUNCT
ejpam-2332	43	1	these	these	DET
ejpam-2332	43	2	two	two	NUM
ejpam-2332	43	3	classes	class	NOUN
ejpam-2332	43	4	of	of	ADP
ejpam-2332	43	5	fuzzy	fuzzy	ADJ
ejpam-2332	43	6	bi	bi	ADJ
ejpam-2332	43	7	-	-	ADJ
ejpam-2332	43	8	matrix	matrix	NOUN
ejpam-2332	43	9	games	game	NOUN
ejpam-2332	43	10	are	be	AUX
ejpam-2332	43	11	referred	refer	VERB
ejpam-2332	43	12	as	as	ADP
ejpam-2332	43	13	bi	bi	ADJ
ejpam-2332	43	14	-	-	ADJ
ejpam-2332	43	15	matrix	matrix	NOUN
ejpam-2332	43	16	games	game	NOUN
ejpam-2332	43	17	with	with	ADP
ejpam-2332	43	18	i	i	NOUN
ejpam-2332	43	19	-	-	PUNCT
ejpam-2332	43	20	fuzzy	fuzzy	ADJ
ejpam-2332	43	21	goals	goal	NOUN
ejpam-2332	43	22	and	and	CCONJ
ejpam-2332	43	23	bi	bi	ADJ
ejpam-2332	43	24	-	-	ADJ
ejpam-2332	43	25	matrix	matrix	NOUN
ejpam-2332	43	26	games	game	NOUN
ejpam-2332	43	27	with	with	ADP
ejpam-2332	43	28	i	i	NOUN
ejpam-2332	43	29	-	-	PUNCT
ejpam-2332	43	30	fuzzy	fuzzy	ADJ
ejpam-2332	43	31	pay	pay	NOUN
ejpam-2332	43	32	-	-	PUNCT
ejpam-2332	43	33	off	off	NOUN
ejpam-2332	43	34	.	.	PUNCT
ejpam-2332	44	1	nayak	nayak	PROPN
ejpam-2332	44	2	and	and	CCONJ
ejpam-2332	44	3	pal	pal	ADJ
ejpam-2332	44	4	[	[	X
ejpam-2332	44	5	19	19	NUM
ejpam-2332	44	6	,	,	PUNCT
ejpam-2332	44	7	20	20	NUM
ejpam-2332	44	8	]	]	PUNCT
ejpam-2332	44	9	studied	study	VERB
ejpam-2332	44	10	bi	bi	ADJ
ejpam-2332	44	11	-	-	ADJ
ejpam-2332	44	12	matrix	matrix	NOUN
ejpam-2332	44	13	games	game	NOUN
ejpam-2332	44	14	and	and	CCONJ
ejpam-2332	44	15	multi	multi	ADJ
ejpam-2332	44	16	-	-	ADJ
ejpam-2332	44	17	objective	objective	ADJ
ejpam-2332	44	18	bi	bi	ADJ
ejpam-2332	44	19	-	-	ADJ
ejpam-2332	44	20	matrix	matrix	NOUN
ejpam-2332	44	21	games	game	NOUN
ejpam-2332	44	22	in	in	ADP
ejpam-2332	44	23	which	which	PRON
ejpam-2332	44	24	goals	goal	NOUN
ejpam-2332	44	25	are	be	AUX
ejpam-2332	44	26	expressed	express	VERB
ejpam-2332	44	27	by	by	ADP
ejpam-2332	44	28	ifs	ifs	PROPN
ejpam-2332	44	29	.	.	PUNCT
ejpam-2332	45	1	li	li	PROPN
ejpam-2332	46	1	[	[	X
ejpam-2332	46	2	12	12	NUM
ejpam-2332	46	3	]	]	PUNCT
ejpam-2332	46	4	implemented	implement	VERB
ejpam-2332	46	5	bi	bi	ADJ
ejpam-2332	46	6	-	-	ADJ
ejpam-2332	46	7	linear	linear	ADJ
ejpam-2332	46	8	programming	programming	NOUN
ejpam-2332	46	9	models	model	NOUN
ejpam-2332	46	10	to	to	PART
ejpam-2332	46	11	solve	solve	VERB
ejpam-2332	46	12	bi	bi	ADJ
ejpam-2332	46	13	-	-	ADJ
ejpam-2332	46	14	matrix	matrix	NOUN
ejpam-2332	46	15	games	game	NOUN
ejpam-2332	46	16	with	with	ADP
ejpam-2332	46	17	pay	pay	NOUN
ejpam-2332	46	18	-	-	PUNCT
ejpam-2332	46	19	offs	off	NOUN
ejpam-2332	46	20	of	of	ADP
ejpam-2332	46	21	ifs	ifs	PROPN
ejpam-2332	46	22	.	.	PROPN
ejpam-2332	47	1	seikh	seikh	PROPN
ejpam-2332	47	2	et	et	PROPN
ejpam-2332	47	3	al	al	PROPN
ejpam-2332	47	4	.	.	PUNCT
ejpam-2332	48	1	[	[	X
ejpam-2332	48	2	26	26	NUM
ejpam-2332	48	3	]	]	PUNCT
ejpam-2332	48	4	used	use	VERB
ejpam-2332	48	5	tifns	tifns	NOUN
ejpam-2332	48	6	in	in	ADP
ejpam-2332	48	7	bi	bi	ADJ
ejpam-2332	48	8	-	-	ADJ
ejpam-2332	48	9	matrix	matrix	NOUN
ejpam-2332	48	10	games	game	NOUN
ejpam-2332	48	11	though	though	SCONJ
ejpam-2332	48	12	this	this	DET
ejpam-2332	48	13	method	method	NOUN
ejpam-2332	48	14	is	be	AUX
ejpam-2332	48	15	limited	limit	VERB
ejpam-2332	48	16	to	to	ADP
ejpam-2332	48	17	pure	pure	ADJ
ejpam-2332	48	18	strategies	strategy	NOUN
ejpam-2332	48	19	only	only	ADV
ejpam-2332	48	20	.	.	PUNCT
ejpam-2332	49	1	li	li	PROPN
ejpam-2332	49	2	and	and	CCONJ
ejpam-2332	49	3	yang	yang	PROPN
ejpam-2332	50	1	[	[	X
ejpam-2332	50	2	11	11	NUM
ejpam-2332	50	3	]	]	PUNCT
ejpam-2332	50	4	developed	develop	VERB
ejpam-2332	50	5	a	a	DET
ejpam-2332	50	6	difference	difference	NOUN
ejpam-2332	50	7	index	index	NOUN
ejpam-2332	50	8	based	base	VERB
ejpam-2332	50	9	bi	bi	ADJ
ejpam-2332	50	10	-	-	ADJ
ejpam-2332	50	11	linear	linear	ADJ
ejpam-2332	50	12	programming	programming	NOUN
ejpam-2332	50	13	approach	approach	NOUN
ejpam-2332	50	14	to	to	PART
ejpam-2332	50	15	solve	solve	VERB
ejpam-2332	50	16	bi	bi	ADJ
ejpam-2332	50	17	-	-	ADJ
ejpam-2332	50	18	matrix	matrix	NOUN
ejpam-2332	50	19	games	game	NOUN
ejpam-2332	50	20	with	with	ADP
ejpam-2332	50	21	pay	pay	NOUN
ejpam-2332	50	22	-	-	PUNCT
ejpam-2332	50	23	offs	off	NOUN
ejpam-2332	50	24	represented	represent	VERB
ejpam-2332	50	25	by	by	ADP
ejpam-2332	50	26	trapezoidal	trapezoidal	ADJ
ejpam-2332	50	27	intuitionistic	intuitionistic	ADJ
ejpam-2332	50	28	fuzzy	fuzzy	ADJ
ejpam-2332	50	29	numbers	number	NOUN
ejpam-2332	50	30	.	.	PUNCT
ejpam-2332	51	1	in	in	ADP
ejpam-2332	51	2	this	this	DET
ejpam-2332	51	3	paper	paper	NOUN
ejpam-2332	51	4	,	,	PUNCT
ejpam-2332	51	5	we	we	PRON
ejpam-2332	51	6	have	have	AUX
ejpam-2332	51	7	considered	consider	VERB
ejpam-2332	51	8	bi	bi	ADJ
ejpam-2332	51	9	-	-	ADJ
ejpam-2332	51	10	matrix	matrix	NOUN
ejpam-2332	51	11	games	game	NOUN
ejpam-2332	51	12	in	in	ADP
ejpam-2332	51	13	which	which	PRON
ejpam-2332	51	14	the	the	DET
ejpam-2332	51	15	pay	pay	NOUN
ejpam-2332	51	16	-	-	PUNCT
ejpam-2332	51	17	offs	off	NOUN
ejpam-2332	51	18	are	be	AUX
ejpam-2332	51	19	represented	represent	VERB
ejpam-2332	51	20	by	by	ADP
ejpam-2332	51	21	tifns	tifns	PROPN
ejpam-2332	51	22	.	.	PUNCT
ejpam-2332	52	1	a	a	DET
ejpam-2332	52	2	new	new	ADJ
ejpam-2332	52	3	ranking	ranking	NOUN
ejpam-2332	52	4	function	function	NOUN
ejpam-2332	52	5	is	be	AUX
ejpam-2332	52	6	defined	define	VERB
ejpam-2332	52	7	to	to	PART
ejpam-2332	52	8	find	find	VERB
ejpam-2332	52	9	a	a	DET
ejpam-2332	52	10	order	order	NOUN
ejpam-2332	52	11	relation	relation	NOUN
ejpam-2332	52	12	between	between	ADP
ejpam-2332	52	13	two	two	NUM
ejpam-2332	52	14	tifns	tifns	NOUN
ejpam-2332	52	15	.	.	PUNCT
ejpam-2332	53	1	a	a	DET
ejpam-2332	53	2	non	non	ADJ
ejpam-2332	53	3	-	-	ADJ
ejpam-2332	53	4	linear	linear	ADJ
ejpam-2332	53	5	i	i	ADJ
ejpam-2332	53	6	-	-	PUNCT
ejpam-2332	53	7	fuzzy	fuzzy	ADJ
ejpam-2332	53	8	programming	programming	NOUN
ejpam-2332	53	9	problem	problem	NOUN
ejpam-2332	53	10	is	be	AUX
ejpam-2332	53	11	formulated	formulate	VERB
ejpam-2332	53	12	to	to	PART
ejpam-2332	53	13	find	find	VERB
ejpam-2332	53	14	the	the	DET
ejpam-2332	53	15	equilibrium	equilibrium	NOUN
ejpam-2332	53	16	solution	solution	NOUN
ejpam-2332	53	17	of	of	ADP
ejpam-2332	53	18	this	this	DET
ejpam-2332	53	19	bi	bi	ADJ
ejpam-2332	53	20	-	-	ADJ
ejpam-2332	53	21	matrix	matrix	NOUN
ejpam-2332	53	22	game	game	NOUN
ejpam-2332	53	23	.	.	PUNCT
ejpam-2332	54	1	utilizing	utilize	VERB
ejpam-2332	54	2	the	the	DET
ejpam-2332	54	3	ranking	rank	VERB
ejpam-2332	54	4	function	function	NOUN
ejpam-2332	54	5	this	this	DET
ejpam-2332	54	6	non	non	ADJ
ejpam-2332	54	7	-	-	ADJ
ejpam-2332	54	8	linear	linear	ADJ
ejpam-2332	54	9	programming	programming	NOUN
ejpam-2332	54	10	problem	problem	NOUN
ejpam-2332	54	11	is	be	AUX
ejpam-2332	54	12	further	far	ADV
ejpam-2332	54	13	transformed	transform	VERB
ejpam-2332	54	14	into	into	ADP
ejpam-2332	54	15	a	a	DET
ejpam-2332	54	16	crisp	crisp	ADJ
ejpam-2332	54	17	equivalent	equivalent	ADJ
ejpam-2332	54	18	non	non	ADJ
ejpam-2332	54	19	-	-	ADJ
ejpam-2332	54	20	linear	linear	ADJ
ejpam-2332	54	21	programming	programming	NOUN
ejpam-2332	54	22	problem	problem	NOUN
ejpam-2332	54	23	which	which	PRON
ejpam-2332	54	24	can	can	AUX
ejpam-2332	54	25	be	be	AUX
ejpam-2332	54	26	easily	easily	ADV
ejpam-2332	54	27	solved	solve	VERB
ejpam-2332	54	28	to	to	PART
ejpam-2332	54	29	find	find	VERB
ejpam-2332	54	30	the	the	DET
ejpam-2332	54	31	equilibrium	equilibrium	NOUN
ejpam-2332	54	32	solution	solution	NOUN
ejpam-2332	54	33	.	.	PUNCT
ejpam-2332	55	1	the	the	DET
ejpam-2332	55	2	paper	paper	NOUN
ejpam-2332	55	3	is	be	AUX
ejpam-2332	55	4	organized	organize	VERB
ejpam-2332	55	5	as	as	SCONJ
ejpam-2332	55	6	follows	follow	VERB
ejpam-2332	55	7	:	:	PUNCT
ejpam-2332	55	8	in	in	ADP
ejpam-2332	55	9	section	section	NOUN
ejpam-2332	55	10	2	2	NUM
ejpam-2332	55	11	,	,	PUNCT
ejpam-2332	55	12	some	some	DET
ejpam-2332	55	13	definitions	definition	NOUN
ejpam-2332	55	14	and	and	CCONJ
ejpam-2332	55	15	preliminaries	preliminary	NOUN
ejpam-2332	55	16	about	about	ADP
ejpam-2332	55	17	tifns	tifns	NOUN
ejpam-2332	55	18	are	be	AUX
ejpam-2332	55	19	recalled	recall	VERB
ejpam-2332	55	20	and	and	CCONJ
ejpam-2332	55	21	a	a	DET
ejpam-2332	55	22	ranking	rank	VERB
ejpam-2332	55	23	function	function	NOUN
ejpam-2332	55	24	is	be	AUX
ejpam-2332	55	25	defined	define	VERB
ejpam-2332	55	26	.	.	PUNCT
ejpam-2332	56	1	section	section	NOUN
ejpam-2332	56	2	3	3	NUM
ejpam-2332	56	3	describes	describe	VERB
ejpam-2332	56	4	concept	concept	NOUN
ejpam-2332	56	5	of	of	ADP
ejpam-2332	56	6	double	double	ADJ
ejpam-2332	56	7	i	i	NOUN
ejpam-2332	56	8	-	-	PUNCT
ejpam-2332	56	9	fuzzy	fuzzy	ADJ
ejpam-2332	56	10	constraint	constraint	NOUN
ejpam-2332	56	11	conditions	condition	NOUN
ejpam-2332	56	12	.	.	PUNCT
ejpam-2332	57	1	the	the	DET
ejpam-2332	57	2	main	main	ADJ
ejpam-2332	57	3	problem	problem	NOUN
ejpam-2332	57	4	about	about	ADP
ejpam-2332	57	5	the	the	DET
ejpam-2332	57	6	bi	bi	ADJ
ejpam-2332	57	7	-	-	ADJ
ejpam-2332	57	8	matrix	matrix	NOUN
ejpam-2332	57	9	games	game	NOUN
ejpam-2332	57	10	with	with	ADP
ejpam-2332	57	11	i	i	NOUN
ejpam-2332	57	12	-	-	PUNCT
ejpam-2332	57	13	fuzzy	fuzzy	ADJ
ejpam-2332	57	14	payoffs	payoff	NOUN
ejpam-2332	57	15	is	be	AUX
ejpam-2332	57	16	formulated	formulate	VERB
ejpam-2332	57	17	in	in	ADP
ejpam-2332	57	18	section	section	NOUN
ejpam-2332	57	19	4	4	NUM
ejpam-2332	57	20	.	.	PUNCT
ejpam-2332	58	1	the	the	DET
ejpam-2332	58	2	results	result	NOUN
ejpam-2332	58	3	are	be	AUX
ejpam-2332	58	4	illustrated	illustrate	VERB
ejpam-2332	58	5	by	by	ADP
ejpam-2332	58	6	considering	consider	VERB
ejpam-2332	58	7	a	a	DET
ejpam-2332	58	8	media	media	NOUN
ejpam-2332	58	9	marketing	marketing	NOUN
ejpam-2332	58	10	problem	problem	NOUN
ejpam-2332	58	11	in	in	ADP
ejpam-2332	58	12	section	section	NOUN
ejpam-2332	58	13	5	5	NUM
ejpam-2332	58	14	.	.	PUNCT
ejpam-2332	58	15	section	section	NOUN
ejpam-2332	58	16	6	6	NUM
ejpam-2332	58	17	concludes	conclude	VERB
ejpam-2332	58	18	the	the	DET
ejpam-2332	58	19	paper	paper	NOUN
ejpam-2332	58	20	.	.	PUNCT
ejpam-2332	59	1	m.	m.	NOUN
ejpam-2332	59	2	seikh	seikh	PROPN
ejpam-2332	59	3	,	,	PUNCT
ejpam-2332	59	4	p.	p.	PROPN
ejpam-2332	59	5	nayak	nayak	PROPN
ejpam-2332	59	6	,	,	PUNCT
ejpam-2332	59	7	m.	m.	NOUN
ejpam-2332	59	8	pal	pal	PROPN
ejpam-2332	59	9	/	/	SYM
ejpam-2332	59	10	eur	eur	PROPN
ejpam-2332	59	11	.	.	PUNCT
ejpam-2332	60	1	j.	j.	PROPN
ejpam-2332	60	2	pure	pure	PROPN
ejpam-2332	60	3	appl	appl	PROPN
ejpam-2332	60	4	.	.	PROPN
ejpam-2332	60	5	math	math	PROPN
ejpam-2332	60	6	,	,	PUNCT
ejpam-2332	60	7	8	8	NUM
ejpam-2332	60	8	(	(	PUNCT
ejpam-2332	60	9	2015	2015	NUM
ejpam-2332	60	10	)	)	PUNCT
ejpam-2332	60	11	,	,	PUNCT
ejpam-2332	60	12	153	153	NUM
ejpam-2332	60	13	-	-	SYM
ejpam-2332	60	14	171	171	NUM
ejpam-2332	60	15	155	155	NUM
ejpam-2332	60	16	2	2	NUM
ejpam-2332	60	17	.	.	PUNCT
ejpam-2332	61	1	definitions	definition	NOUN
ejpam-2332	61	2	and	and	CCONJ
ejpam-2332	61	3	preliminaries	preliminary	NOUN
ejpam-2332	61	4	2.1	2.1	NUM
ejpam-2332	61	5	.	.	PUNCT
ejpam-2332	62	1	triangular	triangular	NOUN
ejpam-2332	62	2	intuitionistic	intuitionistic	ADJ
ejpam-2332	62	3	fuzzy	fuzzy	ADJ
ejpam-2332	62	4	number	number	NOUN
ejpam-2332	62	5	(	(	PUNCT
ejpam-2332	62	6	tifn	tifn	NOUN
ejpam-2332	62	7	)	)	PUNCT
ejpam-2332	62	8	definition	definition	NOUN
ejpam-2332	62	9	1	1	NUM
ejpam-2332	62	10	.	.	PUNCT
ejpam-2332	63	1	a	a	DET
ejpam-2332	63	2	tifn	tifn	NOUN
ejpam-2332	63	3	ã	ã	PROPN
ejpam-2332	63	4	=	=	PUNCT
ejpam-2332	63	5	〈	〈	PROPN
ejpam-2332	63	6	(	(	PUNCT
ejpam-2332	63	7	aµ	aµ	PROPN
ejpam-2332	63	8	,	,	PUNCT
ejpam-2332	63	9	a	a	PRON
ejpam-2332	63	10	,	,	PUNCT
ejpam-2332	63	11	āµ	āµ	PROPN
ejpam-2332	63	12	)	)	PUNCT
ejpam-2332	63	13	;	;	PUNCT
ejpam-2332	63	14	(	(	PUNCT
ejpam-2332	63	15	aν	aν	NOUN
ejpam-2332	63	16	,	,	PUNCT
ejpam-2332	63	17	a	a	DET
ejpam-2332	63	18	,	,	PUNCT
ejpam-2332	63	19	āν	āν	NOUN
ejpam-2332	63	20	)	)	PUNCT
ejpam-2332	63	21	〉	〉	NOUN
ejpam-2332	63	22	is	be	AUX
ejpam-2332	63	23	a	a	DET
ejpam-2332	63	24	convex	convex	ADJ
ejpam-2332	63	25	ifs	if	NOUN
ejpam-2332	63	26	on	on	ADP
ejpam-2332	63	27	the	the	DET
ejpam-2332	63	28	set	set	ADJ
ejpam-2332	63	29	ℜ	ℜ	PROPN
ejpam-2332	63	30	of	of	ADP
ejpam-2332	63	31	real	real	ADJ
ejpam-2332	63	32	numbers	number	NOUN
ejpam-2332	63	33	,	,	PUNCT
ejpam-2332	63	34	whose	whose	DET
ejpam-2332	63	35	membership	membership	NOUN
ejpam-2332	63	36	and	and	CCONJ
ejpam-2332	63	37	non	non	ADJ
ejpam-2332	63	38	-	-	ADJ
ejpam-2332	63	39	membership	membership	ADJ
ejpam-2332	63	40	functions	function	NOUN
ejpam-2332	63	41	are	be	AUX
ejpam-2332	63	42	defined	define	VERB
ejpam-2332	63	43	as	as	SCONJ
ejpam-2332	63	44	follows	follow	VERB
ejpam-2332	63	45	µã(x	µã(x	NOUN
ejpam-2332	63	46	)	)	PUNCT
ejpam-2332	63	47	=	=	SYM
ejpam-2332	64	1			NOUN
ejpam-2332	64	2			PROPN
ejpam-2332	64	3			PROPN
ejpam-2332	64	4	x−aµ	x−aµ	PROPN
ejpam-2332	64	5	a−aµ	a−aµ	PROPN
ejpam-2332	64	6	for	for	ADP
ejpam-2332	64	7	aµ	aµ	PROPN
ejpam-2332	64	8	≤	≤	NUM
ejpam-2332	64	9	x	x	X
ejpam-2332	64	10	<	<	X
ejpam-2332	64	11	a	a	DET
ejpam-2332	64	12	āµ−x	āµ−x	NOUN
ejpam-2332	64	13	āµ−a	āµ−a	NOUN
ejpam-2332	64	14	for	for	ADP
ejpam-2332	64	15	a	a	DET
ejpam-2332	64	16	<	<	X
ejpam-2332	64	17	x	x	SYM
ejpam-2332	64	18	≤	≤	PUNCT
ejpam-2332	64	19	āµ	āµ	PROPN
ejpam-2332	64	20	0	0	NUM
ejpam-2332	64	21	otherwise	otherwise	ADV
ejpam-2332	64	22	(	(	PUNCT
ejpam-2332	64	23	1	1	X
ejpam-2332	64	24	)	)	PUNCT
ejpam-2332	64	25	and	and	CCONJ
ejpam-2332	64	26	νã(x	νã(x	NOUN
ejpam-2332	64	27	)	)	PUNCT
ejpam-2332	64	28	=	=	PUNCT
ejpam-2332	64	29			VERB
ejpam-2332	64	30			NOUN
ejpam-2332	64	31			NOUN
ejpam-2332	64	32	a−x	a−x	VERB
ejpam-2332	64	33	a−aν	a−aν	PROPN
ejpam-2332	64	34	for	for	ADP
ejpam-2332	64	35	aν	aν	NOUN
ejpam-2332	64	36	≤	≤	NUM
ejpam-2332	64	37	x	x	PUNCT
ejpam-2332	64	38	<	<	X
ejpam-2332	64	39	a	a	DET
ejpam-2332	64	40	x−a	x−a	NOUN
ejpam-2332	64	41	āν−a	āν−a	NOUN
ejpam-2332	64	42	for	for	ADP
ejpam-2332	64	43	a	a	DET
ejpam-2332	64	44	<	<	X
ejpam-2332	64	45	x	x	SYM
ejpam-2332	64	46	≤	≤	ADJ
ejpam-2332	64	47	āν	āν	PROPN
ejpam-2332	64	48	1	1	NUM
ejpam-2332	64	49	otherwise	otherwise	ADV
ejpam-2332	64	50	(	(	PUNCT
ejpam-2332	64	51	2	2	X
ejpam-2332	64	52	)	)	PUNCT
ejpam-2332	64	53	respectively	respectively	ADV
ejpam-2332	64	54	,	,	PUNCT
ejpam-2332	64	55	where	where	SCONJ
ejpam-2332	64	56	aν	aν	NOUN
ejpam-2332	64	57	≤	≤	X
ejpam-2332	64	58	aµ	aµ	PROPN
ejpam-2332	64	59	≤	≤	PROPN
ejpam-2332	64	60	a	a	DET
ejpam-2332	64	61	≤	≤	NUM
ejpam-2332	64	62	āµ	āµ	PROPN
ejpam-2332	64	63	≤	≤	ADJ
ejpam-2332	64	64	āν	āν	NOUN
ejpam-2332	64	65	,	,	PUNCT
ejpam-2332	64	66	depicted	depict	VERB
ejpam-2332	64	67	as	as	ADP
ejpam-2332	64	68	in	in	ADP
ejpam-2332	64	69	figure	figure	NOUN
ejpam-2332	64	70	1	1	NUM
ejpam-2332	64	71	.	.	PUNCT
ejpam-2332	64	72	figure	figure	NOUN
ejpam-2332	64	73	1	1	NUM
ejpam-2332	64	74	:	:	PUNCT
ejpam-2332	64	75	membership	membership	NOUN
ejpam-2332	64	76	and	and	CCONJ
ejpam-2332	64	77	non	non	ADJ
ejpam-2332	64	78	-	-	ADJ
ejpam-2332	64	79	membership	membership	ADJ
ejpam-2332	64	80	functions	function	NOUN
ejpam-2332	64	81	of	of	ADP
ejpam-2332	64	82	tifn	tifn	NOUN
ejpam-2332	64	83	note	note	NOUN
ejpam-2332	64	84	:	:	PUNCT
ejpam-2332	65	1	here	here	ADV
ejpam-2332	65	2	µã(x	µã(x	NOUN
ejpam-2332	65	3	)	)	PUNCT
ejpam-2332	65	4	increases	increase	NOUN
ejpam-2332	65	5	with	with	ADP
ejpam-2332	65	6	constant	constant	ADJ
ejpam-2332	65	7	rate	rate	NOUN
ejpam-2332	65	8	for	for	ADP
ejpam-2332	65	9	x	x	PROPN
ejpam-2332	65	10	∈	∈	PROPN
ejpam-2332	66	1	[	[	X
ejpam-2332	66	2	aµ	aµ	PROPN
ejpam-2332	66	3	,	,	PUNCT
ejpam-2332	66	4	a	a	PRON
ejpam-2332	66	5	]	]	PUNCT
ejpam-2332	66	6	and	and	CCONJ
ejpam-2332	66	7	decreases	decrease	VERB
ejpam-2332	66	8	with	with	ADP
ejpam-2332	66	9	constant	constant	ADJ
ejpam-2332	66	10	rate	rate	NOUN
ejpam-2332	66	11	for	for	ADP
ejpam-2332	66	12	x	x	PROPN
ejpam-2332	66	13	∈	∈	PROPN
ejpam-2332	66	14	[	[	X
ejpam-2332	66	15	a	a	X
ejpam-2332	66	16	,	,	PUNCT
ejpam-2332	66	17	āµ	āµ	PROPN
ejpam-2332	66	18	]	]	X
ejpam-2332	66	19	but	but	CCONJ
ejpam-2332	66	20	νã(x	νã(x	NOUN
ejpam-2332	66	21	)	)	PUNCT
ejpam-2332	66	22	decreases	decrease	VERB
ejpam-2332	66	23	with	with	ADP
ejpam-2332	66	24	constant	constant	ADJ
ejpam-2332	66	25	rate	rate	NOUN
ejpam-2332	66	26	for	for	ADP
ejpam-2332	66	27	x	x	PROPN
ejpam-2332	66	28	∈	∈	PROPN
ejpam-2332	67	1	[	[	X
ejpam-2332	67	2	aν	aν	NOUN
ejpam-2332	67	3	,	,	PUNCT
ejpam-2332	67	4	a	a	PRON
ejpam-2332	67	5	]	]	PUNCT
ejpam-2332	67	6	and	and	CCONJ
ejpam-2332	67	7	increases	increase	NOUN
ejpam-2332	67	8	with	with	ADP
ejpam-2332	67	9	constant	constant	ADJ
ejpam-2332	67	10	rate	rate	NOUN
ejpam-2332	67	11	for	for	ADP
ejpam-2332	67	12	x	x	PROPN
ejpam-2332	67	13	∈	∈	PROPN
ejpam-2332	67	14	[	[	X
ejpam-2332	67	15	a	a	DET
ejpam-2332	67	16	,	,	PUNCT
ejpam-2332	67	17	āν	āν	NOUN
ejpam-2332	67	18	]	]	PUNCT
ejpam-2332	67	19	.	.	PUNCT
ejpam-2332	68	1	let	let	VERB
ejpam-2332	68	2	πã(x	πã(x	X
ejpam-2332	68	3	)	)	PUNCT
ejpam-2332	68	4	=	=	SYM
ejpam-2332	68	5	1−µã(x)−νã(x	1−µã(x)−νã(x	NUM
ejpam-2332	68	6	)	)	PUNCT
ejpam-2332	68	7	,	,	PUNCT
ejpam-2332	68	8	which	which	PRON
ejpam-2332	68	9	is	be	AUX
ejpam-2332	68	10	called	call	VERB
ejpam-2332	68	11	as	as	ADP
ejpam-2332	68	12	the	the	DET
ejpam-2332	68	13	intuitionistic	intuitionistic	ADJ
ejpam-2332	68	14	fuzzy	fuzzy	ADJ
ejpam-2332	68	15	index	index	NOUN
ejpam-2332	68	16	of	of	ADP
ejpam-2332	68	17	an	an	DET
ejpam-2332	68	18	element	element	NOUN
ejpam-2332	68	19	x	x	PUNCT
ejpam-2332	68	20	in	in	ADP
ejpam-2332	68	21	the	the	DET
ejpam-2332	68	22	tifn	tifn	NOUN
ejpam-2332	68	23	ã.	ã.	PROPN
ejpam-2332	68	24	obviously	obviously	ADV
ejpam-2332	68	25	,	,	PUNCT
ejpam-2332	68	26	if	if	SCONJ
ejpam-2332	68	27	aν	aν	NOUN
ejpam-2332	68	28	=	=	PUNCT
ejpam-2332	68	29	aµ	aµ	PROPN
ejpam-2332	68	30	=	=	PUNCT
ejpam-2332	68	31	a	a	PROPN
ejpam-2332	68	32	and	and	CCONJ
ejpam-2332	68	33	āµ	āµ	PROPN
ejpam-2332	68	34	=	=	SYM
ejpam-2332	68	35	āν	āν	NOUN
ejpam-2332	68	36	=	=	SYM
ejpam-2332	68	37	ā	ā	NOUN
ejpam-2332	68	38	,	,	PUNCT
ejpam-2332	68	39	then	then	ADV
ejpam-2332	68	40	µã(x	µã(x	NOUN
ejpam-2332	68	41	)	)	PUNCT
ejpam-2332	68	42	+	+	NUM
ejpam-2332	68	43	νã(x	νã(x	NOUN
ejpam-2332	68	44	)	)	PUNCT
ejpam-2332	68	45	=	=	SYM
ejpam-2332	69	1	1	1	NUM
ejpam-2332	69	2	,	,	PUNCT
ejpam-2332	69	3	∀x	∀x	VERB
ejpam-2332	69	4	∈	∈	PROPN
ejpam-2332	69	5	ℜ.	ℜ.	PROPN
ejpam-2332	69	6	in	in	ADP
ejpam-2332	69	7	this	this	DET
ejpam-2332	69	8	case	case	NOUN
ejpam-2332	69	9	tifn	tifn	NOUN
ejpam-2332	69	10	ã	ã	PROPN
ejpam-2332	69	11	=	=	PUNCT
ejpam-2332	69	12	〈	〈	PROPN
ejpam-2332	69	13	(	(	PUNCT
ejpam-2332	69	14	aµ	aµ	PROPN
ejpam-2332	69	15	,	,	PUNCT
ejpam-2332	69	16	a	a	PRON
ejpam-2332	69	17	,	,	PUNCT
ejpam-2332	69	18	āµ	āµ	PROPN
ejpam-2332	69	19	)	)	PUNCT
ejpam-2332	69	20	;	;	PUNCT
ejpam-2332	69	21	(	(	PUNCT
ejpam-2332	69	22	aν	aν	NOUN
ejpam-2332	69	23	,	,	PUNCT
ejpam-2332	69	24	a	a	DET
ejpam-2332	69	25	,	,	PUNCT
ejpam-2332	69	26	āν	āν	NOUN
ejpam-2332	69	27	)	)	PUNCT
ejpam-2332	69	28	〉	〉	NOUN
ejpam-2332	69	29	is	be	AUX
ejpam-2332	69	30	reduced	reduce	VERB
ejpam-2332	69	31	to	to	ADP
ejpam-2332	69	32	ã	ã	PROPN
ejpam-2332	69	33	=	=	SYM
ejpam-2332	69	34	〈	〈	PROPN
ejpam-2332	69	35	(	(	PUNCT
ejpam-2332	69	36	a	a	NOUN
ejpam-2332	69	37	,	,	PUNCT
ejpam-2332	69	38	a	a	DET
ejpam-2332	69	39	,	,	PUNCT
ejpam-2332	69	40	ā	ā	ADJ
ejpam-2332	69	41	)	)	PUNCT
ejpam-2332	69	42	〉	〉	NOUN
ejpam-2332	69	43	which	which	PRON
ejpam-2332	69	44	is	be	AUX
ejpam-2332	69	45	just	just	ADV
ejpam-2332	69	46	a	a	DET
ejpam-2332	69	47	triangular	triangular	NOUN
ejpam-2332	69	48	fuzzy	fuzzy	ADJ
ejpam-2332	69	49	number	number	NOUN
ejpam-2332	69	50	(	(	PUNCT
ejpam-2332	69	51	tfn	tfn	NOUN
ejpam-2332	69	52	)	)	PUNCT
ejpam-2332	69	53	.	.	PUNCT
ejpam-2332	70	1	thus	thus	ADV
ejpam-2332	70	2	,	,	PUNCT
ejpam-2332	70	3	it	it	PRON
ejpam-2332	70	4	is	be	AUX
ejpam-2332	70	5	easy	easy	ADJ
ejpam-2332	70	6	to	to	PART
ejpam-2332	70	7	see	see	VERB
ejpam-2332	70	8	that	that	SCONJ
ejpam-2332	70	9	the	the	DET
ejpam-2332	70	10	definition	definition	NOUN
ejpam-2332	70	11	of	of	ADP
ejpam-2332	70	12	a	a	DET
ejpam-2332	70	13	tifn	tifn	NOUN
ejpam-2332	70	14	is	be	AUX
ejpam-2332	70	15	a	a	DET
ejpam-2332	70	16	generalization	generalization	NOUN
ejpam-2332	70	17	of	of	ADP
ejpam-2332	70	18	that	that	PRON
ejpam-2332	70	19	of	of	ADP
ejpam-2332	70	20	the	the	DET
ejpam-2332	70	21	tfn	tfn	NOUN
ejpam-2332	70	22	,	,	PUNCT
ejpam-2332	70	23	introduced	introduce	VERB
ejpam-2332	70	24	by	by	ADP
ejpam-2332	70	25	dubois	dubois	PROPN
ejpam-2332	70	26	and	and	CCONJ
ejpam-2332	70	27	prade	prade	VERB
ejpam-2332	70	28	[	[	X
ejpam-2332	70	29	6	6	NUM
ejpam-2332	70	30	]	]	PUNCT
ejpam-2332	70	31	.	.	PUNCT
ejpam-2332	71	1	the	the	DET
ejpam-2332	71	2	set	set	NOUN
ejpam-2332	71	3	of	of	ADP
ejpam-2332	71	4	all	all	DET
ejpam-2332	71	5	tifns	tifns	NOUN
ejpam-2332	71	6	is	be	AUX
ejpam-2332	71	7	denoted	denote	VERB
ejpam-2332	71	8	by	by	ADP
ejpam-2332	71	9	f̃	f̃	PROPN
ejpam-2332	71	10	(	(	PUNCT
ejpam-2332	71	11	ℜ	ℜ	PROPN
ejpam-2332	71	12	)	)	PUNCT
ejpam-2332	71	13	.	.	PUNCT
ejpam-2332	72	1	definition	definition	NOUN
ejpam-2332	72	2	2	2	NUM
ejpam-2332	72	3	(	(	PUNCT
ejpam-2332	72	4	arithmetic	arithmetic	ADJ
ejpam-2332	72	5	operations	operation	NOUN
ejpam-2332	72	6	)	)	PUNCT
ejpam-2332	72	7	.	.	PUNCT
ejpam-2332	73	1	let	let	VERB
ejpam-2332	73	2	ã	ã	PROPN
ejpam-2332	73	3	and	and	CCONJ
ejpam-2332	73	4	b̃	b̃	PROPN
ejpam-2332	73	5	be	be	AUX
ejpam-2332	73	6	two	two	NUM
ejpam-2332	73	7	tifns	tifns	NOUN
ejpam-2332	73	8	,	,	PUNCT
ejpam-2332	73	9	denoted	denote	VERB
ejpam-2332	73	10	by	by	ADP
ejpam-2332	73	11	ã	ã	PROPN
ejpam-2332	73	12	=	=	PUNCT
ejpam-2332	73	13	〈	〈	PROPN
ejpam-2332	73	14	(	(	PUNCT
ejpam-2332	73	15	aµ	aµ	PROPN
ejpam-2332	73	16	,	,	PUNCT
ejpam-2332	73	17	a	a	PRON
ejpam-2332	73	18	,	,	PUNCT
ejpam-2332	73	19	āµ	āµ	PROPN
ejpam-2332	73	20	)	)	PUNCT
ejpam-2332	73	21	;	;	PUNCT
ejpam-2332	73	22	(	(	PUNCT
ejpam-2332	73	23	aν	aν	NOUN
ejpam-2332	73	24	,	,	PUNCT
ejpam-2332	73	25	a	a	DET
ejpam-2332	73	26	,	,	PUNCT
ejpam-2332	73	27	āν	āν	NOUN
ejpam-2332	73	28	)	)	PUNCT
ejpam-2332	73	29	〉	〉	NOUN
ejpam-2332	73	30	and	and	CCONJ
ejpam-2332	73	31	b̃	b̃	PROPN
ejpam-2332	73	32	=	=	PUNCT
ejpam-2332	73	33	〈	〈	PROPN
ejpam-2332	73	34	(	(	PUNCT
ejpam-2332	73	35	bµ	bµ	PROPN
ejpam-2332	73	36	,	,	PUNCT
ejpam-2332	73	37	b	b	NOUN
ejpam-2332	73	38	,	,	PUNCT
ejpam-2332	73	39	b̄µ	b̄µ	ADJ
ejpam-2332	73	40	)	)	PUNCT
ejpam-2332	73	41	;	;	PUNCT
ejpam-2332	73	42	(	(	PUNCT
ejpam-2332	73	43	bν	bν	PROPN
ejpam-2332	73	44	,	,	PUNCT
ejpam-2332	73	45	b	b	NOUN
ejpam-2332	73	46	,	,	PUNCT
ejpam-2332	73	47	b̄ν	b̄ν	NOUN
ejpam-2332	73	48	)	)	PUNCT
ejpam-2332	73	49	〉	〉	NOUN
ejpam-2332	73	50	then	then	ADV
ejpam-2332	73	51	the	the	DET
ejpam-2332	73	52	addition	addition	NOUN
ejpam-2332	73	53	and	and	CCONJ
ejpam-2332	73	54	scalar	scalar	ADJ
ejpam-2332	73	55	multiplication	multiplication	NOUN
ejpam-2332	73	56	are	be	AUX
ejpam-2332	73	57	defined	define	VERB
ejpam-2332	73	58	as	as	SCONJ
ejpam-2332	73	59	follows	follow	VERB
ejpam-2332	73	60	:	:	PUNCT
ejpam-2332	73	61	m.	m.	NOUN
ejpam-2332	73	62	seikh	seikh	PROPN
ejpam-2332	73	63	,	,	PUNCT
ejpam-2332	73	64	p.	p.	PROPN
ejpam-2332	73	65	nayak	nayak	PROPN
ejpam-2332	73	66	,	,	PUNCT
ejpam-2332	73	67	m.	m.	NOUN
ejpam-2332	73	68	pal	pal	PROPN
ejpam-2332	73	69	/	/	SYM
ejpam-2332	73	70	eur	eur	PROPN
ejpam-2332	73	71	.	.	PUNCT
ejpam-2332	74	1	j.	j.	PROPN
ejpam-2332	74	2	pure	pure	PROPN
ejpam-2332	74	3	appl	appl	PROPN
ejpam-2332	74	4	.	.	PROPN
ejpam-2332	74	5	math	math	PROPN
ejpam-2332	74	6	,	,	PUNCT
ejpam-2332	74	7	8	8	NUM
ejpam-2332	74	8	(	(	PUNCT
ejpam-2332	74	9	2015	2015	NUM
ejpam-2332	74	10	)	)	PUNCT
ejpam-2332	74	11	,	,	PUNCT
ejpam-2332	74	12	153	153	NUM
ejpam-2332	74	13	-	-	SYM
ejpam-2332	74	14	171	171	NUM
ejpam-2332	74	15	156	156	NUM
ejpam-2332	74	16	addition	addition	NOUN
ejpam-2332	74	17	:	:	PUNCT
ejpam-2332	74	18	ã+	ã+	PROPN
ejpam-2332	74	19	b̃	b̃	PROPN
ejpam-2332	74	20	=	=	PUNCT
ejpam-2332	74	21	¬	¬	PROPN
ejpam-2332	74	22	(	(	PUNCT
ejpam-2332	74	23	aµ	aµ	PROPN
ejpam-2332	74	24	+	+	NUM
ejpam-2332	74	25	bµ	bµ	PROPN
ejpam-2332	74	26	,	,	PUNCT
ejpam-2332	74	27	a+	a+	PUNCT
ejpam-2332	74	28	b	b	NOUN
ejpam-2332	74	29	,	,	PUNCT
ejpam-2332	74	30	āµ	āµ	PROPN
ejpam-2332	74	31	+	+	CCONJ
ejpam-2332	74	32	b̄µ	b̄µ	ADJ
ejpam-2332	74	33	)	)	PUNCT
ejpam-2332	74	34	;	;	PUNCT
ejpam-2332	74	35	(	(	PUNCT
ejpam-2332	74	36	aν	aν	NOUN
ejpam-2332	74	37	+	+	CCONJ
ejpam-2332	74	38	bν	bν	ADJ
ejpam-2332	74	39	,	,	PUNCT
ejpam-2332	74	40	a+	a+	ADJ
ejpam-2332	74	41	b	b	NOUN
ejpam-2332	74	42	,	,	PUNCT
ejpam-2332	74	43	āν	āν	NOUN
ejpam-2332	74	44	+	+	CCONJ
ejpam-2332	74	45	b̄ν	b̄ν	NOUN
ejpam-2332	74	46	)	)	PUNCT
ejpam-2332	74	47	¶	¶	PROPN
ejpam-2332	74	48	.	.	PUNCT
ejpam-2332	75	1	scalar	scalar	ADJ
ejpam-2332	75	2	multiplication	multiplication	NOUN
ejpam-2332	75	3	:	:	PUNCT
ejpam-2332	75	4	kã	kã	PROPN
ejpam-2332	75	5	=	=	PUNCT
ejpam-2332	75	6	(	(	PUNCT
ejpam-2332	75	7	〈	〈	PROPN
ejpam-2332	75	8	(	(	PUNCT
ejpam-2332	75	9	kaµ	kaµ	PROPN
ejpam-2332	75	10	,	,	PUNCT
ejpam-2332	75	11	ka	ka	PROPN
ejpam-2332	75	12	,	,	PUNCT
ejpam-2332	75	13	kāµ	kāµ	PROPN
ejpam-2332	75	14	)	)	PUNCT
ejpam-2332	75	15	;	;	PUNCT
ejpam-2332	75	16	(	(	PUNCT
ejpam-2332	75	17	kaν	kaν	PROPN
ejpam-2332	75	18	,	,	PUNCT
ejpam-2332	75	19	ka	ka	PROPN
ejpam-2332	75	20	,	,	PUNCT
ejpam-2332	75	21	kāν	kāν	NOUN
ejpam-2332	75	22	)	)	PUNCT
ejpam-2332	75	23	〉	〉	NOUN
ejpam-2332	75	24	if	if	SCONJ
ejpam-2332	75	25	k	k	PROPN
ejpam-2332	75	26	>	>	X
ejpam-2332	75	27	0	0	PUNCT
ejpam-2332	76	1	〈	〈	PROPN
ejpam-2332	76	2	(	(	PUNCT
ejpam-2332	76	3	kāµ	kāµ	PROPN
ejpam-2332	76	4	,	,	PUNCT
ejpam-2332	76	5	ka	ka	PROPN
ejpam-2332	76	6	,	,	PUNCT
ejpam-2332	76	7	kaµ	kaµ	PROPN
ejpam-2332	76	8	)	)	PUNCT
ejpam-2332	76	9	;	;	PUNCT
ejpam-2332	76	10	(	(	PUNCT
ejpam-2332	76	11	kāν	kāν	PROPN
ejpam-2332	76	12	,	,	PUNCT
ejpam-2332	76	13	ka	ka	PROPN
ejpam-2332	76	14	,	,	PUNCT
ejpam-2332	76	15	kaν	kaν	NOUN
ejpam-2332	76	16	)	)	PUNCT
ejpam-2332	76	17	〉	〉	NOUN
ejpam-2332	76	18	if	if	SCONJ
ejpam-2332	76	19	k	k	PROPN
ejpam-2332	76	20	<	<	X
ejpam-2332	76	21	0	0	PROPN
ejpam-2332	76	22	,	,	PUNCT
ejpam-2332	76	23	where	where	SCONJ
ejpam-2332	76	24	k	k	PROPN
ejpam-2332	76	25	is	be	AUX
ejpam-2332	76	26	a	a	DET
ejpam-2332	76	27	real	real	ADJ
ejpam-2332	76	28	number	number	NOUN
ejpam-2332	76	29	.	.	PUNCT
ejpam-2332	77	1	definition	definition	NOUN
ejpam-2332	77	2	3	3	NUM
ejpam-2332	77	3	(	(	PUNCT
ejpam-2332	77	4	cut	cut	VERB
ejpam-2332	77	5	sets	set	NOUN
ejpam-2332	77	6	of	of	ADP
ejpam-2332	77	7	tifns	tifns	NOUN
ejpam-2332	77	8	)	)	PUNCT
ejpam-2332	77	9	.	.	PUNCT
ejpam-2332	78	1	for	for	ADP
ejpam-2332	78	2	anyα	anyα	NOUN
ejpam-2332	78	3	∈	∈	PROPN
ejpam-2332	79	1	[	[	X
ejpam-2332	79	2	0,1	0,1	NUM
ejpam-2332	79	3	]	]	PUNCT
ejpam-2332	79	4	,	,	PUNCT
ejpam-2332	79	5	aα	aα	NOUN
ejpam-2332	79	6	-	-	PUNCT
ejpam-2332	79	7	cut	cut	VERB
ejpam-2332	79	8	set	set	NOUN
ejpam-2332	79	9	of	of	ADP
ejpam-2332	79	10	tifn	tifn	NOUN
ejpam-2332	79	11	ã	ã	PROPN
ejpam-2332	79	12	=	=	PUNCT
ejpam-2332	79	13	〈	〈	PROPN
ejpam-2332	79	14	(	(	PUNCT
ejpam-2332	79	15	aµ	aµ	PROPN
ejpam-2332	79	16	,	,	PUNCT
ejpam-2332	79	17	a	a	PRON
ejpam-2332	79	18	,	,	PUNCT
ejpam-2332	79	19	āµ	āµ	PROPN
ejpam-2332	79	20	)	)	PUNCT
ejpam-2332	79	21	;	;	PUNCT
ejpam-2332	79	22	(	(	PUNCT
ejpam-2332	79	23	aν	aν	NOUN
ejpam-2332	79	24	,	,	PUNCT
ejpam-2332	79	25	a	a	DET
ejpam-2332	79	26	,	,	PUNCT
ejpam-2332	79	27	āν	āν	NOUN
ejpam-2332	79	28	)	)	PUNCT
ejpam-2332	79	29	〉	〉	NOUN
ejpam-2332	79	30	can	can	AUX
ejpam-2332	79	31	be	be	AUX
ejpam-2332	79	32	expressed	express	VERB
ejpam-2332	79	33	as	as	ADP
ejpam-2332	79	34	a	a	DET
ejpam-2332	79	35	crisp	crisp	ADJ
ejpam-2332	79	36	subset	subset	NOUN
ejpam-2332	79	37	of	of	ADP
ejpam-2332	79	38	ℜ	ℜ	PROPN
ejpam-2332	79	39	,	,	PUNCT
ejpam-2332	79	40	denoted	denote	VERB
ejpam-2332	79	41	by	by	ADP
ejpam-2332	79	42	ãα	ãα	NOUN
ejpam-2332	79	43	=	=	SYM
ejpam-2332	79	44	{	{	PUNCT
ejpam-2332	79	45	x	x	NOUN
ejpam-2332	79	46	|µã(x	|µã(x	NOUN
ejpam-2332	79	47	)	)	PUNCT
ejpam-2332	79	48	≥	≥	NUM
ejpam-2332	79	49	α	α	NOUN
ejpam-2332	79	50	,	,	PUNCT
ejpam-2332	79	51	x	x	SYM
ejpam-2332	79	52	∈	∈	PROPN
ejpam-2332	79	53	ℜ	ℜ	PROPN
ejpam-2332	79	54	}	}	PUNCT
ejpam-2332	79	55	.	.	PUNCT
ejpam-2332	80	1	according	accord	VERB
ejpam-2332	80	2	to	to	ADP
ejpam-2332	80	3	the	the	DET
ejpam-2332	80	4	definition	definition	NOUN
ejpam-2332	80	5	of	of	ADP
ejpam-2332	80	6	the	the	DET
ejpam-2332	80	7	tifn	tifn	NOUN
ejpam-2332	80	8	,	,	PUNCT
ejpam-2332	80	9	it	it	PRON
ejpam-2332	80	10	can	can	AUX
ejpam-2332	80	11	be	be	AUX
ejpam-2332	80	12	easily	easily	ADV
ejpam-2332	80	13	seen	see	VERB
ejpam-2332	80	14	that	that	SCONJ
ejpam-2332	80	15	ãα	ãα	PRON
ejpam-2332	80	16	is	be	AUX
ejpam-2332	80	17	a	a	DET
ejpam-2332	80	18	closed	closed	ADJ
ejpam-2332	80	19	interval	interval	NOUN
ejpam-2332	80	20	,	,	PUNCT
ejpam-2332	80	21	denoted	denote	VERB
ejpam-2332	80	22	by	by	ADP
ejpam-2332	80	23	ãα	ãα	NOUN
ejpam-2332	80	24	=	=	PUNCT
ejpam-2332	81	1	[	[	X
ejpam-2332	81	2	lα(ã),rα(ã	lα(ã),rα(ã	NOUN
ejpam-2332	81	3	)	)	PUNCT
ejpam-2332	81	4	]	]	PUNCT
ejpam-2332	81	5	.	.	PUNCT
ejpam-2332	82	1	it	it	PRON
ejpam-2332	82	2	directly	directly	ADV
ejpam-2332	82	3	follows	follow	VERB
ejpam-2332	82	4	from	from	ADP
ejpam-2332	82	5	(	(	PUNCT
ejpam-2332	82	6	1	1	NUM
ejpam-2332	82	7	)	)	PUNCT
ejpam-2332	82	8	that	that	SCONJ
ejpam-2332	83	1	[	[	X
ejpam-2332	83	2	lα(ã),rα(ã	lα(ã),rα(ã	NOUN
ejpam-2332	83	3	)	)	PUNCT
ejpam-2332	83	4	]	]	PUNCT
ejpam-2332	83	5	=	=	SYM
ejpam-2332	83	6	�	�	PROPN
ejpam-2332	83	7	aµ	aµ	PROPN
ejpam-2332	83	8	+	+	PROPN
ejpam-2332	83	9	α(a−	α(a−	PROPN
ejpam-2332	83	10	aµ	aµ	NOUN
ejpam-2332	83	11	)	)	PUNCT
ejpam-2332	83	12	,	,	PUNCT
ejpam-2332	83	13	āµ	āµ	PROPN
ejpam-2332	83	14	−α(āµ	−α(āµ	INTJ
ejpam-2332	83	15	−	−	NOUN
ejpam-2332	83	16	a	a	PRON
ejpam-2332	83	17	)	)	PUNCT
ejpam-2332	83	18	�	�	PROPN
ejpam-2332	83	19	.	.	PUNCT
ejpam-2332	84	1	similarly	similarly	ADV
ejpam-2332	84	2	,	,	PUNCT
ejpam-2332	84	3	for	for	ADP
ejpam-2332	84	4	any	any	DET
ejpam-2332	84	5	β	β	X
ejpam-2332	84	6	∈	∈	PROPN
ejpam-2332	84	7	[	[	X
ejpam-2332	84	8	0,1	0,1	NUM
ejpam-2332	84	9	]	]	PUNCT
ejpam-2332	84	10	,	,	PUNCT
ejpam-2332	84	11	a	a	DET
ejpam-2332	84	12	β	β	X
ejpam-2332	84	13	-cut	-cut	X
ejpam-2332	84	14	set	set	NOUN
ejpam-2332	84	15	of	of	ADP
ejpam-2332	84	16	an	an	DET
ejpam-2332	84	17	tifn	tifn	NOUN
ejpam-2332	84	18	ã	ã	PROPN
ejpam-2332	84	19	=	=	PUNCT
ejpam-2332	84	20	〈	〈	PROPN
ejpam-2332	84	21	(	(	PUNCT
ejpam-2332	84	22	aµ	aµ	PROPN
ejpam-2332	84	23	,	,	PUNCT
ejpam-2332	84	24	a	a	PRON
ejpam-2332	84	25	,	,	PUNCT
ejpam-2332	84	26	āµ	āµ	PROPN
ejpam-2332	84	27	)	)	PUNCT
ejpam-2332	84	28	;	;	PUNCT
ejpam-2332	84	29	(	(	PUNCT
ejpam-2332	84	30	aν	aν	NOUN
ejpam-2332	84	31	,	,	PUNCT
ejpam-2332	84	32	a	a	DET
ejpam-2332	84	33	,	,	PUNCT
ejpam-2332	84	34	āν	āν	NOUN
ejpam-2332	84	35	)	)	PUNCT
ejpam-2332	84	36	〉	〉	NOUN
ejpam-2332	84	37	can	can	AUX
ejpam-2332	84	38	be	be	AUX
ejpam-2332	84	39	expressed	express	VERB
ejpam-2332	84	40	as	as	ADP
ejpam-2332	84	41	a	a	DET
ejpam-2332	84	42	crisp	crisp	ADJ
ejpam-2332	84	43	subset	subset	NOUN
ejpam-2332	84	44	ofℜ	ofℜ	ADV
ejpam-2332	84	45	,	,	PUNCT
ejpam-2332	84	46	denoted	denote	VERB
ejpam-2332	84	47	by	by	ADP
ejpam-2332	84	48	ãβ	ãβ	X
ejpam-2332	84	49	=	=	SYM
ejpam-2332	84	50	{	{	PUNCT
ejpam-2332	84	51	x	x	X
ejpam-2332	84	52	|νã(x)≤	|νã(x)≤	PROPN
ejpam-2332	84	53	β	β	X
ejpam-2332	84	54	,	,	PUNCT
ejpam-2332	84	55	x	x	PUNCT
ejpam-2332	84	56	∈	∈	PROPN
ejpam-2332	84	57	ℜ	ℜ	PROPN
ejpam-2332	84	58	}	}	PUNCT
ejpam-2332	84	59	.	.	PUNCT
ejpam-2332	85	1	obviously	obviously	ADV
ejpam-2332	85	2	,	,	PUNCT
ejpam-2332	85	3	ãβ	ãβ	PROPN
ejpam-2332	85	4	is	be	AUX
ejpam-2332	85	5	a	a	DET
ejpam-2332	85	6	closed	closed	ADJ
ejpam-2332	85	7	interval	interval	NOUN
ejpam-2332	85	8	,	,	PUNCT
ejpam-2332	85	9	denoted	denote	VERB
ejpam-2332	85	10	by	by	ADP
ejpam-2332	85	11	ãβ	ãβ	NOUN
ejpam-2332	85	12	=	=	PUNCT
ejpam-2332	86	1	[	[	X
ejpam-2332	86	2	lβ	lβ	ADP
ejpam-2332	86	3	(	(	PUNCT
ejpam-2332	86	4	ã),rβ	ã),rβ	NOUN
ejpam-2332	86	5	(	(	PUNCT
ejpam-2332	86	6	ã	ã	PROPN
ejpam-2332	86	7	)	)	PUNCT
ejpam-2332	86	8	]	]	PUNCT
ejpam-2332	86	9	.	.	PUNCT
ejpam-2332	87	1	it	it	PRON
ejpam-2332	87	2	directly	directly	ADV
ejpam-2332	87	3	follows	follow	VERB
ejpam-2332	87	4	from	from	ADP
ejpam-2332	87	5	(	(	PUNCT
ejpam-2332	87	6	2	2	NUM
ejpam-2332	87	7	)	)	PUNCT
ejpam-2332	87	8	that	that	SCONJ
ejpam-2332	87	9	[	[	X
ejpam-2332	87	10	lβ	lβ	ADP
ejpam-2332	87	11	(	(	PUNCT
ejpam-2332	87	12	ã),rβ	ã),rβ	NOUN
ejpam-2332	87	13	(	(	PUNCT
ejpam-2332	87	14	ã	ã	PROPN
ejpam-2332	87	15	)	)	PUNCT
ejpam-2332	87	16	]	]	PUNCT
ejpam-2332	88	1	=	=	SYM
ejpam-2332	88	2	�	�	PROPN
ejpam-2332	88	3	a−	a−	PROPN
ejpam-2332	88	4	β(a−	β(a−	PROPN
ejpam-2332	88	5	aν	aν	NOUN
ejpam-2332	88	6	)	)	PUNCT
ejpam-2332	88	7	,	,	PUNCT
ejpam-2332	88	8	a+	a+	PUNCT
ejpam-2332	88	9	β(āν	β(āν	PROPN
ejpam-2332	88	10	−	−	PROPN
ejpam-2332	88	11	a	a	PRON
ejpam-2332	88	12	)	)	PUNCT
ejpam-2332	88	13	�	�	PROPN
ejpam-2332	88	14	.	.	PUNCT
ejpam-2332	89	1	in	in	ADP
ejpam-2332	89	2	the	the	DET
ejpam-2332	89	3	next	next	ADJ
ejpam-2332	89	4	context	context	NOUN
ejpam-2332	89	5	,	,	PUNCT
ejpam-2332	89	6	we	we	PRON
ejpam-2332	89	7	discuss	discuss	VERB
ejpam-2332	89	8	about	about	ADP
ejpam-2332	89	9	the	the	DET
ejpam-2332	89	10	value	value	NOUN
ejpam-2332	89	11	index	index	NOUN
ejpam-2332	89	12	and	and	CCONJ
ejpam-2332	89	13	ambiguity	ambiguity	NOUN
ejpam-2332	89	14	index	index	NOUN
ejpam-2332	89	15	of	of	ADP
ejpam-2332	89	16	a	a	DET
ejpam-2332	89	17	tifn	tifn	NOUN
ejpam-2332	89	18	,	,	PUNCT
ejpam-2332	89	19	inspired	inspire	VERB
ejpam-2332	89	20	by	by	ADP
ejpam-2332	89	21	li	li	PROPN
ejpam-2332	90	1	[	[	X
ejpam-2332	90	2	8	8	NUM
ejpam-2332	90	3	]	]	PUNCT
ejpam-2332	90	4	.	.	PUNCT
ejpam-2332	91	1	definition	definition	NOUN
ejpam-2332	91	2	4	4	NUM
ejpam-2332	91	3	.	.	PUNCT
ejpam-2332	92	1	let	let	VERB
ejpam-2332	92	2	ãα	ãα	PRON
ejpam-2332	93	1	=	=	PUNCT
ejpam-2332	94	1	[	[	X
ejpam-2332	94	2	lα(ã),rα(ã	lα(ã),rα(ã	NOUN
ejpam-2332	94	3	)	)	PUNCT
ejpam-2332	94	4	]	]	PUNCT
ejpam-2332	94	5	and	and	CCONJ
ejpam-2332	94	6	ãβ	ãβ	NOUN
ejpam-2332	95	1	=	=	PUNCT
ejpam-2332	96	1	[	[	X
ejpam-2332	96	2	lβ	lβ	ADP
ejpam-2332	96	3	(	(	PUNCT
ejpam-2332	96	4	ã),rβ	ã),rβ	NOUN
ejpam-2332	96	5	(	(	PUNCT
ejpam-2332	96	6	ã	ã	PROPN
ejpam-2332	96	7	)	)	PUNCT
ejpam-2332	96	8	]	]	PUNCT
ejpam-2332	96	9	be	be	AUX
ejpam-2332	96	10	any	any	DET
ejpam-2332	96	11	α	α	NOUN
ejpam-2332	96	12	-	-	PUNCT
ejpam-2332	96	13	cut	cut	VERB
ejpam-2332	96	14	set	set	NOUN
ejpam-2332	96	15	and	and	CCONJ
ejpam-2332	96	16	a	a	DET
ejpam-2332	96	17	β	β	X
ejpam-2332	96	18	-cut	-cut	X
ejpam-2332	96	19	set	set	NOUN
ejpam-2332	96	20	of	of	ADP
ejpam-2332	96	21	a	a	DET
ejpam-2332	96	22	tifn	tifn	NOUN
ejpam-2332	96	23	ã	ã	PROPN
ejpam-2332	96	24	=	=	PUNCT
ejpam-2332	96	25	〈	〈	PROPN
ejpam-2332	96	26	(	(	PUNCT
ejpam-2332	96	27	aµ	aµ	PROPN
ejpam-2332	96	28	,	,	PUNCT
ejpam-2332	96	29	a	a	PRON
ejpam-2332	96	30	,	,	PUNCT
ejpam-2332	96	31	āµ	āµ	PROPN
ejpam-2332	96	32	)	)	PUNCT
ejpam-2332	96	33	;	;	PUNCT
ejpam-2332	96	34	(	(	PUNCT
ejpam-2332	96	35	aν	aν	NOUN
ejpam-2332	96	36	,	,	PUNCT
ejpam-2332	96	37	a	a	PRON
ejpam-2332	96	38	,	,	PUNCT
ejpam-2332	96	39	āν	āν	NOUN
ejpam-2332	96	40	)	)	PUNCT
ejpam-2332	96	41	〉	〉	NOUN
ejpam-2332	96	42	,	,	PUNCT
ejpam-2332	96	43	respectively	respectively	ADV
ejpam-2332	96	44	.	.	PUNCT
ejpam-2332	97	1	then	then	ADV
ejpam-2332	97	2	the	the	DET
ejpam-2332	97	3	values	value	NOUN
ejpam-2332	97	4	of	of	ADP
ejpam-2332	97	5	the	the	DET
ejpam-2332	97	6	membership	membership	NOUN
ejpam-2332	97	7	and	and	CCONJ
ejpam-2332	97	8	non	non	ADJ
ejpam-2332	97	9	-	-	ADJ
ejpam-2332	97	10	membership	membership	ADJ
ejpam-2332	97	11	functions	function	NOUN
ejpam-2332	97	12	are	be	AUX
ejpam-2332	97	13	defined	define	VERB
ejpam-2332	97	14	as	as	ADP
ejpam-2332	97	15	follows	follow	VERB
ejpam-2332	97	16	.	.	PUNCT
ejpam-2332	98	1	gµ(ã	gµ(ã	NOUN
ejpam-2332	98	2	)	)	PUNCT
ejpam-2332	98	3	=	=	PUNCT
ejpam-2332	99	1	1∫	1∫	NUM
ejpam-2332	99	2	0	0	NUM
ejpam-2332	99	3	lα(ã	lα(ã	NOUN
ejpam-2332	99	4	)	)	PUNCT
ejpam-2332	99	5	+	+	CCONJ
ejpam-2332	99	6	rα(ã	rα(ã	NOUN
ejpam-2332	99	7	)	)	PUNCT
ejpam-2332	99	8	2	2	NUM
ejpam-2332	99	9	f	f	NOUN
ejpam-2332	99	10	(	(	PUNCT
ejpam-2332	99	11	α)dα	α)dα	PROPN
ejpam-2332	99	12	and	and	CCONJ
ejpam-2332	99	13	gν(ã	gν(ã	NOUN
ejpam-2332	99	14	)	)	PUNCT
ejpam-2332	99	15	=	=	PUNCT
ejpam-2332	100	1	1∫	1∫	NUM
ejpam-2332	100	2	0	0	NUM
ejpam-2332	100	3	lβ	lβ	PROPN
ejpam-2332	100	4	(	(	PUNCT
ejpam-2332	100	5	ã	ã	PROPN
ejpam-2332	100	6	)	)	PUNCT
ejpam-2332	100	7	+	+	NUM
ejpam-2332	100	8	rβ	rβ	X
ejpam-2332	100	9	(	(	PUNCT
ejpam-2332	100	10	ã	ã	PROPN
ejpam-2332	100	11	)	)	PUNCT
ejpam-2332	100	12	2	2	NUM
ejpam-2332	100	13	g(β)dβ	g(β)dβ	NOUN
ejpam-2332	100	14	respectively	respectively	ADV
ejpam-2332	100	15	.	.	PUNCT
ejpam-2332	101	1	here	here	ADV
ejpam-2332	101	2	f	f	X
ejpam-2332	101	3	(	(	PUNCT
ejpam-2332	101	4	α	α	NOUN
ejpam-2332	101	5	)	)	PUNCT
ejpam-2332	101	6	is	be	AUX
ejpam-2332	101	7	a	a	DET
ejpam-2332	101	8	non	non	ADJ
ejpam-2332	101	9	-	-	ADJ
ejpam-2332	101	10	negative	negative	ADJ
ejpam-2332	101	11	and	and	CCONJ
ejpam-2332	101	12	non	non	ADJ
ejpam-2332	101	13	-	-	ADJ
ejpam-2332	101	14	decreasing	decrease	VERB
ejpam-2332	101	15	function	function	NOUN
ejpam-2332	101	16	on	on	ADP
ejpam-2332	101	17	the	the	DET
ejpam-2332	101	18	interval	interval	NOUN
ejpam-2332	101	19	[	[	X
ejpam-2332	101	20	0,1	0,1	NUM
ejpam-2332	101	21	]	]	PUNCT
ejpam-2332	101	22	,	,	PUNCT
ejpam-2332	101	23	satisfying	satisfy	VERB
ejpam-2332	101	24	the	the	DET
ejpam-2332	101	25	conditions	condition	NOUN
ejpam-2332	101	26	,	,	PUNCT
ejpam-2332	101	27	f	f	PROPN
ejpam-2332	101	28	(	(	PUNCT
ejpam-2332	101	29	0	0	NUM
ejpam-2332	101	30	)	)	PUNCT
ejpam-2332	101	31	=	=	SYM
ejpam-2332	101	32	0	0	NUM
ejpam-2332	101	33	and	and	CCONJ
ejpam-2332	101	34	f	f	PROPN
ejpam-2332	101	35	(	(	PUNCT
ejpam-2332	101	36	1	1	NUM
ejpam-2332	101	37	)	)	PUNCT
ejpam-2332	101	38	=	=	SYM
ejpam-2332	101	39	1	1	X
ejpam-2332	101	40	.	.	X
ejpam-2332	101	41	also	also	ADV
ejpam-2332	101	42	g(β	g(β	PROPN
ejpam-2332	101	43	)	)	PUNCT
ejpam-2332	101	44	is	be	AUX
ejpam-2332	101	45	a	a	DET
ejpam-2332	101	46	non	non	ADJ
ejpam-2332	101	47	-	-	ADJ
ejpam-2332	101	48	negative	negative	ADJ
ejpam-2332	101	49	and	and	CCONJ
ejpam-2332	101	50	non	non	ADJ
ejpam-2332	101	51	-	-	ADJ
ejpam-2332	101	52	increasing	increasing	ADJ
ejpam-2332	101	53	function	function	NOUN
ejpam-2332	101	54	on	on	ADP
ejpam-2332	101	55	the	the	DET
ejpam-2332	101	56	interval	interval	NOUN
ejpam-2332	101	57	[	[	X
ejpam-2332	101	58	0,1	0,1	NUM
ejpam-2332	101	59	]	]	PUNCT
ejpam-2332	101	60	,	,	PUNCT
ejpam-2332	101	61	satisfying	satisfy	VERB
ejpam-2332	101	62	g(0	g(0	NOUN
ejpam-2332	101	63	)	)	PUNCT
ejpam-2332	101	64	=	=	SYM
ejpam-2332	101	65	1	1	NUM
ejpam-2332	101	66	and	and	CCONJ
ejpam-2332	101	67	g(1	g(1	NOUN
ejpam-2332	101	68	)	)	PUNCT
ejpam-2332	102	1	=	=	PUNCT
ejpam-2332	102	2	0	0	X
ejpam-2332	102	3	.	.	PUNCT
ejpam-2332	103	1	the	the	DET
ejpam-2332	103	2	functions	function	NOUN
ejpam-2332	103	3	f	f	X
ejpam-2332	103	4	(	(	PUNCT
ejpam-2332	103	5	α	α	NOUN
ejpam-2332	103	6	)	)	PUNCT
ejpam-2332	103	7	and	and	CCONJ
ejpam-2332	103	8	g(β	g(β	PROPN
ejpam-2332	103	9	)	)	PUNCT
ejpam-2332	103	10	may	may	AUX
ejpam-2332	103	11	be	be	AUX
ejpam-2332	103	12	considered	consider	VERB
ejpam-2332	103	13	as	as	ADP
ejpam-2332	103	14	weighting	weight	VERB
ejpam-2332	103	15	functions	function	NOUN
ejpam-2332	103	16	and	and	CCONJ
ejpam-2332	103	17	are	be	AUX
ejpam-2332	103	18	chosen	choose	VERB
ejpam-2332	103	19	as	as	ADP
ejpam-2332	103	20	f	f	PROPN
ejpam-2332	103	21	(	(	PUNCT
ejpam-2332	103	22	α	α	NOUN
ejpam-2332	103	23	)	)	PUNCT
ejpam-2332	103	24	=	=	SYM
ejpam-2332	103	25	2α	2α	NOUN
ejpam-2332	103	26	,	,	PUNCT
ejpam-2332	103	27	α	α	PROPN
ejpam-2332	103	28	∈	∈	PROPN
ejpam-2332	104	1	[	[	X
ejpam-2332	104	2	0,1	0,1	NUM
ejpam-2332	104	3	]	]	PUNCT
ejpam-2332	104	4	(	(	PUNCT
ejpam-2332	104	5	3	3	X
ejpam-2332	104	6	)	)	PUNCT
ejpam-2332	104	7	m.	m.	NOUN
ejpam-2332	104	8	seikh	seikh	NOUN
ejpam-2332	104	9	,	,	PUNCT
ejpam-2332	104	10	p.	p.	PROPN
ejpam-2332	104	11	nayak	nayak	PROPN
ejpam-2332	104	12	,	,	PUNCT
ejpam-2332	104	13	m.	m.	NOUN
ejpam-2332	104	14	pal	pal	PROPN
ejpam-2332	104	15	/	/	SYM
ejpam-2332	104	16	eur	eur	PROPN
ejpam-2332	104	17	.	.	PUNCT
ejpam-2332	105	1	j.	j.	PROPN
ejpam-2332	105	2	pure	pure	PROPN
ejpam-2332	105	3	appl	appl	PROPN
ejpam-2332	105	4	.	.	PROPN
ejpam-2332	105	5	math	math	PROPN
ejpam-2332	105	6	,	,	PUNCT
ejpam-2332	105	7	8	8	NUM
ejpam-2332	105	8	(	(	PUNCT
ejpam-2332	105	9	2015	2015	NUM
ejpam-2332	105	10	)	)	PUNCT
ejpam-2332	105	11	,	,	PUNCT
ejpam-2332	105	12	153	153	NUM
ejpam-2332	105	13	-	-	SYM
ejpam-2332	105	14	171	171	NUM
ejpam-2332	105	15	157	157	NUM
ejpam-2332	105	16	and	and	CCONJ
ejpam-2332	105	17	g(β	g(β	NOUN
ejpam-2332	105	18	)	)	PUNCT
ejpam-2332	105	19	=	=	PUNCT
ejpam-2332	106	1	2(1−	2(1−	NUM
ejpam-2332	106	2	β),β	β),β	PROPN
ejpam-2332	106	3	∈	∈	PROPN
ejpam-2332	107	1	[	[	X
ejpam-2332	107	2	0,1	0,1	NUM
ejpam-2332	107	3	]	]	PUNCT
ejpam-2332	107	4	(	(	PUNCT
ejpam-2332	107	5	4	4	NUM
ejpam-2332	107	6	)	)	PUNCT
ejpam-2332	107	7	then	then	ADV
ejpam-2332	107	8	the	the	DET
ejpam-2332	107	9	values	value	NOUN
ejpam-2332	107	10	of	of	ADP
ejpam-2332	107	11	membership	membership	NOUN
ejpam-2332	107	12	an	an	DET
ejpam-2332	107	13	non	non	ADJ
ejpam-2332	107	14	-	-	ADJ
ejpam-2332	107	15	membership	membership	ADJ
ejpam-2332	107	16	functions	function	NOUN
ejpam-2332	107	17	of	of	ADP
ejpam-2332	107	18	a	a	DET
ejpam-2332	107	19	tifn	tifn	NOUN
ejpam-2332	107	20	ã	ã	PROPN
ejpam-2332	107	21	=	=	PUNCT
ejpam-2332	107	22	〈	〈	PROPN
ejpam-2332	107	23	(	(	PUNCT
ejpam-2332	107	24	aµ	aµ	PROPN
ejpam-2332	107	25	,	,	PUNCT
ejpam-2332	107	26	a	a	PRON
ejpam-2332	107	27	,	,	PUNCT
ejpam-2332	107	28	āµ	āµ	PROPN
ejpam-2332	107	29	)	)	PUNCT
ejpam-2332	107	30	;	;	PUNCT
ejpam-2332	107	31	(	(	PUNCT
ejpam-2332	107	32	aν	aν	NOUN
ejpam-2332	107	33	,	,	PUNCT
ejpam-2332	107	34	a	a	DET
ejpam-2332	107	35	,	,	PUNCT
ejpam-2332	107	36	āν	āν	NOUN
ejpam-2332	107	37	)	)	PUNCT
ejpam-2332	107	38	〉	〉	NOUN
ejpam-2332	107	39	are	be	AUX
ejpam-2332	107	40	calculated	calculate	VERB
ejpam-2332	107	41	as	as	SCONJ
ejpam-2332	107	42	follows	follow	VERB
ejpam-2332	107	43	:	:	PUNCT
ejpam-2332	107	44	gµ(ã	gµ(ã	NOUN
ejpam-2332	107	45	)	)	PUNCT
ejpam-2332	107	46	=	=	PUNCT
ejpam-2332	108	1	1∫	1∫	NUM
ejpam-2332	108	2	0	0	NUM
ejpam-2332	108	3	�	�	PROPN
ejpam-2332	108	4	aµ	aµ	PROPN
ejpam-2332	108	5	+	+	PROPN
ejpam-2332	108	6	α(a−	α(a−	PROPN
ejpam-2332	108	7	aµ	aµ	NOUN
ejpam-2332	108	8	)	)	PUNCT
ejpam-2332	109	1	+	+	CCONJ
ejpam-2332	109	2	āµ	āµ	VERB
ejpam-2332	109	3	−α(āµ	−α(āµ	INTJ
ejpam-2332	109	4	−	−	NOUN
ejpam-2332	109	5	a	a	PRON
ejpam-2332	109	6	)	)	PUNCT
ejpam-2332	109	7	�	�	PROPN
ejpam-2332	109	8	αdα=	αdα=	PROPN
ejpam-2332	109	9	(	(	PUNCT
ejpam-2332	109	10	aµ	aµ	PROPN
ejpam-2332	109	11	+	+	NUM
ejpam-2332	109	12	4a+	4a+	NUM
ejpam-2332	109	13	āµ	āµ	NOUN
ejpam-2332	109	14	)	)	PUNCT
ejpam-2332	109	15	6	6	NUM
ejpam-2332	109	16	(	(	PUNCT
ejpam-2332	109	17	5	5	NUM
ejpam-2332	109	18	)	)	PUNCT
ejpam-2332	109	19	gν(ã	gν(ã	NOUN
ejpam-2332	109	20	)	)	PUNCT
ejpam-2332	110	1	=	=	PUNCT
ejpam-2332	111	1	1∫	1∫	NUM
ejpam-2332	111	2	0	0	NUM
ejpam-2332	111	3	�	�	PROPN
ejpam-2332	111	4	a−	a−	PROPN
ejpam-2332	111	5	β(a−	β(a−	PROPN
ejpam-2332	111	6	aν	aν	NOUN
ejpam-2332	111	7	)	)	PUNCT
ejpam-2332	111	8	+	+	CCONJ
ejpam-2332	111	9	a+	a+	PUNCT
ejpam-2332	111	10	β(āν	β(āν	ADJ
ejpam-2332	111	11	−	−	PROPN
ejpam-2332	111	12	a	a	PRON
ejpam-2332	111	13	)	)	PUNCT
ejpam-2332	111	14	�	�	PROPN
ejpam-2332	111	15	(	(	PUNCT
ejpam-2332	111	16	1−	1−	NUM
ejpam-2332	111	17	β)dβ	β)dβ	NOUN
ejpam-2332	111	18	=	=	PRON
ejpam-2332	111	19	(	(	PUNCT
ejpam-2332	111	20	aν	aν	NOUN
ejpam-2332	111	21	+	+	CCONJ
ejpam-2332	111	22	4a+	4a+	NUM
ejpam-2332	111	23	āν	āν	NOUN
ejpam-2332	111	24	)	)	PUNCT
ejpam-2332	111	25	6	6	NUM
ejpam-2332	111	26	.	.	PUNCT
ejpam-2332	112	1	(	(	PUNCT
ejpam-2332	112	2	6	6	NUM
ejpam-2332	112	3	)	)	PUNCT
ejpam-2332	112	4	obviously	obviously	ADV
ejpam-2332	112	5	,	,	PUNCT
ejpam-2332	112	6	gµ(ã	gµ(ã	NOUN
ejpam-2332	112	7	)	)	PUNCT
ejpam-2332	112	8	and	and	CCONJ
ejpam-2332	112	9	gν(ã	gν(ã	NOUN
ejpam-2332	112	10	)	)	PUNCT
ejpam-2332	112	11	synthetically	synthetically	ADV
ejpam-2332	112	12	reflect	reflect	VERB
ejpam-2332	112	13	information	information	NOUN
ejpam-2332	112	14	on	on	ADP
ejpam-2332	112	15	membership	membership	NOUN
ejpam-2332	112	16	degrees	degree	NOUN
ejpam-2332	112	17	and	and	CCONJ
ejpam-2332	112	18	nonmembership	nonmembership	NOUN
ejpam-2332	112	19	degrees	degree	NOUN
ejpam-2332	112	20	at	at	ADP
ejpam-2332	112	21	all	all	DET
ejpam-2332	112	22	levels	level	NOUN
ejpam-2332	112	23	,	,	PUNCT
ejpam-2332	112	24	respectively	respectively	ADV
ejpam-2332	112	25	.	.	PUNCT
ejpam-2332	113	1	also	also	ADV
ejpam-2332	113	2	it	it	PRON
ejpam-2332	113	3	directly	directly	ADV
ejpam-2332	113	4	follows	follow	VERB
ejpam-2332	113	5	that	that	PRON
ejpam-2332	113	6	gµ(ã)≤	gµ(ã)≤	VERB
ejpam-2332	113	7	gν(ã	gν(ã	NOUN
ejpam-2332	113	8	)	)	PUNCT
ejpam-2332	113	9	.	.	PUNCT
ejpam-2332	114	1	similarly	similarly	ADV
ejpam-2332	114	2	,	,	PUNCT
ejpam-2332	114	3	the	the	DET
ejpam-2332	114	4	ambiguities	ambiguity	NOUN
ejpam-2332	114	5	of	of	ADP
ejpam-2332	114	6	the	the	DET
ejpam-2332	114	7	membership	membership	NOUN
ejpam-2332	114	8	and	and	CCONJ
ejpam-2332	114	9	non	non	ADJ
ejpam-2332	114	10	-	-	ADJ
ejpam-2332	114	11	membership	membership	ADJ
ejpam-2332	114	12	functions	function	NOUN
ejpam-2332	114	13	for	for	ADP
ejpam-2332	114	14	any	any	DET
ejpam-2332	114	15	tifn	tifn	NOUN
ejpam-2332	114	16	ã	ã	PROPN
ejpam-2332	114	17	are	be	AUX
ejpam-2332	114	18	defined	define	VERB
ejpam-2332	114	19	by	by	ADP
ejpam-2332	114	20	hµ(ã	hµ(ã	NOUN
ejpam-2332	114	21	)	)	PUNCT
ejpam-2332	114	22	=	=	PUNCT
ejpam-2332	115	1	1∫	1∫	NUM
ejpam-2332	115	2	0	0	NUM
ejpam-2332	116	1	[	[	X
ejpam-2332	116	2	rα(ã)−	rα(ã)−	NOUN
ejpam-2332	116	3	lα(ã	lα(ã	NOUN
ejpam-2332	116	4	)	)	PUNCT
ejpam-2332	116	5	]	]	PUNCT
ejpam-2332	117	1	f	f	X
ejpam-2332	117	2	(	(	PUNCT
ejpam-2332	117	3	α)dα	α)dα	PROPN
ejpam-2332	117	4	and	and	CCONJ
ejpam-2332	117	5	hν(ã	hν(ã	NUM
ejpam-2332	117	6	)	)	PUNCT
ejpam-2332	117	7	=	=	PUNCT
ejpam-2332	118	1	1∫	1∫	NUM
ejpam-2332	118	2	0	0	NUM
ejpam-2332	119	1	[	[	X
ejpam-2332	119	2	rβ	rβ	X
ejpam-2332	119	3	(	(	PUNCT
ejpam-2332	119	4	ã)−	ã)−	NOUN
ejpam-2332	119	5	lβ	lβ	PROPN
ejpam-2332	119	6	(	(	PUNCT
ejpam-2332	119	7	ã)]g(β)dβ	ã)]g(β)dβ	PRON
ejpam-2332	119	8	,	,	PUNCT
ejpam-2332	119	9	respectively	respectively	ADV
ejpam-2332	119	10	.	.	PUNCT
ejpam-2332	120	1	obviously	obviously	ADV
ejpam-2332	120	2	,	,	PUNCT
ejpam-2332	120	3	rα(ã)−	rα(ã)−	PROPN
ejpam-2332	120	4	lα(ã	lα(ã	NOUN
ejpam-2332	120	5	)	)	PUNCT
ejpam-2332	120	6	and	and	CCONJ
ejpam-2332	120	7	rβ	rβ	INTJ
ejpam-2332	120	8	(	(	PUNCT
ejpam-2332	120	9	ã)−	ã)−	NOUN
ejpam-2332	120	10	lβ	lβ	PROPN
ejpam-2332	120	11	(	(	PUNCT
ejpam-2332	120	12	ã	ã	PROPN
ejpam-2332	120	13	)	)	PUNCT
ejpam-2332	120	14	represent	represent	VERB
ejpam-2332	120	15	the	the	DET
ejpam-2332	120	16	lengths	length	NOUN
ejpam-2332	120	17	of	of	ADP
ejpam-2332	120	18	the	the	DET
ejpam-2332	120	19	intervals	interval	NOUN
ejpam-2332	120	20	ãα	ãα	PRON
ejpam-2332	120	21	and	and	CCONJ
ejpam-2332	120	22	ãβ	ãβ	NOUN
ejpam-2332	120	23	.	.	PUNCT
ejpam-2332	121	1	therefore	therefore	ADV
ejpam-2332	121	2	,	,	PUNCT
ejpam-2332	121	3	hµ(ã	hµ(ã	NOUN
ejpam-2332	121	4	)	)	PUNCT
ejpam-2332	121	5	and	and	CCONJ
ejpam-2332	121	6	hν(ã	hν(ã	X
ejpam-2332	121	7	)	)	PUNCT
ejpam-2332	121	8	measure	measure	VERB
ejpam-2332	121	9	the	the	DET
ejpam-2332	121	10	uncertainty	uncertainty	NOUN
ejpam-2332	121	11	in	in	ADP
ejpam-2332	121	12	ã.	ã.	NOUN
ejpam-2332	121	13	using	use	VERB
ejpam-2332	121	14	(	(	PUNCT
ejpam-2332	121	15	3	3	NUM
ejpam-2332	121	16	)	)	PUNCT
ejpam-2332	121	17	and	and	CCONJ
ejpam-2332	121	18	(	(	PUNCT
ejpam-2332	121	19	4	4	NUM
ejpam-2332	121	20	)	)	PUNCT
ejpam-2332	121	21	,	,	PUNCT
ejpam-2332	121	22	the	the	DET
ejpam-2332	121	23	ambiguities	ambiguity	NOUN
ejpam-2332	121	24	of	of	ADP
ejpam-2332	121	25	membership	membership	NOUN
ejpam-2332	121	26	and	and	CCONJ
ejpam-2332	121	27	non	non	ADJ
ejpam-2332	121	28	-	-	ADJ
ejpam-2332	121	29	membership	membership	ADJ
ejpam-2332	121	30	functions	function	NOUN
ejpam-2332	121	31	of	of	ADP
ejpam-2332	121	32	a	a	DET
ejpam-2332	121	33	tifn	tifn	NOUN
ejpam-2332	121	34	ã	ã	PROPN
ejpam-2332	121	35	are	be	AUX
ejpam-2332	121	36	calculated	calculate	VERB
ejpam-2332	121	37	as	as	ADP
ejpam-2332	121	38	hµ(ã	hµ(ã	NOUN
ejpam-2332	121	39	)	)	PUNCT
ejpam-2332	121	40	=	=	PUNCT
ejpam-2332	122	1	1∫	1∫	NUM
ejpam-2332	122	2	0	0	NUM
ejpam-2332	122	3	�	�	PROPN
ejpam-2332	122	4	āµ	āµ	PROPN
ejpam-2332	122	5	−α(āµ	−α(āµ	PRON
ejpam-2332	122	6	−	−	PUNCT
ejpam-2332	122	7	a)−	a)−	ADV
ejpam-2332	122	8	aµ	aµ	PROPN
ejpam-2332	122	9	−α(a−	−α(a−	PROPN
ejpam-2332	122	10	aµ	aµ	PROPN
ejpam-2332	122	11	)	)	PUNCT
ejpam-2332	122	12	�	�	PROPN
ejpam-2332	122	13	2αdα=	2αdα=	NUM
ejpam-2332	122	14	āµ	āµ	PROPN
ejpam-2332	122	15	−	−	PROPN
ejpam-2332	122	16	aµ	aµ	NOUN
ejpam-2332	122	17	3	3	NUM
ejpam-2332	122	18	(	(	PUNCT
ejpam-2332	122	19	7	7	NUM
ejpam-2332	122	20	)	)	PUNCT
ejpam-2332	122	21	and	and	CCONJ
ejpam-2332	122	22	gν(ã	gν(ã	NOUN
ejpam-2332	122	23	)	)	PUNCT
ejpam-2332	123	1	=	=	PUNCT
ejpam-2332	124	1	1∫	1∫	NUM
ejpam-2332	124	2	0	0	NUM
ejpam-2332	124	3	�	�	PROPN
ejpam-2332	124	4	β(āν	β(āν	NOUN
ejpam-2332	124	5	−	−	PROPN
ejpam-2332	124	6	a)−	a)−	PROPN
ejpam-2332	124	7	β(a−	β(a−	PROPN
ejpam-2332	124	8	aν	aν	NOUN
ejpam-2332	124	9	)	)	PUNCT
ejpam-2332	124	10	�	�	PROPN
ejpam-2332	124	11	2(1−	2(1−	NUM
ejpam-2332	124	12	β)dβ	β)dβ	PROPN
ejpam-2332	124	13	=	=	SYM
ejpam-2332	124	14	āν	āν	PROPN
ejpam-2332	124	15	−	−	PROPN
ejpam-2332	124	16	aν	aν	NOUN
ejpam-2332	124	17	3	3	NUM
ejpam-2332	124	18	.	.	PUNCT
ejpam-2332	125	1	(	(	PUNCT
ejpam-2332	125	2	8)	8)	NUM
ejpam-2332	125	3	it	it	PRON
ejpam-2332	125	4	can	can	AUX
ejpam-2332	125	5	be	be	AUX
ejpam-2332	125	6	easily	easily	ADV
ejpam-2332	125	7	shown	show	VERB
ejpam-2332	125	8	that	that	SCONJ
ejpam-2332	125	9	eµ(ã)≤	eµ(ã)≤	ADP
ejpam-2332	125	10	eν(ã	eν(ã	NOUN
ejpam-2332	125	11	)	)	PUNCT
ejpam-2332	125	12	.	.	PUNCT
ejpam-2332	126	1	proposition	proposition	NOUN
ejpam-2332	126	2	1	1	NUM
ejpam-2332	126	3	.	.	PUNCT
ejpam-2332	127	1	let	let	VERB
ejpam-2332	127	2	ã	ã	PROPN
ejpam-2332	127	3	and	and	CCONJ
ejpam-2332	127	4	b̃	b̃	PROPN
ejpam-2332	127	5	be	be	AUX
ejpam-2332	127	6	two	two	NUM
ejpam-2332	127	7	any	any	DET
ejpam-2332	127	8	tifns	tifns	NOUN
ejpam-2332	127	9	and	and	CCONJ
ejpam-2332	127	10	k	k	PROPN
ejpam-2332	127	11	be	be	AUX
ejpam-2332	127	12	any	any	DET
ejpam-2332	127	13	nonnegative	nonnegative	ADJ
ejpam-2332	127	14	real	real	ADJ
ejpam-2332	127	15	number	number	NOUN
ejpam-2332	127	16	.	.	PUNCT
ejpam-2332	128	1	then	then	ADV
ejpam-2332	128	2	the	the	DET
ejpam-2332	128	3	following	follow	VERB
ejpam-2332	128	4	equalities	equality	NOUN
ejpam-2332	128	5	are	be	AUX
ejpam-2332	128	6	valid	valid	ADJ
ejpam-2332	128	7	.	.	PUNCT
ejpam-2332	129	1	(	(	PUNCT
ejpam-2332	129	2	i	i	NOUN
ejpam-2332	129	3	)	)	PUNCT
ejpam-2332	129	4	gµ(kã+	gµ(kã+	PROPN
ejpam-2332	129	5	b̃	b̃	PROPN
ejpam-2332	129	6	)	)	PUNCT
ejpam-2332	130	1	=	=	SYM
ejpam-2332	130	2	kgµ(ã	kgµ(ã	NOUN
ejpam-2332	130	3	)	)	PUNCT
ejpam-2332	131	1	+	+	CCONJ
ejpam-2332	131	2	gµ	gµ	PROPN
ejpam-2332	131	3	(	(	PUNCT
ejpam-2332	131	4	b̃	b̃	PROPN
ejpam-2332	131	5	)	)	PUNCT
ejpam-2332	131	6	m.	m.	NOUN
ejpam-2332	131	7	seikh	seikh	PROPN
ejpam-2332	131	8	,	,	PUNCT
ejpam-2332	131	9	p.	p.	PROPN
ejpam-2332	131	10	nayak	nayak	PROPN
ejpam-2332	131	11	,	,	PUNCT
ejpam-2332	131	12	m.	m.	NOUN
ejpam-2332	131	13	pal	pal	PROPN
ejpam-2332	131	14	/	/	SYM
ejpam-2332	131	15	eur	eur	PROPN
ejpam-2332	131	16	.	.	PUNCT
ejpam-2332	132	1	j.	j.	PROPN
ejpam-2332	132	2	pure	pure	PROPN
ejpam-2332	132	3	appl	appl	PROPN
ejpam-2332	132	4	.	.	PROPN
ejpam-2332	132	5	math	math	PROPN
ejpam-2332	132	6	,	,	PUNCT
ejpam-2332	132	7	8	8	NUM
ejpam-2332	132	8	(	(	PUNCT
ejpam-2332	132	9	2015	2015	NUM
ejpam-2332	132	10	)	)	PUNCT
ejpam-2332	132	11	,	,	PUNCT
ejpam-2332	132	12	153	153	NUM
ejpam-2332	132	13	-	-	SYM
ejpam-2332	132	14	171	171	NUM
ejpam-2332	132	15	158	158	NUM
ejpam-2332	132	16	(	(	PUNCT
ejpam-2332	132	17	ii	ii	NOUN
ejpam-2332	132	18	)	)	PUNCT
ejpam-2332	132	19	gν(kã+	gν(kã+	PROPN
ejpam-2332	132	20	b̃	b̃	PROPN
ejpam-2332	132	21	)	)	PUNCT
ejpam-2332	132	22	=	=	SYM
ejpam-2332	132	23	kgν(ã	kgν(ã	NOUN
ejpam-2332	132	24	)	)	PUNCT
ejpam-2332	133	1	+	+	CCONJ
ejpam-2332	133	2	gν	gν	ADJ
ejpam-2332	133	3	(	(	PUNCT
ejpam-2332	133	4	b̃	b̃	PROPN
ejpam-2332	133	5	)	)	PUNCT
ejpam-2332	133	6	(	(	PUNCT
ejpam-2332	133	7	iii	iii	NOUN
ejpam-2332	133	8	)	)	PUNCT
ejpam-2332	133	9	hµ(kã+	hµ(kã+	PROPN
ejpam-2332	133	10	b̃	b̃	PROPN
ejpam-2332	133	11	)	)	PUNCT
ejpam-2332	133	12	=	=	PUNCT
ejpam-2332	133	13	khµ(ã	khµ(ã	NOUN
ejpam-2332	133	14	)	)	PUNCT
ejpam-2332	134	1	+	+	CCONJ
ejpam-2332	134	2	hµ	hµ	X
ejpam-2332	134	3	(	(	PUNCT
ejpam-2332	134	4	b̃	b̃	PROPN
ejpam-2332	134	5	)	)	PUNCT
ejpam-2332	134	6	(	(	PUNCT
ejpam-2332	134	7	iv	iv	X
ejpam-2332	134	8	)	)	PUNCT
ejpam-2332	134	9	hν(kã+	hν(kã+	PROPN
ejpam-2332	134	10	b̃	b̃	PROPN
ejpam-2332	134	11	)	)	PUNCT
ejpam-2332	134	12	=	=	PUNCT
ejpam-2332	135	1	khν(ã	khν(ã	X
ejpam-2332	135	2	)	)	PUNCT
ejpam-2332	136	1	+	+	CCONJ
ejpam-2332	136	2	hν	hν	NOUN
ejpam-2332	136	3	(	(	PUNCT
ejpam-2332	136	4	b̃	b̃	PROPN
ejpam-2332	136	5	)	)	PUNCT
ejpam-2332	136	6	.	.	PUNCT
ejpam-2332	137	1	definition	definition	NOUN
ejpam-2332	137	2	5	5	NUM
ejpam-2332	137	3	(	(	PUNCT
ejpam-2332	137	4	value	value	NOUN
ejpam-2332	137	5	index	index	NOUN
ejpam-2332	137	6	and	and	CCONJ
ejpam-2332	137	7	ambiguity	ambiguity	NOUN
ejpam-2332	137	8	index	index	NOUN
ejpam-2332	137	9	)	)	PUNCT
ejpam-2332	137	10	.	.	PUNCT
ejpam-2332	138	1	the	the	DET
ejpam-2332	138	2	value	value	NOUN
ejpam-2332	138	3	index	index	NOUN
ejpam-2332	138	4	and	and	CCONJ
ejpam-2332	138	5	ambiguity	ambiguity	NOUN
ejpam-2332	138	6	index	index	NOUN
ejpam-2332	138	7	of	of	ADP
ejpam-2332	138	8	any	any	DET
ejpam-2332	138	9	tifn	tifn	NOUN
ejpam-2332	138	10	ã	ã	PROPN
ejpam-2332	138	11	are	be	AUX
ejpam-2332	138	12	defined	define	VERB
ejpam-2332	138	13	as	as	SCONJ
ejpam-2332	138	14	follows	follow	VERB
ejpam-2332	138	15	:	:	PUNCT
ejpam-2332	138	16	value	value	NOUN
ejpam-2332	138	17	index	index	NOUN
ejpam-2332	138	18	v	v	NOUN
ejpam-2332	138	19	(	(	PUNCT
ejpam-2332	138	20	ã,λ	ã,λ	PROPN
ejpam-2332	138	21	)	)	PUNCT
ejpam-2332	138	22	=	=	PUNCT
ejpam-2332	139	1	λgν(ã	λgν(ã	X
ejpam-2332	139	2	)	)	PUNCT
ejpam-2332	140	1	+	+	CCONJ
ejpam-2332	140	2	(	(	PUNCT
ejpam-2332	140	3	1−λ)gµ(ã	1−λ)gµ(ã	NUM
ejpam-2332	140	4	)	)	PUNCT
ejpam-2332	140	5	and	and	CCONJ
ejpam-2332	140	6	ambiguity	ambiguity	NOUN
ejpam-2332	140	7	index	index	NOUN
ejpam-2332	140	8	a(ã,λ	a(ã,λ	PROPN
ejpam-2332	140	9	)	)	PUNCT
ejpam-2332	140	10	=	=	SYM
ejpam-2332	140	11	λhµ(ã	λhµ(ã	X
ejpam-2332	140	12	)	)	PUNCT
ejpam-2332	140	13	+	+	CCONJ
ejpam-2332	140	14	(	(	PUNCT
ejpam-2332	140	15	1−λ)hν(ã	1−λ)hν(ã	NUM
ejpam-2332	140	16	)	)	PUNCT
ejpam-2332	140	17	,	,	PUNCT
ejpam-2332	140	18	respectively	respectively	ADV
ejpam-2332	140	19	,	,	PUNCT
ejpam-2332	140	20	where	where	SCONJ
ejpam-2332	140	21	λ	λ	PROPN
ejpam-2332	140	22	∈	∈	PROPN
ejpam-2332	140	23	[	[	X
ejpam-2332	140	24	0,1	0,1	NUM
ejpam-2332	140	25	]	]	PUNCT
ejpam-2332	140	26	is	be	AUX
ejpam-2332	140	27	the	the	DET
ejpam-2332	140	28	weight	weight	NOUN
ejpam-2332	140	29	represents	represent	VERB
ejpam-2332	140	30	the	the	DET
ejpam-2332	140	31	players	player	NOUN
ejpam-2332	140	32	/	/	SYM
ejpam-2332	140	33	dms	dms	PROPN
ejpam-2332	140	34	preference	preference	NOUN
ejpam-2332	140	35	information	information	NOUN
ejpam-2332	140	36	.	.	PUNCT
ejpam-2332	141	1	λ	λ	X
ejpam-2332	141	2	∈	∈	PROPN
ejpam-2332	142	1	[	[	X
ejpam-2332	142	2	0	0	NUM
ejpam-2332	142	3	,	,	PUNCT
ejpam-2332	142	4	1	1	NUM
ejpam-2332	142	5	2	2	NUM
ejpam-2332	142	6	)	)	PUNCT
ejpam-2332	142	7	indicates	indicate	VERB
ejpam-2332	142	8	players	player	NOUN
ejpam-2332	142	9	/	/	SYM
ejpam-2332	142	10	dms	dms	X
ejpam-2332	142	11	pessimistic	pessimistic	ADJ
ejpam-2332	142	12	attitude	attitude	NOUN
ejpam-2332	142	13	towards	towards	ADP
ejpam-2332	142	14	uncertainty	uncertainty	NOUN
ejpam-2332	142	15	while	while	SCONJ
ejpam-2332	142	16	λ	λ	PROPN
ejpam-2332	142	17	∈	∈	PROPN
ejpam-2332	142	18	(	(	PUNCT
ejpam-2332	142	19	1	1	NUM
ejpam-2332	142	20	2	2	NUM
ejpam-2332	142	21	,	,	PUNCT
ejpam-2332	142	22	1	1	NUM
ejpam-2332	142	23	]	]	PUNCT
ejpam-2332	142	24	indicates	indicate	VERB
ejpam-2332	142	25	players	player	NOUN
ejpam-2332	142	26	/	/	SYM
ejpam-2332	142	27	dms	dms	ADJ
ejpam-2332	142	28	optimistic	optimistic	ADJ
ejpam-2332	142	29	attitude	attitude	NOUN
ejpam-2332	142	30	towards	towards	ADP
ejpam-2332	142	31	uncertainty	uncertainty	NOUN
ejpam-2332	142	32	.	.	PUNCT
ejpam-2332	143	1	also	also	ADV
ejpam-2332	143	2	λ	λ	X
ejpam-2332	143	3	=	=	SYM
ejpam-2332	143	4	1	1	NUM
ejpam-2332	143	5	2	2	NUM
ejpam-2332	143	6	shows	show	VERB
ejpam-2332	143	7	that	that	SCONJ
ejpam-2332	143	8	players	player	NOUN
ejpam-2332	143	9	/	/	SYM
ejpam-2332	143	10	dms	dm	NOUN
ejpam-2332	143	11	are	be	AUX
ejpam-2332	143	12	indifferent	indifferent	ADJ
ejpam-2332	143	13	.	.	PUNCT
ejpam-2332	144	1	thus	thus	ADV
ejpam-2332	144	2	,	,	PUNCT
ejpam-2332	144	3	the	the	DET
ejpam-2332	144	4	value	value	NOUN
ejpam-2332	144	5	index	index	NOUN
ejpam-2332	144	6	and	and	CCONJ
ejpam-2332	144	7	ambiguity	ambiguity	NOUN
ejpam-2332	144	8	index	index	NOUN
ejpam-2332	144	9	may	may	AUX
ejpam-2332	144	10	reflect	reflect	VERB
ejpam-2332	144	11	players	player	NOUN
ejpam-2332	144	12	/	/	SYM
ejpam-2332	144	13	dms	dms	PROPN
ejpam-2332	144	14	attitude	attitude	NOUN
ejpam-2332	144	15	to	to	ADP
ejpam-2332	144	16	the	the	DET
ejpam-2332	144	17	tifns	tifns	NOUN
ejpam-2332	144	18	.	.	PUNCT
ejpam-2332	145	1	if	if	SCONJ
ejpam-2332	145	2	we	we	PRON
ejpam-2332	145	3	choose	choose	VERB
ejpam-2332	145	4	λ	λ	NOUN
ejpam-2332	145	5	=	=	NOUN
ejpam-2332	145	6	1	1	NUM
ejpam-2332	145	7	2	2	NUM
ejpam-2332	145	8	,	,	PUNCT
ejpam-2332	145	9	then	then	ADV
ejpam-2332	145	10	v	v	X
ejpam-2332	145	11	(	(	PUNCT
ejpam-2332	145	12	ã	ã	PROPN
ejpam-2332	145	13	,	,	PUNCT
ejpam-2332	145	14	1	1	NUM
ejpam-2332	145	15	2	2	NUM
ejpam-2332	145	16	)	)	PUNCT
ejpam-2332	145	17	=	=	SYM
ejpam-2332	145	18	gν(ã	gν(ã	NOUN
ejpam-2332	145	19	)	)	PUNCT
ejpam-2332	146	1	+	+	CCONJ
ejpam-2332	146	2	gµ(ã	gµ(ã	NOUN
ejpam-2332	146	3	)	)	PUNCT
ejpam-2332	146	4	2	2	NUM
ejpam-2332	146	5	and	and	CCONJ
ejpam-2332	146	6	a(ã	a(ã	PROPN
ejpam-2332	146	7	,	,	PUNCT
ejpam-2332	146	8	1	1	NUM
ejpam-2332	146	9	2	2	NUM
ejpam-2332	146	10	)	)	PUNCT
ejpam-2332	146	11	=	=	SYM
ejpam-2332	147	1	hµ(ã	hµ(ã	NOUN
ejpam-2332	147	2	)	)	PUNCT
ejpam-2332	148	1	+	+	CCONJ
ejpam-2332	148	2	hν(ã	hν(ã	X
ejpam-2332	148	3	)	)	PUNCT
ejpam-2332	148	4	2	2	NUM
ejpam-2332	148	5	.	.	PUNCT
ejpam-2332	149	1	proposition	proposition	NOUN
ejpam-2332	149	2	2	2	NUM
ejpam-2332	149	3	.	.	PUNCT
ejpam-2332	150	1	let	let	VERB
ejpam-2332	150	2	ã	ã	PROPN
ejpam-2332	150	3	and	and	CCONJ
ejpam-2332	150	4	b̃	b̃	PROPN
ejpam-2332	150	5	be	be	AUX
ejpam-2332	150	6	two	two	NUM
ejpam-2332	150	7	any	any	DET
ejpam-2332	150	8	tifns	tifns	NOUN
ejpam-2332	150	9	.	.	PUNCT
ejpam-2332	151	1	then	then	ADV
ejpam-2332	151	2	for	for	ADP
ejpam-2332	151	3	any	any	DET
ejpam-2332	151	4	real	real	ADJ
ejpam-2332	151	5	number	number	NOUN
ejpam-2332	151	6	k	k	PROPN
ejpam-2332	151	7	,	,	PUNCT
ejpam-2332	151	8	the	the	DET
ejpam-2332	151	9	following	follow	VERB
ejpam-2332	151	10	equalities	equality	NOUN
ejpam-2332	151	11	are	be	AUX
ejpam-2332	151	12	valid	valid	ADJ
ejpam-2332	151	13	:	:	PUNCT
ejpam-2332	151	14	(	(	PUNCT
ejpam-2332	151	15	i	i	NOUN
ejpam-2332	151	16	)	)	PUNCT
ejpam-2332	151	17	v	v	PROPN
ejpam-2332	151	18	(	(	PUNCT
ejpam-2332	151	19	kã+	kã+	PROPN
ejpam-2332	151	20	b̃	b̃	PROPN
ejpam-2332	151	21	,	,	PUNCT
ejpam-2332	151	22	1	1	NUM
ejpam-2332	151	23	2	2	NUM
ejpam-2332	151	24	)	)	PUNCT
ejpam-2332	151	25	=	=	SYM
ejpam-2332	151	26	kv	kv	PROPN
ejpam-2332	151	27	(	(	PUNCT
ejpam-2332	151	28	ã	ã	PROPN
ejpam-2332	151	29	,	,	PUNCT
ejpam-2332	151	30	1	1	NUM
ejpam-2332	151	31	2	2	NUM
ejpam-2332	151	32	)	)	PUNCT
ejpam-2332	152	1	+	+	NUM
ejpam-2332	152	2	v	v	X
ejpam-2332	152	3	(	(	PUNCT
ejpam-2332	152	4	b̃	b̃	PROPN
ejpam-2332	152	5	,	,	PUNCT
ejpam-2332	152	6	1	1	NUM
ejpam-2332	152	7	2	2	NUM
ejpam-2332	152	8	)	)	PUNCT
ejpam-2332	152	9	(	(	PUNCT
ejpam-2332	152	10	ii	ii	NOUN
ejpam-2332	152	11	)	)	PUNCT
ejpam-2332	152	12	a(kã+	a(kã+	PROPN
ejpam-2332	152	13	b̃	b̃	PROPN
ejpam-2332	152	14	,	,	PUNCT
ejpam-2332	152	15	1	1	NUM
ejpam-2332	152	16	2	2	NUM
ejpam-2332	152	17	)	)	PUNCT
ejpam-2332	152	18	=	=	SYM
ejpam-2332	153	1	ka(ã	ka(ã	NOUN
ejpam-2332	153	2	,	,	PUNCT
ejpam-2332	153	3	1	1	NUM
ejpam-2332	153	4	2	2	NUM
ejpam-2332	153	5	)	)	PUNCT
ejpam-2332	153	6	+	+	CCONJ
ejpam-2332	153	7	a	a	DET
ejpam-2332	153	8	(	(	PUNCT
ejpam-2332	153	9	b̃	b̃	PROPN
ejpam-2332	153	10	,	,	PUNCT
ejpam-2332	153	11	1	1	NUM
ejpam-2332	153	12	2	2	NUM
ejpam-2332	153	13	)	)	PUNCT
ejpam-2332	153	14	.	.	PUNCT
ejpam-2332	154	1	it	it	PRON
ejpam-2332	154	2	can	can	AUX
ejpam-2332	154	3	be	be	AUX
ejpam-2332	154	4	easily	easily	ADV
ejpam-2332	154	5	seen	see	VERB
ejpam-2332	154	6	that	that	SCONJ
ejpam-2332	154	7	more	more	ADJ
ejpam-2332	154	8	is	be	AUX
ejpam-2332	154	9	the	the	DET
ejpam-2332	154	10	value	value	NOUN
ejpam-2332	154	11	and	and	CCONJ
ejpam-2332	154	12	lesser	less	ADJ
ejpam-2332	154	13	is	be	AUX
ejpam-2332	154	14	the	the	DET
ejpam-2332	154	15	ambiguity	ambiguity	NOUN
ejpam-2332	154	16	of	of	ADP
ejpam-2332	154	17	the	the	DET
ejpam-2332	154	18	tifn	tifn	NOUN
ejpam-2332	154	19	,	,	PUNCT
ejpam-2332	154	20	larger	large	ADJ
ejpam-2332	154	21	the	the	DET
ejpam-2332	154	22	tifn	tifn	NOUN
ejpam-2332	154	23	.	.	PUNCT
ejpam-2332	155	1	in	in	ADP
ejpam-2332	155	2	the	the	DET
ejpam-2332	155	3	following	following	NOUN
ejpam-2332	155	4	,	,	PUNCT
ejpam-2332	155	5	a	a	DET
ejpam-2332	155	6	ranking	ranking	NOUN
ejpam-2332	155	7	function	function	NOUN
ejpam-2332	155	8	is	be	AUX
ejpam-2332	155	9	defined	define	VERB
ejpam-2332	155	10	based	base	VERB
ejpam-2332	155	11	on	on	ADP
ejpam-2332	155	12	difference	difference	NOUN
ejpam-2332	155	13	of	of	ADP
ejpam-2332	155	14	value	value	NOUN
ejpam-2332	155	15	index	index	NOUN
ejpam-2332	155	16	and	and	CCONJ
ejpam-2332	155	17	ambiguity	ambiguity	NOUN
ejpam-2332	155	18	index	index	NOUN
ejpam-2332	155	19	to	to	PART
ejpam-2332	155	20	find	find	VERB
ejpam-2332	155	21	an	an	DET
ejpam-2332	155	22	order	order	NOUN
ejpam-2332	155	23	relation	relation	NOUN
ejpam-2332	155	24	between	between	ADP
ejpam-2332	155	25	two	two	NUM
ejpam-2332	155	26	tifns	tifns	NOUN
ejpam-2332	155	27	.	.	PUNCT
ejpam-2332	156	1	definition	definition	NOUN
ejpam-2332	156	2	6	6	NUM
ejpam-2332	156	3	.	.	PUNCT
ejpam-2332	157	1	a	a	DET
ejpam-2332	157	2	ranking	rank	VERB
ejpam-2332	157	3	function	function	NOUN
ejpam-2332	157	4	(	(	PUNCT
ejpam-2332	157	5	or	or	CCONJ
ejpam-2332	157	6	defuzzification	defuzzification	NOUN
ejpam-2332	157	7	function	function	NOUN
ejpam-2332	157	8	)	)	PUNCT
ejpam-2332	157	9	is	be	AUX
ejpam-2332	157	10	a	a	DET
ejpam-2332	157	11	function	function	NOUN
ejpam-2332	157	12	r	r	NOUN
ejpam-2332	157	13	:	:	PUNCT
ejpam-2332	157	14	f̃	f̃	PROPN
ejpam-2332	157	15	(	(	PUNCT
ejpam-2332	157	16	ℜ	ℜ	PROPN
ejpam-2332	157	17	)	)	PUNCT
ejpam-2332	157	18	→	→	SYM
ejpam-2332	157	19	ℜ	ℜ	PROPN
ejpam-2332	157	20	,	,	PUNCT
ejpam-2332	157	21	where	where	SCONJ
ejpam-2332	157	22	f̃	f̃	PROPN
ejpam-2332	157	23	(	(	PUNCT
ejpam-2332	157	24	ℜ	ℜ	PROPN
ejpam-2332	157	25	)	)	PUNCT
ejpam-2332	157	26	is	be	AUX
ejpam-2332	157	27	a	a	DET
ejpam-2332	157	28	set	set	NOUN
ejpam-2332	157	29	of	of	ADP
ejpam-2332	157	30	all	all	DET
ejpam-2332	157	31	tifns	tifns	NOUN
ejpam-2332	157	32	defined	define	VERB
ejpam-2332	157	33	on	on	ADP
ejpam-2332	157	34	ℜ	ℜ	PROPN
ejpam-2332	157	35	,	,	PUNCT
ejpam-2332	157	36	which	which	PRON
ejpam-2332	157	37	maps	map	VERB
ejpam-2332	157	38	each	each	DET
ejpam-2332	157	39	tifn	tifn	NOUN
ejpam-2332	157	40	into	into	ADP
ejpam-2332	157	41	the	the	DET
ejpam-2332	157	42	real	real	ADJ
ejpam-2332	157	43	line	line	NOUN
ejpam-2332	157	44	,	,	PUNCT
ejpam-2332	157	45	where	where	SCONJ
ejpam-2332	157	46	a	a	DET
ejpam-2332	157	47	natural	natural	ADJ
ejpam-2332	157	48	order	order	NOUN
ejpam-2332	157	49	exists	exist	VERB
ejpam-2332	157	50	.	.	PUNCT
ejpam-2332	158	1	let	let	VERB
ejpam-2332	158	2	ã	ã	PROPN
ejpam-2332	158	3	be	be	AUX
ejpam-2332	158	4	a	a	DET
ejpam-2332	158	5	tifn	tifn	NOUN
ejpam-2332	158	6	,	,	PUNCT
ejpam-2332	158	7	then	then	ADV
ejpam-2332	158	8	r(ã	r(ã	PROPN
ejpam-2332	158	9	)	)	PUNCT
ejpam-2332	158	10	=	=	SYM
ejpam-2332	158	11	v	v	X
ejpam-2332	158	12	(	(	PUNCT
ejpam-2332	158	13	ã	ã	PROPN
ejpam-2332	158	14	,	,	PUNCT
ejpam-2332	158	15	1	1	NUM
ejpam-2332	158	16	2)−	2)−	NUM
ejpam-2332	158	17	a(ã	a(ã	PROPN
ejpam-2332	158	18	,	,	PUNCT
ejpam-2332	158	19	1	1	NUM
ejpam-2332	158	20	2	2	NUM
ejpam-2332	158	21	)	)	PUNCT
ejpam-2332	158	22	.	.	PUNCT
ejpam-2332	159	1	suppose	suppose	VERB
ejpam-2332	159	2	that	that	SCONJ
ejpam-2332	159	3	ã	ã	PROPN
ejpam-2332	159	4	and	and	CCONJ
ejpam-2332	159	5	b̃	b̃	PROPN
ejpam-2332	159	6	be	be	AUX
ejpam-2332	159	7	two	two	NUM
ejpam-2332	159	8	tifns	tifns	NOUN
ejpam-2332	159	9	and	and	CCONJ
ejpam-2332	159	10	λ	λ	X
ejpam-2332	159	11	∈	∈	PROPN
ejpam-2332	160	1	[	[	X
ejpam-2332	160	2	0,1	0,1	NUM
ejpam-2332	160	3	]	]	PUNCT
ejpam-2332	160	4	be	be	VERB
ejpam-2332	160	5	any	any	DET
ejpam-2332	160	6	real	real	ADJ
ejpam-2332	160	7	number	number	NOUN
ejpam-2332	160	8	.	.	PUNCT
ejpam-2332	161	1	then	then	ADV
ejpam-2332	161	2	a	a	DET
ejpam-2332	161	3	new	new	ADJ
ejpam-2332	161	4	order	order	NOUN
ejpam-2332	161	5	relation	relation	NOUN
ejpam-2332	161	6	between	between	ADP
ejpam-2332	161	7	ã	ã	PROPN
ejpam-2332	161	8	and	and	CCONJ
ejpam-2332	161	9	b̃	b̃	PROPN
ejpam-2332	161	10	is	be	AUX
ejpam-2332	161	11	defined	define	VERB
ejpam-2332	161	12	as	as	SCONJ
ejpam-2332	161	13	follows	follow	VERB
ejpam-2332	161	14	:	:	PUNCT
ejpam-2332	161	15	(	(	PUNCT
ejpam-2332	161	16	i	i	NOUN
ejpam-2332	161	17	)	)	PUNCT
ejpam-2332	161	18	ãe≥	ãe≥	PROPN
ejpam-2332	162	1	b̃	b̃	PROPN
ejpam-2332	162	2	iff	iff	VERB
ejpam-2332	162	3	r(ã)≥	r(ã)≥	PROPN
ejpam-2332	162	4	r	r	PROPN
ejpam-2332	162	5	(	(	PUNCT
ejpam-2332	162	6	b̃	b̃	PROPN
ejpam-2332	162	7	)	)	PUNCT
ejpam-2332	162	8	(	(	PUNCT
ejpam-2332	162	9	ii	ii	NOUN
ejpam-2332	162	10	)	)	PUNCT
ejpam-2332	162	11	ãe≤	ãe≤	PROPN
ejpam-2332	163	1	b̃	b̃	PROPN
ejpam-2332	163	2	iff	iff	PROPN
ejpam-2332	163	3	r(ã)≤	r(ã)≤	PRON
ejpam-2332	163	4	r	r	NOUN
ejpam-2332	163	5	(	(	PUNCT
ejpam-2332	163	6	b̃	b̃	PROPN
ejpam-2332	163	7	)	)	PUNCT
ejpam-2332	163	8	(	(	PUNCT
ejpam-2332	163	9	iii	iii	NOUN
ejpam-2332	163	10	)	)	PUNCT
ejpam-2332	163	11	ãe=	ãe=	PROPN
ejpam-2332	163	12	b̃	b̃	PROPN
ejpam-2332	163	13	iff	iff	PROPN
ejpam-2332	163	14	r(ã	r(ã	PROPN
ejpam-2332	163	15	)	)	PUNCT
ejpam-2332	163	16	=	=	SYM
ejpam-2332	164	1	r	r	X
ejpam-2332	164	2	(	(	PUNCT
ejpam-2332	164	3	b̃	b̃	PROPN
ejpam-2332	164	4	)	)	PUNCT
ejpam-2332	164	5	.	.	PUNCT
ejpam-2332	165	1	m.	m.	NOUN
ejpam-2332	165	2	seikh	seikh	PROPN
ejpam-2332	165	3	,	,	PUNCT
ejpam-2332	165	4	p.	p.	PROPN
ejpam-2332	165	5	nayak	nayak	PROPN
ejpam-2332	165	6	,	,	PUNCT
ejpam-2332	165	7	m.	m.	NOUN
ejpam-2332	165	8	pal	pal	PROPN
ejpam-2332	165	9	/	/	SYM
ejpam-2332	165	10	eur	eur	PROPN
ejpam-2332	165	11	.	.	PUNCT
ejpam-2332	166	1	j.	j.	PROPN
ejpam-2332	166	2	pure	pure	PROPN
ejpam-2332	166	3	appl	appl	PROPN
ejpam-2332	166	4	.	.	PROPN
ejpam-2332	166	5	math	math	PROPN
ejpam-2332	166	6	,	,	PUNCT
ejpam-2332	166	7	8	8	NUM
ejpam-2332	166	8	(	(	PUNCT
ejpam-2332	166	9	2015	2015	NUM
ejpam-2332	166	10	)	)	PUNCT
ejpam-2332	166	11	,	,	PUNCT
ejpam-2332	166	12	153	153	NUM
ejpam-2332	166	13	-	-	SYM
ejpam-2332	166	14	171	171	NUM
ejpam-2332	166	15	159	159	NUM
ejpam-2332	166	16	the	the	DET
ejpam-2332	166	17	symbol	symbol	NOUN
ejpam-2332	166	18	“	"	PUNCT
ejpam-2332	166	19	e≥	e≥	PROPN
ejpam-2332	166	20	”	"	PUNCT
ejpam-2332	166	21	is	be	AUX
ejpam-2332	166	22	an	an	DET
ejpam-2332	166	23	intuitionistic	intuitionistic	ADJ
ejpam-2332	166	24	fuzzy	fuzzy	ADJ
ejpam-2332	166	25	version	version	NOUN
ejpam-2332	166	26	of	of	ADP
ejpam-2332	166	27	the	the	DET
ejpam-2332	166	28	order	order	NOUN
ejpam-2332	166	29	relation	relation	NOUN
ejpam-2332	166	30	“	"	PUNCT
ejpam-2332	166	31	≥	≥	NOUN
ejpam-2332	166	32	”	"	PUNCT
ejpam-2332	166	33	on	on	ADP
ejpam-2332	166	34	the	the	DET
ejpam-2332	166	35	set	set	NOUN
ejpam-2332	166	36	of	of	ADP
ejpam-2332	166	37	real	real	ADJ
ejpam-2332	166	38	numbers	number	NOUN
ejpam-2332	166	39	and	and	CCONJ
ejpam-2332	166	40	has	have	VERB
ejpam-2332	166	41	the	the	DET
ejpam-2332	166	42	linguistic	linguistic	ADJ
ejpam-2332	166	43	interpretation	interpretation	NOUN
ejpam-2332	166	44	as	as	ADP
ejpam-2332	166	45	“	"	PUNCT
ejpam-2332	166	46	essentially	essentially	ADV
ejpam-2332	166	47	greater	great	ADJ
ejpam-2332	166	48	than	than	ADP
ejpam-2332	166	49	or	or	CCONJ
ejpam-2332	166	50	equal	equal	ADJ
ejpam-2332	166	51	to”ṡimilarly	to”ṡimilarly	ADP
ejpam-2332	166	52	,	,	PUNCT
ejpam-2332	166	53	the	the	DET
ejpam-2332	166	54	symbols	symbol	NOUN
ejpam-2332	166	55	“	"	PUNCT
ejpam-2332	166	56	e≤	e≤	PROPN
ejpam-2332	166	57	”	"	PUNCT
ejpam-2332	166	58	and	and	CCONJ
ejpam-2332	166	59	“	"	PUNCT
ejpam-2332	166	60	e=	e=	NOUN
ejpam-2332	166	61	”	"	PUNCT
ejpam-2332	166	62	are	be	AUX
ejpam-2332	166	63	the	the	DET
ejpam-2332	166	64	intuitionistic	intuitionistic	ADJ
ejpam-2332	166	65	fuzzy	fuzzy	ADJ
ejpam-2332	166	66	versions	version	NOUN
ejpam-2332	166	67	of	of	ADP
ejpam-2332	166	68	the	the	DET
ejpam-2332	166	69	order	order	NOUN
ejpam-2332	166	70	relations	relation	NOUN
ejpam-2332	166	71	“	"	PUNCT
ejpam-2332	166	72	≤	≤	NUM
ejpam-2332	166	73	”	"	PUNCT
ejpam-2332	166	74	and	and	CCONJ
ejpam-2332	166	75	“	"	PUNCT
ejpam-2332	166	76	=	=	NOUN
ejpam-2332	166	77	”	"	PUNCT
ejpam-2332	166	78	on	on	ADP
ejpam-2332	166	79	the	the	DET
ejpam-2332	166	80	set	set	NOUN
ejpam-2332	166	81	of	of	ADP
ejpam-2332	166	82	real	real	ADJ
ejpam-2332	166	83	numbers	number	NOUN
ejpam-2332	166	84	and	and	CCONJ
ejpam-2332	166	85	have	have	VERB
ejpam-2332	166	86	the	the	DET
ejpam-2332	166	87	linguistic	linguistic	ADJ
ejpam-2332	166	88	interpretations	interpretation	NOUN
ejpam-2332	166	89	“	"	PUNCT
ejpam-2332	166	90	essentially	essentially	ADV
ejpam-2332	166	91	less	less	ADJ
ejpam-2332	166	92	than	than	ADP
ejpam-2332	166	93	or	or	CCONJ
ejpam-2332	166	94	equal	equal	ADJ
ejpam-2332	166	95	to	to	ADP
ejpam-2332	166	96	”	"	PUNCT
ejpam-2332	166	97	and	and	CCONJ
ejpam-2332	166	98	“	"	PUNCT
ejpam-2332	166	99	essentially	essentially	ADV
ejpam-2332	166	100	equal	equal	ADJ
ejpam-2332	166	101	to	to	ADP
ejpam-2332	166	102	”	"	PUNCT
ejpam-2332	166	103	,	,	PUNCT
ejpam-2332	166	104	respectively	respectively	ADV
ejpam-2332	166	105	.	.	PUNCT
ejpam-2332	167	1	it	it	PRON
ejpam-2332	167	2	can	can	AUX
ejpam-2332	167	3	be	be	AUX
ejpam-2332	167	4	easily	easily	ADV
ejpam-2332	167	5	verified	verify	VERB
ejpam-2332	167	6	that	that	SCONJ
ejpam-2332	167	7	the	the	DET
ejpam-2332	167	8	above	above	ADJ
ejpam-2332	167	9	proposed	propose	VERB
ejpam-2332	167	10	ranking	ranking	NOUN
ejpam-2332	167	11	method	method	NOUN
ejpam-2332	167	12	satisfies	satisfy	VERB
ejpam-2332	167	13	some	some	PRON
ejpam-2332	167	14	of	of	ADP
ejpam-2332	167	15	the	the	DET
ejpam-2332	167	16	axioms	axiom	NOUN
ejpam-2332	167	17	namely	namely	ADV
ejpam-2332	167	18	the	the	DET
ejpam-2332	167	19	reasonable	reasonable	ADJ
ejpam-2332	167	20	properties	property	NOUN
ejpam-2332	167	21	proposed	propose	VERB
ejpam-2332	167	22	by	by	ADP
ejpam-2332	167	23	wang	wang	PROPN
ejpam-2332	167	24	and	and	CCONJ
ejpam-2332	167	25	kerre	kerre	PRON
ejpam-2332	168	1	[	[	X
ejpam-2332	168	2	35	35	NUM
ejpam-2332	168	3	]	]	PUNCT
ejpam-2332	168	4	.	.	PUNCT
ejpam-2332	169	1	proposition	proposition	NOUN
ejpam-2332	169	2	3	3	X
ejpam-2332	169	3	.	.	PUNCT
ejpam-2332	170	1	let	let	VERB
ejpam-2332	170	2	ã	ã	PROPN
ejpam-2332	170	3	and	and	CCONJ
ejpam-2332	170	4	b̃	b̃	PROPN
ejpam-2332	170	5	be	be	AUX
ejpam-2332	170	6	any	any	DET
ejpam-2332	170	7	two	two	NUM
ejpam-2332	170	8	tifns	tifns	NOUN
ejpam-2332	170	9	,	,	PUNCT
ejpam-2332	170	10	then	then	ADV
ejpam-2332	170	11	for	for	ADP
ejpam-2332	170	12	any	any	DET
ejpam-2332	170	13	real	real	ADJ
ejpam-2332	170	14	number	number	NOUN
ejpam-2332	170	15	k	k	PROPN
ejpam-2332	170	16	,	,	PUNCT
ejpam-2332	170	17	the	the	DET
ejpam-2332	170	18	following	follow	VERB
ejpam-2332	170	19	equality	equality	NOUN
ejpam-2332	170	20	is	be	AUX
ejpam-2332	170	21	valid	valid	ADJ
ejpam-2332	170	22	r(kã+	r(kã+	NOUN
ejpam-2332	170	23	b̃	b̃	PROPN
ejpam-2332	170	24	)	)	PUNCT
ejpam-2332	171	1	=	=	PUNCT
ejpam-2332	171	2	kr(ã	kr(ã	PROPN
ejpam-2332	171	3	)	)	PUNCT
ejpam-2332	172	1	+	+	X
ejpam-2332	172	2	r	r	X
ejpam-2332	172	3	(	(	PUNCT
ejpam-2332	172	4	b̃	b̃	PROPN
ejpam-2332	172	5	)	)	PUNCT
ejpam-2332	172	6	.	.	PUNCT
ejpam-2332	173	1	this	this	PRON
ejpam-2332	173	2	shows	show	VERB
ejpam-2332	173	3	that	that	SCONJ
ejpam-2332	173	4	the	the	DET
ejpam-2332	173	5	proposed	propose	VERB
ejpam-2332	173	6	ranking	ranking	NOUN
ejpam-2332	173	7	function	function	NOUN
ejpam-2332	173	8	is	be	AUX
ejpam-2332	173	9	linear	linear	ADJ
ejpam-2332	173	10	.	.	PUNCT
ejpam-2332	174	1	in	in	ADP
ejpam-2332	174	2	the	the	DET
ejpam-2332	174	3	next	next	ADJ
ejpam-2332	174	4	section	section	NOUN
ejpam-2332	174	5	the	the	DET
ejpam-2332	174	6	concept	concept	NOUN
ejpam-2332	174	7	of	of	ADP
ejpam-2332	174	8	double	double	ADJ
ejpam-2332	174	9	i	i	NOUN
ejpam-2332	174	10	-	-	PUNCT
ejpam-2332	174	11	fuzzy	fuzzy	ADJ
ejpam-2332	174	12	inequalities	inequality	NOUN
ejpam-2332	174	13	,	,	PUNCT
ejpam-2332	174	14	i.e.	i.e.	X
ejpam-2332	174	15	,	,	PUNCT
ejpam-2332	174	16	the	the	DET
ejpam-2332	174	17	i	i	NOUN
ejpam-2332	174	18	-	-	PUNCT
ejpam-2332	174	19	fuzzy	fuzzy	ADJ
ejpam-2332	174	20	constraints	constraint	NOUN
ejpam-2332	174	21	involving	involve	VERB
ejpam-2332	174	22	i	i	PROPN
ejpam-2332	174	23	-	-	PUNCT
ejpam-2332	174	24	fuzzy	fuzzy	ADJ
ejpam-2332	174	25	numbers	number	NOUN
ejpam-2332	174	26	is	be	AUX
ejpam-2332	174	27	interpreted	interpret	VERB
ejpam-2332	174	28	.	.	PUNCT
ejpam-2332	175	1	3	3	X
ejpam-2332	175	2	.	.	X
ejpam-2332	175	3	interpretation	interpretation	NOUN
ejpam-2332	175	4	of	of	ADP
ejpam-2332	175	5	double	double	ADJ
ejpam-2332	175	6	i	i	NOUN
ejpam-2332	175	7	-	-	PUNCT
ejpam-2332	175	8	fuzzy	fuzzy	ADJ
ejpam-2332	175	9	constraints	constraint	NOUN
ejpam-2332	175	10	let	let	VERB
ejpam-2332	175	11	us	we	PRON
ejpam-2332	175	12	recall	recall	VERB
ejpam-2332	175	13	the	the	DET
ejpam-2332	175	14	concept	concept	NOUN
ejpam-2332	175	15	of	of	ADP
ejpam-2332	175	16	double	double	ADJ
ejpam-2332	175	17	fuzzy	fuzzy	ADJ
ejpam-2332	175	18	constraints	constraint	NOUN
ejpam-2332	175	19	(	(	PUNCT
ejpam-2332	175	20	vidyottama	vidyottama	NOUN
ejpam-2332	175	21	et	et	PROPN
ejpam-2332	175	22	al	al	PROPN
ejpam-2332	175	23	.	.	PUNCT
ejpam-2332	176	1	[	[	X
ejpam-2332	176	2	32	32	NUM
ejpam-2332	176	3	]	]	NUM
ejpam-2332	176	4	)	)	PUNCT
ejpam-2332	176	5	,	,	PUNCT
ejpam-2332	176	6	i.e.	i.e.	X
ejpam-2332	176	7	,	,	PUNCT
ejpam-2332	176	8	constraints	constraint	NOUN
ejpam-2332	176	9	which	which	PRON
ejpam-2332	176	10	are	be	AUX
ejpam-2332	176	11	expressed	express	VERB
ejpam-2332	176	12	as	as	ADP
ejpam-2332	176	13	fuzzy	fuzzy	ADJ
ejpam-2332	176	14	inequalities	inequality	NOUN
ejpam-2332	176	15	involving	involve	VERB
ejpam-2332	176	16	fuzzy	fuzzy	ADJ
ejpam-2332	176	17	numbers	number	NOUN
ejpam-2332	176	18	.	.	PUNCT
ejpam-2332	177	1	for	for	ADP
ejpam-2332	177	2	this	this	PRON
ejpam-2332	177	3	,	,	PUNCT
ejpam-2332	177	4	letn	letn	NOUN
ejpam-2332	177	5	(	(	PUNCT
ejpam-2332	177	6	ℜ	ℜ	PROPN
ejpam-2332	177	7	)	)	PUNCT
ejpam-2332	177	8	be	be	AUX
ejpam-2332	177	9	the	the	DET
ejpam-2332	177	10	set	set	NOUN
ejpam-2332	177	11	of	of	ADP
ejpam-2332	177	12	all	all	DET
ejpam-2332	177	13	fuzzy	fuzzy	ADJ
ejpam-2332	177	14	numbers	number	NOUN
ejpam-2332	177	15	.	.	PUNCT
ejpam-2332	178	1	also	also	ADV
ejpam-2332	178	2	let	let	VERB
ejpam-2332	178	3	s̃	s̃	PROPN
ejpam-2332	178	4	,	,	PUNCT
ejpam-2332	178	5	w̃	w̃	PROPN
ejpam-2332	178	6	,	,	PUNCT
ejpam-2332	178	7	respectively	respectively	ADV
ejpam-2332	178	8	,	,	PUNCT
ejpam-2332	178	9	be	be	AUX
ejpam-2332	178	10	m×	m×	PROPN
ejpam-2332	178	11	n	n	DET
ejpam-2332	178	12	matrix	matrix	VERB
ejpam-2332	178	13	and	and	CCONJ
ejpam-2332	178	14	m×	m×	PROPN
ejpam-2332	178	15	1	1	NUM
ejpam-2332	178	16	vector	vector	NOUN
ejpam-2332	178	17	having	have	VERB
ejpam-2332	178	18	entries	entry	NOUN
ejpam-2332	178	19	from	from	ADP
ejpam-2332	178	20	n	n	PRON
ejpam-2332	178	21	(	(	PUNCT
ejpam-2332	178	22	ℜ	ℜ	PROPN
ejpam-2332	178	23	)	)	PUNCT
ejpam-2332	178	24	and	and	CCONJ
ejpam-2332	178	25	the	the	DET
ejpam-2332	178	26	double	double	ADJ
ejpam-2332	178	27	fuzzy	fuzzy	ADJ
ejpam-2332	178	28	constraints	constraint	NOUN
ejpam-2332	178	29	under	under	ADP
ejpam-2332	178	30	consideration	consideration	NOUN
ejpam-2332	178	31	be	be	AUX
ejpam-2332	178	32	given	give	VERB
ejpam-2332	178	33	by	by	ADP
ejpam-2332	178	34	x	x	PROPN
ejpam-2332	178	35	t	t	PROPN
ejpam-2332	178	36	s̃y	s̃y	PROPN
ejpam-2332	178	37	�	�	PROPN
ejpam-2332	178	38	p̃	p̃	PROPN
ejpam-2332	178	39	w̃	w̃	PROPN
ejpam-2332	178	40	and	and	CCONJ
ejpam-2332	178	41	x	x	PROPN
ejpam-2332	178	42	t	t	PROPN
ejpam-2332	178	43	s̃y	s̃y	PROPN
ejpam-2332	178	44	�	�	PROPN
ejpam-2332	178	45	p̃′	p̃′	PROPN
ejpam-2332	178	46	w̃	w̃	PROPN
ejpam-2332	178	47	,	,	PUNCT
ejpam-2332	178	48	with	with	ADP
ejpam-2332	178	49	adequacies	adequacy	NOUN
ejpam-2332	178	50	p̃	p̃	PROPN
ejpam-2332	178	51	and	and	CCONJ
ejpam-2332	178	52	p̃′	p̃′	PROPN
ejpam-2332	178	53	,	,	PUNCT
ejpam-2332	178	54	respectively	respectively	ADV
ejpam-2332	178	55	.	.	PUNCT
ejpam-2332	179	1	then	then	ADV
ejpam-2332	179	2	the	the	DET
ejpam-2332	179	3	double	double	ADJ
ejpam-2332	179	4	fuzzy	fuzzy	ADJ
ejpam-2332	179	5	constraints	constraint	NOUN
ejpam-2332	179	6	x	x	X
ejpam-2332	179	7	t	t	PROPN
ejpam-2332	179	8	s̃y	s̃y	PROPN
ejpam-2332	179	9	�	�	PROPN
ejpam-2332	179	10	p̃	p̃	PROPN
ejpam-2332	179	11	w̃	w̃	PROPN
ejpam-2332	179	12	and	and	CCONJ
ejpam-2332	179	13	x	x	PROPN
ejpam-2332	179	14	t	t	PROPN
ejpam-2332	179	15	s̃y	s̃y	PROPN
ejpam-2332	179	16	�	�	PROPN
ejpam-2332	179	17	p̃′	p̃′	PROPN
ejpam-2332	179	18	w̃	w̃	PROPN
ejpam-2332	179	19	can	can	AUX
ejpam-2332	179	20	be	be	AUX
ejpam-2332	179	21	expressed	express	VERB
ejpam-2332	179	22	as	as	ADP
ejpam-2332	179	23	x	x	PROPN
ejpam-2332	179	24	t	t	PROPN
ejpam-2332	179	25	s̃y	s̃y	PROPN
ejpam-2332	179	26	�	�	PROPN
ejpam-2332	179	27	f	f	PROPN
ejpam-2332	179	28	w̃+	w̃+	PROPN
ejpam-2332	179	29	p̃(1−ρ	p̃(1−ρ	NOUN
ejpam-2332	179	30	)	)	PUNCT
ejpam-2332	179	31	,	,	PUNCT
ejpam-2332	179	32	ρ	ρ	PROPN
ejpam-2332	179	33	∈	∈	PROPN
ejpam-2332	180	1	[	[	X
ejpam-2332	180	2	0,1	0,1	NUM
ejpam-2332	180	3	]	]	PUNCT
ejpam-2332	180	4	and	and	CCONJ
ejpam-2332	180	5	x	x	SYM
ejpam-2332	180	6	t	t	PROPN
ejpam-2332	180	7	s̃y	s̃y	PROPN
ejpam-2332	180	8	�	�	PROPN
ejpam-2332	180	9	f	f	PROPN
ejpam-2332	180	10	w̃−	w̃−	PROPN
ejpam-2332	180	11	p̃′(1−ρ	p̃′(1−ρ	NOUN
ejpam-2332	180	12	)	)	PUNCT
ejpam-2332	180	13	,	,	PUNCT
ejpam-2332	180	14	ρ	ρ	PROPN
ejpam-2332	180	15	∈	∈	PROPN
ejpam-2332	181	1	[	[	X
ejpam-2332	181	2	0,1	0,1	NUM
ejpam-2332	181	3	]	]	PUNCT
ejpam-2332	181	4	,	,	PUNCT
ejpam-2332	181	5	where	where	SCONJ
ejpam-2332	181	6	p̃	p̃	PROPN
ejpam-2332	181	7	and	and	CCONJ
ejpam-2332	181	8	p̃′	p̃′	PROPN
ejpam-2332	181	9	measure	measure	NOUN
ejpam-2332	181	10	the	the	DET
ejpam-2332	181	11	adequacy	adequacy	NOUN
ejpam-2332	181	12	between	between	ADP
ejpam-2332	181	13	the	the	DET
ejpam-2332	181	14	fuzzy	fuzzy	ADJ
ejpam-2332	181	15	numbers	number	NOUN
ejpam-2332	181	16	x	x	X
ejpam-2332	181	17	t	t	X
ejpam-2332	181	18	s̃y	s̃y	NOUN
ejpam-2332	181	19	and	and	CCONJ
ejpam-2332	181	20	w̃.	w̃.	PROPN
ejpam-2332	181	21	here	here	ADV
ejpam-2332	181	22	�	�	PROPN
ejpam-2332	181	23	f	f	PROPN
ejpam-2332	181	24	and	and	CCONJ
ejpam-2332	181	25	�	�	PROPN
ejpam-2332	181	26	f	f	PROPN
ejpam-2332	181	27	are	be	AUX
ejpam-2332	181	28	the	the	DET
ejpam-2332	181	29	relations	relation	NOUN
ejpam-2332	181	30	between	between	ADP
ejpam-2332	181	31	fuzzy	fuzzy	ADJ
ejpam-2332	181	32	numbers	number	NOUN
ejpam-2332	181	33	.	.	PUNCT
ejpam-2332	182	1	we	we	PRON
ejpam-2332	182	2	now	now	ADV
ejpam-2332	182	3	extend	extend	VERB
ejpam-2332	182	4	the	the	DET
ejpam-2332	182	5	interpretation	interpretation	NOUN
ejpam-2332	182	6	of	of	ADP
ejpam-2332	182	7	double	double	ADJ
ejpam-2332	182	8	fuzzy	fuzzy	ADJ
ejpam-2332	182	9	constraints	constraint	NOUN
ejpam-2332	182	10	to	to	ADP
ejpam-2332	182	11	the	the	DET
ejpam-2332	182	12	i	i	NOUN
ejpam-2332	182	13	-	-	PUNCT
ejpam-2332	182	14	fuzzy	fuzzy	ADJ
ejpam-2332	182	15	sense	sense	NOUN
ejpam-2332	182	16	.	.	PUNCT
ejpam-2332	183	1	let	let	VERB
ejpam-2332	183	2	s̃	s̃	PROPN
ejpam-2332	183	3	,	,	PUNCT
ejpam-2332	183	4	b̃	b̃	PROPN
ejpam-2332	183	5	and	and	CCONJ
ejpam-2332	183	6	c̃	c̃	PROPN
ejpam-2332	183	7	respectively	respectively	ADV
ejpam-2332	183	8	,	,	PUNCT
ejpam-2332	183	9	be	be	AUX
ejpam-2332	183	10	m×n	m×n	ADJ
ejpam-2332	183	11	matrix	matrix	NOUN
ejpam-2332	183	12	,	,	PUNCT
ejpam-2332	183	13	m×1	m×1	NOUN
ejpam-2332	183	14	and	and	CCONJ
ejpam-2332	183	15	n×1	n×1	NOUN
ejpam-2332	183	16	vectors	vector	NOUN
ejpam-2332	183	17	having	have	VERB
ejpam-2332	183	18	entries	entry	NOUN
ejpam-2332	183	19	from	from	ADP
ejpam-2332	183	20	f̃	f̃	PROPN
ejpam-2332	183	21	(	(	PUNCT
ejpam-2332	183	22	ℜ	ℜ	PROPN
ejpam-2332	183	23	)	)	PUNCT
ejpam-2332	183	24	,	,	PUNCT
ejpam-2332	183	25	and	and	CCONJ
ejpam-2332	183	26	the	the	DET
ejpam-2332	183	27	double	double	ADJ
ejpam-2332	183	28	i	i	NOUN
ejpam-2332	183	29	-	-	PUNCT
ejpam-2332	183	30	fuzzy	fuzzy	ADJ
ejpam-2332	183	31	constraints	constraint	NOUN
ejpam-2332	183	32	under	under	ADP
ejpam-2332	183	33	consideration	consideration	NOUN
ejpam-2332	183	34	be	be	AUX
ejpam-2332	183	35	given	give	VERB
ejpam-2332	183	36	by	by	ADP
ejpam-2332	183	37	s̃t	s̃t	NUM
ejpam-2332	183	38	y	y	PROPN
ejpam-2332	183	39	e	e	PROPN
ejpam-2332	183	40	�	�	PROPN
ejpam-2332	183	41	p̃,q̃	p̃,q̃	PROPN
ejpam-2332	183	42	c̃	c̃	PROPN
ejpam-2332	183	43	and	and	CCONJ
ejpam-2332	183	44	s̃x	s̃x	PROPN
ejpam-2332	183	45	e	e	PROPN
ejpam-2332	183	46	�	�	PROPN
ejpam-2332	183	47	r̃,s̃	r̃,s̃	PROPN
ejpam-2332	183	48	b̃	b̃	PROPN
ejpam-2332	183	49	,	,	PUNCT
ejpam-2332	183	50	with	with	ADP
ejpam-2332	183	51	the	the	DET
ejpam-2332	183	52	adequacies	adequacy	NOUN
ejpam-2332	183	53	/	/	SYM
ejpam-2332	183	54	tolerances	tolerance	NOUN
ejpam-2332	183	55	p̃	p̃	PROPN
ejpam-2332	183	56	,	,	PUNCT
ejpam-2332	183	57	q̃	q̃	PROPN
ejpam-2332	183	58	and	and	CCONJ
ejpam-2332	183	59	r̃	r̃	PROPN
ejpam-2332	183	60	,	,	PUNCT
ejpam-2332	183	61	s̃	s̃	PROPN
ejpam-2332	183	62	,	,	PUNCT
ejpam-2332	183	63	respectively	respectively	ADV
ejpam-2332	183	64	,	,	PUNCT
ejpam-2332	183	65	which	which	PRON
ejpam-2332	183	66	are	be	AUX
ejpam-2332	183	67	also	also	ADV
ejpam-2332	183	68	i	i	NOUN
ejpam-2332	183	69	-	-	PUNCT
ejpam-2332	183	70	fuzzy	fuzzy	ADJ
ejpam-2332	183	71	vectors	vector	NOUN
ejpam-2332	183	72	.	.	PUNCT
ejpam-2332	184	1	based	base	VERB
ejpam-2332	184	2	on	on	ADP
ejpam-2332	184	3	the	the	DET
ejpam-2332	184	4	resolution	resolution	NOUN
ejpam-2332	184	5	method	method	NOUN
ejpam-2332	184	6	discussed	discuss	VERB
ejpam-2332	184	7	above	above	ADV
ejpam-2332	184	8	we	we	PRON
ejpam-2332	184	9	extend	extend	VERB
ejpam-2332	184	10	the	the	DET
ejpam-2332	184	11	interpretation	interpretation	NOUN
ejpam-2332	184	12	of	of	ADP
ejpam-2332	184	13	i	i	PROPN
ejpam-2332	184	14	-	-	PUNCT
ejpam-2332	184	15	fuzzy	fuzzy	ADJ
ejpam-2332	184	16	inequalities	inequality	NOUN
ejpam-2332	184	17	to	to	ADP
ejpam-2332	184	18	the	the	DET
ejpam-2332	184	19	case	case	NOUN
ejpam-2332	184	20	where	where	SCONJ
ejpam-2332	184	21	the	the	DET
ejpam-2332	184	22	parameters	parameter	NOUN
ejpam-2332	184	23	and	and	CCONJ
ejpam-2332	184	24	the	the	DET
ejpam-2332	184	25	adequacies	adequacy	NOUN
ejpam-2332	184	26	are	be	AUX
ejpam-2332	184	27	also	also	ADV
ejpam-2332	184	28	i	i	NOUN
ejpam-2332	184	29	-	-	PUNCT
ejpam-2332	184	30	fuzzy	fuzzy	ADJ
ejpam-2332	184	31	number	number	NOUN
ejpam-2332	184	32	.	.	PUNCT
ejpam-2332	185	1	therefore	therefore	ADV
ejpam-2332	185	2	,	,	PUNCT
ejpam-2332	185	3	the	the	DET
ejpam-2332	185	4	double	double	ADJ
ejpam-2332	185	5	i	i	NOUN
ejpam-2332	185	6	-	-	PUNCT
ejpam-2332	185	7	fuzzy	fuzzy	ADJ
ejpam-2332	185	8	constraint	constraint	NOUN
ejpam-2332	185	9	conditions	condition	NOUN
ejpam-2332	185	10	are	be	AUX
ejpam-2332	185	11	to	to	PART
ejpam-2332	185	12	be	be	AUX
ejpam-2332	185	13	understood	understand	VERB
ejpam-2332	185	14	as	as	ADP
ejpam-2332	185	15	s̃t	s̃t	PROPN
ejpam-2332	185	16	y	y	PROPN
ejpam-2332	185	17	e	e	PROPN
ejpam-2332	185	18	�	�	PROPN
ejpam-2332	185	19	p̃,q̃	p̃,q̃	PROPN
ejpam-2332	185	20	c̃	c̃	PROPN
ejpam-2332	185	21	⇒	⇒	NOUN
ejpam-2332	185	22	¨	¨	NOUN
ejpam-2332	185	23	s̃iy	s̃iy	PROPN
ejpam-2332	185	24	e	e	PROPN
ejpam-2332	185	25	�	�	PROPN
ejpam-2332	185	26	c̃i	c̃i	NOUN
ejpam-2332	185	27	+	+	CCONJ
ejpam-2332	185	28	p̃i(1−	p̃i(1−	NUM
ejpam-2332	185	29	ξ	ξ	NOUN
ejpam-2332	185	30	)	)	PUNCT
ejpam-2332	185	31	,	,	PUNCT
ejpam-2332	185	32	0≤	0≤	SYM
ejpam-2332	185	33	ξ≤	ξ≤	PROPN
ejpam-2332	185	34	1	1	NUM
ejpam-2332	185	35	s̃iy	s̃iy	PROPN
ejpam-2332	185	36	e	e	PROPN
ejpam-2332	185	37	�	�	PROPN
ejpam-2332	185	38	(c̃i	(c̃i	ADJ
ejpam-2332	185	39	+	+	NUM
ejpam-2332	185	40	p̃i)−	p̃i)−	PROPN
ejpam-2332	185	41	q̃i(1−η	q̃i(1−η	NOUN
ejpam-2332	185	42	)	)	PUNCT
ejpam-2332	185	43	,	,	PUNCT
ejpam-2332	185	44	0≤	0≤	NUM
ejpam-2332	185	45	η	η	PROPN
ejpam-2332	185	46	≤	≤	ADJ
ejpam-2332	185	47	1	1	NUM
ejpam-2332	185	48	(	(	PUNCT
ejpam-2332	185	49	9	9	NUM
ejpam-2332	185	50	)	)	PUNCT
ejpam-2332	185	51	and	and	CCONJ
ejpam-2332	185	52	s̃x	s̃x	NUM
ejpam-2332	185	53	e	e	NOUN
ejpam-2332	185	54	�	�	PROPN
ejpam-2332	185	55	r̃,s̃	r̃,s̃	NOUN
ejpam-2332	185	56	b̃⇒	b̃⇒	X
ejpam-2332	185	57	¨	¨	NOUN
ejpam-2332	185	58	s̃	s̃	PROPN
ejpam-2332	185	59	jx	jx	PROPN
ejpam-2332	185	60	e	e	PROPN
ejpam-2332	185	61	�	�	PROPN
ejpam-2332	185	62	b̃	b̃	PROPN
ejpam-2332	185	63	j	j	PROPN
ejpam-2332	186	1	−	−	PROPN
ejpam-2332	186	2	r̃	r̃	PROPN
ejpam-2332	186	3	j(1−	j(1−	PROPN
ejpam-2332	186	4	γ	γ	PROPN
ejpam-2332	186	5	)	)	PUNCT
ejpam-2332	186	6	,	,	PUNCT
ejpam-2332	186	7	0≤	0≤	NUM
ejpam-2332	186	8	γ≤	γ≤	NUM
ejpam-2332	186	9	1	1	NUM
ejpam-2332	186	10	s̃	s̃	PROPN
ejpam-2332	187	1	jx	jx	PROPN
ejpam-2332	187	2	e	e	PROPN
ejpam-2332	187	3	�	�	PROPN
ejpam-2332	187	4	(b̃	(b̃	PROPN
ejpam-2332	187	5	j	j	PROPN
ejpam-2332	187	6	−	−	PROPN
ejpam-2332	187	7	r̃	r̃	PROPN
ejpam-2332	187	8	j	j	NOUN
ejpam-2332	187	9	)	)	PUNCT
ejpam-2332	188	1	+	+	CCONJ
ejpam-2332	188	2	s̃	s̃	PROPN
ejpam-2332	188	3	j(1−	j(1−	PROPN
ejpam-2332	188	4	δ	δ	PROPN
ejpam-2332	188	5	)	)	PUNCT
ejpam-2332	188	6	,	,	PUNCT
ejpam-2332	188	7	0≤	0≤	NUM
ejpam-2332	188	8	δ	δ	NOUN
ejpam-2332	188	9	≤	≤	ADV
ejpam-2332	188	10	1	1	NUM
ejpam-2332	188	11	(	(	PUNCT
ejpam-2332	188	12	10	10	NUM
ejpam-2332	188	13	)	)	PUNCT
ejpam-2332	188	14	m.	m.	NOUN
ejpam-2332	188	15	seikh	seikh	NOUN
ejpam-2332	188	16	,	,	PUNCT
ejpam-2332	188	17	p.	p.	PROPN
ejpam-2332	188	18	nayak	nayak	PROPN
ejpam-2332	188	19	,	,	PUNCT
ejpam-2332	188	20	m.	m.	NOUN
ejpam-2332	188	21	pal	pal	PROPN
ejpam-2332	188	22	/	/	SYM
ejpam-2332	188	23	eur	eur	PROPN
ejpam-2332	188	24	.	.	PUNCT
ejpam-2332	189	1	j.	j.	PROPN
ejpam-2332	189	2	pure	pure	PROPN
ejpam-2332	189	3	appl	appl	PROPN
ejpam-2332	189	4	.	.	PROPN
ejpam-2332	189	5	math	math	PROPN
ejpam-2332	189	6	,	,	PUNCT
ejpam-2332	189	7	8	8	NUM
ejpam-2332	189	8	(	(	PUNCT
ejpam-2332	189	9	2015	2015	NUM
ejpam-2332	189	10	)	)	PUNCT
ejpam-2332	189	11	,	,	PUNCT
ejpam-2332	189	12	153	153	NUM
ejpam-2332	189	13	-	-	SYM
ejpam-2332	189	14	171	171	NUM
ejpam-2332	189	15	160	160	NUM
ejpam-2332	189	16	respectively	respectively	ADV
ejpam-2332	189	17	,	,	PUNCT
ejpam-2332	189	18	where	where	SCONJ
ejpam-2332	189	19	i	i	PRON
ejpam-2332	189	20	=	=	SYM
ejpam-2332	189	21	1,2	1,2	NUM
ejpam-2332	189	22	,	,	PUNCT
ejpam-2332	189	23	.	.	PUNCT
ejpam-2332	189	24	.	.	PUNCT
ejpam-2332	190	1	.	.	PUNCT
ejpam-2332	191	1	,	,	PUNCT
ejpam-2332	191	2	n	n	PROPN
ejpam-2332	191	3	and	and	CCONJ
ejpam-2332	191	4	j	j	PROPN
ejpam-2332	191	5	=	=	SYM
ejpam-2332	191	6	1,2	1,2	NUM
ejpam-2332	191	7	,	,	PUNCT
ejpam-2332	191	8	.	.	PUNCT
ejpam-2332	192	1	.	.	PUNCT
ejpam-2332	193	1	.	.	PUNCT
ejpam-2332	194	1	,	,	PUNCT
ejpam-2332	194	2	n.	n.	NOUN
ejpam-2332	194	3	here	here	ADV
ejpam-2332	194	4	e	e	ADP
ejpam-2332	194	5	�	�	PROPN
ejpam-2332	194	6	and	and	CCONJ
ejpam-2332	194	7	e	e	NOUN
ejpam-2332	194	8	�	�	PROPN
ejpam-2332	194	9	are	be	AUX
ejpam-2332	194	10	relation	relation	NOUN
ejpam-2332	194	11	between	between	ADP
ejpam-2332	194	12	i	i	NOUN
ejpam-2332	194	13	-	-	PUNCT
ejpam-2332	194	14	fuzzy	fuzzy	ADJ
ejpam-2332	194	15	numbers	number	NOUN
ejpam-2332	194	16	which	which	PRON
ejpam-2332	194	17	preserves	preserve	VERB
ejpam-2332	194	18	the	the	DET
ejpam-2332	194	19	ranking	ranking	NOUN
ejpam-2332	194	20	when	when	SCONJ
ejpam-2332	194	21	i	i	PRON
ejpam-2332	194	22	-	-	PUNCT
ejpam-2332	194	23	fuzzy	fuzzy	ADJ
ejpam-2332	194	24	numbers	number	NOUN
ejpam-2332	194	25	are	be	AUX
ejpam-2332	194	26	multiplied	multiply	VERB
ejpam-2332	194	27	by	by	ADP
ejpam-2332	194	28	positive	positive	ADJ
ejpam-2332	194	29	scalars	scalar	NOUN
ejpam-2332	194	30	.	.	PUNCT
ejpam-2332	195	1	also	also	ADV
ejpam-2332	195	2	,	,	PUNCT
ejpam-2332	195	3	p̃	p̃	PROPN
ejpam-2332	195	4	j	j	PROPN
ejpam-2332	195	5	,	,	PUNCT
ejpam-2332	195	6	q̃	q̃	PROPN
ejpam-2332	195	7	j	j	PROPN
ejpam-2332	195	8	(	(	PUNCT
ejpam-2332	195	9	j	j	PROPN
ejpam-2332	195	10	=	=	SYM
ejpam-2332	195	11	1,2	1,2	NUM
ejpam-2332	195	12	,	,	PUNCT
ejpam-2332	195	13	.	.	PUNCT
ejpam-2332	195	14	.	.	PUNCT
ejpam-2332	196	1	.	.	PUNCT
ejpam-2332	197	1	,	,	PUNCT
ejpam-2332	198	1	n	n	CCONJ
ejpam-2332	198	2	)	)	PUNCT
ejpam-2332	198	3	represent	represent	VERB
ejpam-2332	198	4	the	the	DET
ejpam-2332	198	5	j	j	PROPN
ejpam-2332	198	6	th	th	X
ejpam-2332	198	7	component	component	NOUN
ejpam-2332	198	8	of	of	ADP
ejpam-2332	198	9	i	i	PROPN
ejpam-2332	198	10	-	-	PUNCT
ejpam-2332	198	11	fuzzy	fuzzy	ADJ
ejpam-2332	198	12	vectors	vector	NOUN
ejpam-2332	198	13	p̃	p̃	PROPN
ejpam-2332	198	14	and	and	CCONJ
ejpam-2332	198	15	q̃	q̃	PROPN
ejpam-2332	198	16	,	,	PUNCT
ejpam-2332	198	17	respectively	respectively	ADV
ejpam-2332	198	18	.	.	PUNCT
ejpam-2332	199	1	similarly	similarly	ADV
ejpam-2332	199	2	,	,	PUNCT
ejpam-2332	199	3	r̃i	r̃i	NOUN
ejpam-2332	199	4	,	,	PUNCT
ejpam-2332	199	5	s̃i(i	s̃i(i	X
ejpam-2332	199	6	=	=	SYM
ejpam-2332	199	7	1,2	1,2	NUM
ejpam-2332	199	8	,	,	PUNCT
ejpam-2332	199	9	.	.	PUNCT
ejpam-2332	199	10	.	.	PUNCT
ejpam-2332	200	1	.	.	PUNCT
ejpam-2332	201	1	,	,	PUNCT
ejpam-2332	201	2	m	m	AUX
ejpam-2332	201	3	)	)	PUNCT
ejpam-2332	201	4	represent	represent	VERB
ejpam-2332	201	5	the	the	DET
ejpam-2332	201	6	i	i	PROPN
ejpam-2332	201	7	th	th	PROPN
ejpam-2332	201	8	component	component	NOUN
ejpam-2332	201	9	of	of	ADP
ejpam-2332	201	10	i	i	PROPN
ejpam-2332	201	11	-	-	PUNCT
ejpam-2332	201	12	fuzzy	fuzzy	ADJ
ejpam-2332	201	13	vectors	vector	NOUN
ejpam-2332	201	14	r̃	r̃	NOUN
ejpam-2332	201	15	and	and	CCONJ
ejpam-2332	201	16	s̃	s̃	PROPN
ejpam-2332	201	17	,	,	PUNCT
ejpam-2332	201	18	respectively	respectively	ADV
ejpam-2332	201	19	.	.	PUNCT
ejpam-2332	202	1	4	4	X
ejpam-2332	202	2	.	.	NOUN
ejpam-2332	202	3	mathematical	mathematical	ADJ
ejpam-2332	202	4	model	model	NOUN
ejpam-2332	202	5	of	of	ADP
ejpam-2332	202	6	a	a	DET
ejpam-2332	202	7	bi	bi	ADJ
ejpam-2332	202	8	-	-	ADJ
ejpam-2332	202	9	matrix	matrix	NOUN
ejpam-2332	202	10	game	game	NOUN
ejpam-2332	202	11	a	a	DET
ejpam-2332	202	12	bi	bi	ADJ
ejpam-2332	202	13	-	-	ADJ
ejpam-2332	202	14	matrix	matrix	NOUN
ejpam-2332	202	15	game	game	NOUN
ejpam-2332	202	16	can	can	AUX
ejpam-2332	202	17	be	be	AUX
ejpam-2332	202	18	considered	consider	VERB
ejpam-2332	202	19	as	as	ADP
ejpam-2332	202	20	a	a	DET
ejpam-2332	202	21	natural	natural	ADJ
ejpam-2332	202	22	extension	extension	NOUN
ejpam-2332	202	23	of	of	ADP
ejpam-2332	202	24	the	the	DET
ejpam-2332	202	25	matrix	matrix	NOUN
ejpam-2332	202	26	game	game	NOUN
ejpam-2332	202	27	.	.	PUNCT
ejpam-2332	203	1	let	let	VERB
ejpam-2332	203	2	i	i	PRON
ejpam-2332	203	3	,	,	PUNCT
ejpam-2332	203	4	i	i	PRON
ejpam-2332	203	5	i	i	PRON
ejpam-2332	203	6	denote	denote	VERB
ejpam-2332	203	7	two	two	NUM
ejpam-2332	203	8	players	player	NOUN
ejpam-2332	203	9	and	and	CCONJ
ejpam-2332	203	10	let	let	VERB
ejpam-2332	203	11	m	m	VERB
ejpam-2332	203	12	=	=	PUNCT
ejpam-2332	203	13	{	{	PUNCT
ejpam-2332	203	14	1,2	1,2	NUM
ejpam-2332	203	15	,	,	PUNCT
ejpam-2332	203	16	.	.	PUNCT
ejpam-2332	203	17	.	.	PUNCT
ejpam-2332	204	1	.	.	PUNCT
ejpam-2332	205	1	,	,	PUNCT
ejpam-2332	205	2	m	m	VERB
ejpam-2332	205	3	}	}	PUNCT
ejpam-2332	205	4	and	and	CCONJ
ejpam-2332	205	5	n	n	CCONJ
ejpam-2332	205	6	=	=	SYM
ejpam-2332	205	7	{	{	PUNCT
ejpam-2332	205	8	1,2	1,2	NUM
ejpam-2332	205	9	,	,	PUNCT
ejpam-2332	205	10	.	.	PUNCT
ejpam-2332	205	11	.	.	PUNCT
ejpam-2332	206	1	.	.	PUNCT
ejpam-2332	207	1	,	,	PUNCT
ejpam-2332	207	2	n	n	CCONJ
ejpam-2332	207	3	}	}	PUNCT
ejpam-2332	207	4	be	be	AUX
ejpam-2332	207	5	the	the	DET
ejpam-2332	207	6	sets	set	NOUN
ejpam-2332	207	7	of	of	ADP
ejpam-2332	207	8	all	all	DET
ejpam-2332	207	9	pure	pure	ADJ
ejpam-2332	207	10	strategies	strategy	NOUN
ejpam-2332	207	11	available	available	ADJ
ejpam-2332	207	12	for	for	ADP
ejpam-2332	207	13	players	player	NOUN
ejpam-2332	208	1	i	i	PRON
ejpam-2332	208	2	,	,	PUNCT
ejpam-2332	208	3	i	i	PRON
ejpam-2332	208	4	i	i	PRON
ejpam-2332	208	5	respectively	respectively	ADV
ejpam-2332	208	6	.	.	PUNCT
ejpam-2332	209	1	by	by	ADP
ejpam-2332	209	2	ai	ai	PROPN
ejpam-2332	209	3	j	j	PROPN
ejpam-2332	209	4	and	and	CCONJ
ejpam-2332	209	5	bi	bi	PROPN
ejpam-2332	209	6	j	j	PROPN
ejpam-2332	209	7	,	,	PUNCT
ejpam-2332	209	8	we	we	PRON
ejpam-2332	209	9	denote	denote	VERB
ejpam-2332	209	10	the	the	DET
ejpam-2332	209	11	pay	pay	NOUN
ejpam-2332	209	12	-	-	PUNCT
ejpam-2332	209	13	offs	off	NOUN
ejpam-2332	209	14	that	that	PRON
ejpam-2332	209	15	the	the	DET
ejpam-2332	209	16	player	player	NOUN
ejpam-2332	209	17	i	i	PRON
ejpam-2332	209	18	and	and	CCONJ
ejpam-2332	209	19	i	i	PRON
ejpam-2332	209	20	i	i	PRON
ejpam-2332	209	21	receive	receive	VERB
ejpam-2332	209	22	when	when	SCONJ
ejpam-2332	209	23	player	player	NOUN
ejpam-2332	209	24	i	i	PRON
ejpam-2332	209	25	plays	play	VERB
ejpam-2332	209	26	the	the	DET
ejpam-2332	209	27	pure	pure	ADJ
ejpam-2332	209	28	strategy	strategy	NOUN
ejpam-2332	209	29	i	i	PRON
ejpam-2332	209	30	and	and	CCONJ
ejpam-2332	209	31	player	player	NOUN
ejpam-2332	210	1	i	i	PRON
ejpam-2332	210	2	i	i	PRON
ejpam-2332	210	3	plays	play	VERB
ejpam-2332	210	4	the	the	DET
ejpam-2332	210	5	pure	pure	ADJ
ejpam-2332	210	6	strategy	strategy	NOUN
ejpam-2332	211	1	j.	j.	PROPN
ejpam-2332	211	2	then	then	ADV
ejpam-2332	211	3	we	we	PRON
ejpam-2332	211	4	have	have	VERB
ejpam-2332	211	5	the	the	DET
ejpam-2332	211	6	following	follow	VERB
ejpam-2332	211	7	pay	pay	VERB
ejpam-2332	211	8	-	-	PUNCT
ejpam-2332	211	9	off	off	ADP
ejpam-2332	211	10	matrix	matrix	NOUN
ejpam-2332	211	11	a=	a=	NOUN
ejpam-2332	211	12			PROPN
ejpam-2332	211	13			PROPN
ejpam-2332	211	14	a11	a11	PROPN
ejpam-2332	211	15	a12	a12	PROPN
ejpam-2332	211	16	·	·	PUNCT
ejpam-2332	211	17	·	·	PUNCT
ejpam-2332	211	18	·	·	PUNCT
ejpam-2332	212	1	a1n	a1n	ADP
ejpam-2332	212	2	a21	a21	PROPN
ejpam-2332	212	3	a22	a22	PROPN
ejpam-2332	212	4	·	·	PUNCT
ejpam-2332	212	5	·	·	PUNCT
ejpam-2332	212	6	·	·	PUNCT
ejpam-2332	212	7	a2n	a2n	PUNCT
ejpam-2332	212	8	·	·	PUNCT
ejpam-2332	212	9	·	·	PUNCT
ejpam-2332	212	10	·	·	PUNCT
ejpam-2332	212	11	·	·	PUNCT
ejpam-2332	212	12	·	·	PUNCT
ejpam-2332	212	13	·	·	PUNCT
ejpam-2332	212	14	·	·	PUNCT
ejpam-2332	212	15	·	·	PUNCT
ejpam-2332	212	16	·	·	PUNCT
ejpam-2332	212	17	am1	am1	X
ejpam-2332	212	18	am2	am2	X
ejpam-2332	212	19	·	·	PUNCT
ejpam-2332	212	20	·	·	PUNCT
ejpam-2332	212	21	·	·	PUNCT
ejpam-2332	212	22	amn	amn	PROPN
ejpam-2332	212	23			PROPN
ejpam-2332	212	24			PROPN
ejpam-2332	212	25	;	;	PUNCT
ejpam-2332	212	26	b	b	X
ejpam-2332	212	27	=	=	SYM
ejpam-2332	212	28			PROPN
ejpam-2332	212	29			NOUN
ejpam-2332	212	30	b11	b11	PROPN
ejpam-2332	212	31	b12	b12	NOUN
ejpam-2332	212	32	·	·	PUNCT
ejpam-2332	212	33	·	·	PUNCT
ejpam-2332	212	34	·	·	PUNCT
ejpam-2332	213	1	b1n	b1n	PROPN
ejpam-2332	213	2	b21	b21	PROPN
ejpam-2332	213	3	b22	b22	PROPN
ejpam-2332	213	4	·	·	PUNCT
ejpam-2332	213	5	·	·	PUNCT
ejpam-2332	213	6	·	·	PUNCT
ejpam-2332	213	7	b2n	b2n	X
ejpam-2332	213	8	·	·	PUNCT
ejpam-2332	213	9	·	·	PUNCT
ejpam-2332	213	10	·	·	PUNCT
ejpam-2332	213	11	·	·	PUNCT
ejpam-2332	213	12	·	·	PUNCT
ejpam-2332	213	13	·	·	PUNCT
ejpam-2332	213	14	bm1	bm1	ADJ
ejpam-2332	213	15	bm1	bm1	X
ejpam-2332	213	16	·	·	PUNCT
ejpam-2332	213	17	·	·	PUNCT
ejpam-2332	213	18	·	·	PUNCT
ejpam-2332	213	19	bmn	bmn	PROPN
ejpam-2332	213	20			PROPN
ejpam-2332	213	21			PROPN
ejpam-2332	213	22	.	.	PUNCT
ejpam-2332	214	1	where	where	SCONJ
ejpam-2332	214	2	we	we	PRON
ejpam-2332	214	3	assume	assume	VERB
ejpam-2332	214	4	that	that	SCONJ
ejpam-2332	214	5	each	each	PRON
ejpam-2332	214	6	of	of	ADP
ejpam-2332	214	7	the	the	DET
ejpam-2332	214	8	two	two	NUM
ejpam-2332	214	9	players	player	NOUN
ejpam-2332	214	10	chooses	choose	VERB
ejpam-2332	214	11	a	a	DET
ejpam-2332	214	12	strategy	strategy	NOUN
ejpam-2332	214	13	,	,	PUNCT
ejpam-2332	214	14	a	a	DET
ejpam-2332	214	15	pay	pay	NOUN
ejpam-2332	214	16	-	-	PUNCT
ejpam-2332	214	17	off	off	NOUN
ejpam-2332	214	18	for	for	ADP
ejpam-2332	214	19	each	each	PRON
ejpam-2332	214	20	of	of	ADP
ejpam-2332	214	21	them	they	PRON
ejpam-2332	214	22	is	be	AUX
ejpam-2332	214	23	represented	represent	VERB
ejpam-2332	214	24	as	as	ADP
ejpam-2332	214	25	a	a	DET
ejpam-2332	214	26	crisp	crisp	ADJ
ejpam-2332	214	27	number	number	NOUN
ejpam-2332	214	28	.	.	PUNCT
ejpam-2332	215	1	we	we	PRON
ejpam-2332	215	2	denote	denote	VERB
ejpam-2332	215	3	the	the	DET
ejpam-2332	215	4	game	game	NOUN
ejpam-2332	215	5	by	by	ADP
ejpam-2332	215	6	γ	γ	PROPN
ejpam-2332	215	7	=	=	SYM
ejpam-2332	215	8	〈	〈	PROPN
ejpam-2332	215	9	{	{	PUNCT
ejpam-2332	215	10	i	i	PRON
ejpam-2332	215	11	,	,	PUNCT
ejpam-2332	215	12	i	i	PRON
ejpam-2332	215	13	i},a	i},a	VERB
ejpam-2332	215	14	,	,	PUNCT
ejpam-2332	215	15	b	b	NOUN
ejpam-2332	215	16	〉	〉	NOUN
ejpam-2332	215	17	.	.	PUNCT
ejpam-2332	216	1	4.1	4.1	NUM
ejpam-2332	216	2	.	.	PUNCT
ejpam-2332	216	3	nash	nash	PROPN
ejpam-2332	216	4	equilibrium	equilibrium	NOUN
ejpam-2332	216	5	solution	solution	NOUN
ejpam-2332	216	6	nash	nash	NOUN
ejpam-2332	216	7	[	[	X
ejpam-2332	216	8	17	17	NUM
ejpam-2332	216	9	]	]	PUNCT
ejpam-2332	216	10	defined	define	VERB
ejpam-2332	216	11	the	the	DET
ejpam-2332	216	12	concept	concept	NOUN
ejpam-2332	216	13	of	of	ADP
ejpam-2332	216	14	nash	nash	PROPN
ejpam-2332	216	15	equilibrium	equilibrium	NOUN
ejpam-2332	216	16	solutions	solution	NOUN
ejpam-2332	216	17	(	(	PUNCT
ejpam-2332	216	18	nes	ne	NOUN
ejpam-2332	216	19	)	)	PUNCT
ejpam-2332	216	20	in	in	ADP
ejpam-2332	216	21	bi	bi	ADJ
ejpam-2332	216	22	-	-	ADJ
ejpam-2332	216	23	matrix	matrix	NOUN
ejpam-2332	216	24	games	game	NOUN
ejpam-2332	216	25	for	for	ADP
ejpam-2332	216	26	single	single	ADJ
ejpam-2332	216	27	pair	pair	NOUN
ejpam-2332	216	28	of	of	ADP
ejpam-2332	216	29	payoff	payoff	NOUN
ejpam-2332	216	30	matrices	matrix	NOUN
ejpam-2332	216	31	and	and	CCONJ
ejpam-2332	216	32	presented	present	VERB
ejpam-2332	216	33	methodology	methodology	NOUN
ejpam-2332	216	34	for	for	ADP
ejpam-2332	216	35	obtaining	obtain	VERB
ejpam-2332	216	36	them	they	PRON
ejpam-2332	216	37	.	.	PUNCT
ejpam-2332	217	1	definition	definition	NOUN
ejpam-2332	217	2	7	7	NUM
ejpam-2332	217	3	(	(	PUNCT
ejpam-2332	217	4	pure	pure	ADJ
ejpam-2332	217	5	strategy	strategy	NOUN
ejpam-2332	217	6	)	)	PUNCT
ejpam-2332	217	7	.	.	PUNCT
ejpam-2332	218	1	let	let	VERB
ejpam-2332	218	2	i	i	PRON
ejpam-2332	218	3	and	and	CCONJ
ejpam-2332	218	4	i	i	PRON
ejpam-2332	218	5	i	i	PRON
ejpam-2332	218	6	denote	denote	VERB
ejpam-2332	218	7	two	two	NUM
ejpam-2332	218	8	players	player	NOUN
ejpam-2332	218	9	and	and	CCONJ
ejpam-2332	218	10	let	let	VERB
ejpam-2332	218	11	m	m	VERB
ejpam-2332	218	12	=	=	PUNCT
ejpam-2332	218	13	{	{	PUNCT
ejpam-2332	218	14	1,2	1,2	NUM
ejpam-2332	218	15	,	,	PUNCT
ejpam-2332	218	16	.	.	PUNCT
ejpam-2332	218	17	.	.	PUNCT
ejpam-2332	219	1	.	.	PUNCT
ejpam-2332	220	1	,	,	PUNCT
ejpam-2332	220	2	m	m	VERB
ejpam-2332	220	3	}	}	PUNCT
ejpam-2332	220	4	and	and	CCONJ
ejpam-2332	220	5	n	n	CCONJ
ejpam-2332	220	6	=	=	SYM
ejpam-2332	220	7	{	{	PUNCT
ejpam-2332	220	8	1,2	1,2	NUM
ejpam-2332	220	9	,	,	PUNCT
ejpam-2332	220	10	.	.	PUNCT
ejpam-2332	220	11	.	.	PUNCT
ejpam-2332	221	1	.	.	PUNCT
ejpam-2332	222	1	,	,	PUNCT
ejpam-2332	222	2	n	n	CCONJ
ejpam-2332	222	3	}	}	PUNCT
ejpam-2332	222	4	be	be	AUX
ejpam-2332	222	5	the	the	DET
ejpam-2332	222	6	sets	set	NOUN
ejpam-2332	222	7	of	of	ADP
ejpam-2332	222	8	all	all	DET
ejpam-2332	222	9	pure	pure	ADJ
ejpam-2332	222	10	strategies	strategy	NOUN
ejpam-2332	222	11	available	available	ADJ
ejpam-2332	222	12	for	for	ADP
ejpam-2332	222	13	players	player	NOUN
ejpam-2332	223	1	i	i	PRON
ejpam-2332	223	2	and	and	CCONJ
ejpam-2332	223	3	i	i	PRON
ejpam-2332	223	4	i	i	PRON
ejpam-2332	223	5	respectively	respectively	ADV
ejpam-2332	223	6	.	.	PUNCT
ejpam-2332	224	1	a	a	DET
ejpam-2332	224	2	pair	pair	NOUN
ejpam-2332	224	3	of	of	ADP
ejpam-2332	224	4	strategies	strategy	NOUN
ejpam-2332	224	5	(	(	PUNCT
ejpam-2332	224	6	row	row	NOUN
ejpam-2332	224	7	r	r	NOUN
ejpam-2332	224	8	,	,	PUNCT
ejpam-2332	224	9	column	column	NOUN
ejpam-2332	224	10	s	s	PART
ejpam-2332	224	11	)	)	PUNCT
ejpam-2332	224	12	is	be	AUX
ejpam-2332	224	13	said	say	VERB
ejpam-2332	224	14	to	to	PART
ejpam-2332	224	15	constitute	constitute	VERB
ejpam-2332	224	16	a	a	DET
ejpam-2332	224	17	nes	ne	NOUN
ejpam-2332	224	18	to	to	ADP
ejpam-2332	224	19	a	a	DET
ejpam-2332	224	20	bi	bi	ADJ
ejpam-2332	224	21	-	-	ADJ
ejpam-2332	224	22	matrix	matrix	NOUN
ejpam-2332	224	23	game	game	NOUN
ejpam-2332	224	24	γ	γ	NOUN
ejpam-2332	224	25	if	if	SCONJ
ejpam-2332	224	26	the	the	DET
ejpam-2332	224	27	following	follow	VERB
ejpam-2332	224	28	pair	pair	NOUN
ejpam-2332	224	29	of	of	ADP
ejpam-2332	224	30	inequalities	inequality	NOUN
ejpam-2332	224	31	is	be	AUX
ejpam-2332	224	32	satisfied	satisfied	ADJ
ejpam-2332	224	33	for	for	ADP
ejpam-2332	224	34	all	all	DET
ejpam-2332	224	35	i	i	PRON
ejpam-2332	224	36	=	=	SYM
ejpam-2332	224	37	1,2	1,2	NUM
ejpam-2332	224	38	,	,	PUNCT
ejpam-2332	224	39	.	.	PUNCT
ejpam-2332	224	40	.	.	PUNCT
ejpam-2332	225	1	.	.	PUNCT
ejpam-2332	226	1	,	,	PUNCT
ejpam-2332	226	2	m	m	VERB
ejpam-2332	226	3	and	and	CCONJ
ejpam-2332	226	4	for	for	ADP
ejpam-2332	226	5	all	all	PRON
ejpam-2332	226	6	j	j	NOUN
ejpam-2332	226	7	=	=	SYM
ejpam-2332	226	8	1,2	1,2	NUM
ejpam-2332	226	9	,	,	PUNCT
ejpam-2332	226	10	.	.	PUNCT
ejpam-2332	226	11	.	.	PUNCT
ejpam-2332	227	1	.	.	PUNCT
ejpam-2332	228	1	,	,	PUNCT
ejpam-2332	228	2	n	n	CCONJ
ejpam-2332	228	3	:	:	PUNCT
ejpam-2332	228	4	ais	ais	PROPN
ejpam-2332	228	5	≤	≤	PROPN
ejpam-2332	228	6	ars	ar	NOUN
ejpam-2332	228	7	;	;	PUNCT
ejpam-2332	228	8	br	br	PROPN
ejpam-2332	228	9	j	j	PROPN
ejpam-2332	228	10	≤	≤	PROPN
ejpam-2332	228	11	brs	br	VERB
ejpam-2332	228	12	since	since	SCONJ
ejpam-2332	228	13	the	the	DET
ejpam-2332	228	14	strategy	strategy	NOUN
ejpam-2332	228	15	sets	set	NOUN
ejpam-2332	228	16	are	be	AUX
ejpam-2332	228	17	finite	finite	ADJ
ejpam-2332	228	18	,	,	PUNCT
ejpam-2332	228	19	these	these	DET
ejpam-2332	228	20	expressions	expression	NOUN
ejpam-2332	228	21	may	may	AUX
ejpam-2332	228	22	exist	exist	VERB
ejpam-2332	228	23	and	and	CCONJ
ejpam-2332	228	24	in	in	ADP
ejpam-2332	228	25	such	such	ADJ
ejpam-2332	228	26	case	case	NOUN
ejpam-2332	228	27	,	,	PUNCT
ejpam-2332	228	28	bi	bi	ADJ
ejpam-2332	228	29	-	-	ADJ
ejpam-2332	228	30	matrix	matrix	NOUN
ejpam-2332	228	31	game	game	NOUN
ejpam-2332	228	32	admits	admit	VERB
ejpam-2332	228	33	a	a	DET
ejpam-2332	228	34	nes	ne	NOUN
ejpam-2332	228	35	for	for	ADP
ejpam-2332	228	36	pure	pure	ADJ
ejpam-2332	228	37	strategy	strategy	NOUN
ejpam-2332	228	38	.	.	PUNCT
ejpam-2332	229	1	the	the	DET
ejpam-2332	229	2	pair	pair	NOUN
ejpam-2332	229	3	(	(	PUNCT
ejpam-2332	229	4	ars	ars	PROPN
ejpam-2332	229	5	,	,	PUNCT
ejpam-2332	229	6	brs	br	VERB
ejpam-2332	229	7	)	)	PUNCT
ejpam-2332	229	8	is	be	AUX
ejpam-2332	229	9	known	know	VERB
ejpam-2332	229	10	as	as	ADP
ejpam-2332	229	11	a	a	DET
ejpam-2332	229	12	nash	nash	ADJ
ejpam-2332	229	13	equilibrium	equilibrium	NOUN
ejpam-2332	229	14	outcome	outcome	NOUN
ejpam-2332	229	15	of	of	ADP
ejpam-2332	229	16	the	the	DET
ejpam-2332	229	17	bi	bi	ADJ
ejpam-2332	229	18	-	-	ADJ
ejpam-2332	229	19	matrix	matrix	NOUN
ejpam-2332	229	20	game	game	NOUN
ejpam-2332	229	21	in	in	ADP
ejpam-2332	229	22	pure	pure	ADJ
ejpam-2332	229	23	strategies	strategy	NOUN
ejpam-2332	229	24	.	.	PUNCT
ejpam-2332	230	1	a	a	DET
ejpam-2332	230	2	bi	bi	ADJ
ejpam-2332	230	3	-	-	ADJ
ejpam-2332	230	4	matrix	matrix	NOUN
ejpam-2332	230	5	game	game	NOUN
ejpam-2332	230	6	can	can	AUX
ejpam-2332	230	7	admit	admit	VERB
ejpam-2332	230	8	more	more	ADJ
ejpam-2332	230	9	than	than	ADP
ejpam-2332	230	10	one	one	NUM
ejpam-2332	230	11	nes	ne	NOUN
ejpam-2332	230	12	,	,	PUNCT
ejpam-2332	230	13	with	with	ADP
ejpam-2332	230	14	the	the	DET
ejpam-2332	230	15	equilibrium	equilibrium	NOUN
ejpam-2332	230	16	outcomes	outcome	NOUN
ejpam-2332	230	17	being	be	AUX
ejpam-2332	230	18	different	different	ADJ
ejpam-2332	230	19	in	in	ADP
ejpam-2332	230	20	each	each	DET
ejpam-2332	230	21	case	case	NOUN
ejpam-2332	230	22	.	.	PUNCT
ejpam-2332	231	1	4.2	4.2	NUM
ejpam-2332	231	2	.	.	PUNCT
ejpam-2332	231	3	mixed	mixed	ADJ
ejpam-2332	231	4	strategy	strategy	NOUN
ejpam-2332	231	5	we	we	PRON
ejpam-2332	231	6	denote	denote	VERB
ejpam-2332	231	7	the	the	DET
ejpam-2332	231	8	sets	set	NOUN
ejpam-2332	231	9	of	of	ADP
ejpam-2332	231	10	all	all	DET
ejpam-2332	231	11	mixed	mixed	ADJ
ejpam-2332	231	12	strategies	strategy	NOUN
ejpam-2332	231	13	,	,	PUNCT
ejpam-2332	231	14	called	call	VERB
ejpam-2332	231	15	strategy	strategy	NOUN
ejpam-2332	231	16	spaces	space	NOUN
ejpam-2332	231	17	,	,	PUNCT
ejpam-2332	231	18	available	available	ADJ
ejpam-2332	231	19	for	for	ADP
ejpam-2332	231	20	players	player	NOUN
ejpam-2332	232	1	i	i	PRON
ejpam-2332	232	2	,	,	PUNCT
ejpam-2332	232	3	i	i	PRON
ejpam-2332	232	4	i	i	PRON
ejpam-2332	232	5	by	by	ADP
ejpam-2332	232	6	si	si	X
ejpam-2332	232	7	=	=	SYM
ejpam-2332	232	8	¦	¦	PROPN
ejpam-2332	232	9	x=	x=	PUNCT
ejpam-2332	233	1	(	(	PUNCT
ejpam-2332	233	2	x1	x1	PROPN
ejpam-2332	233	3	,	,	PUNCT
ejpam-2332	233	4	x2	x2	PROPN
ejpam-2332	233	5	,	,	PUNCT
ejpam-2332	233	6	.	.	PUNCT
ejpam-2332	233	7	.	.	PUNCT
ejpam-2332	233	8	.	.	PUNCT
ejpam-2332	234	1	,	,	PUNCT
ejpam-2332	234	2	xm	xm	X
ejpam-2332	234	3	)	)	PUNCT
ejpam-2332	234	4	∈	∈	PROPN
ejpam-2332	234	5	ℜ	ℜ	PROPN
ejpam-2332	234	6	m	m	PROPN
ejpam-2332	234	7	+	+	ADJ
ejpam-2332	234	8	:	:	PUNCT
ejpam-2332	234	9	x	x	X
ejpam-2332	234	10	i	i	PRON
ejpam-2332	234	11	≥	≥	NOUN
ejpam-2332	234	12	0	0	NUM
ejpam-2332	234	13	;	;	PUNCT
ejpam-2332	234	14	i	i	PRON
ejpam-2332	234	15	=	=	SYM
ejpam-2332	234	16	1,2	1,2	NUM
ejpam-2332	234	17	,	,	PUNCT
ejpam-2332	234	18	.	.	PUNCT
ejpam-2332	234	19	.	.	PUNCT
ejpam-2332	234	20	.	.	PUNCT
ejpam-2332	235	1	,	,	PUNCT
ejpam-2332	235	2	m	m	VERB
ejpam-2332	235	3	and	and	CCONJ
ejpam-2332	235	4	m∑	m∑	ADV
ejpam-2332	235	5	i=1	i=1	NOUN
ejpam-2332	235	6	x	x	PUNCT
ejpam-2332	236	1	i	i	NOUN
ejpam-2332	236	2	=	=	NOUN
ejpam-2332	236	3	1	1	NUM
ejpam-2332	236	4	©	©	PROPN
ejpam-2332	236	5	m.	m.	NOUN
ejpam-2332	236	6	seikh	seikh	NOUN
ejpam-2332	236	7	,	,	PUNCT
ejpam-2332	236	8	p.	p.	PROPN
ejpam-2332	236	9	nayak	nayak	PROPN
ejpam-2332	236	10	,	,	PUNCT
ejpam-2332	236	11	m.	m.	NOUN
ejpam-2332	236	12	pal	pal	PROPN
ejpam-2332	236	13	/	/	SYM
ejpam-2332	236	14	eur	eur	PROPN
ejpam-2332	236	15	.	.	PUNCT
ejpam-2332	237	1	j.	j.	PROPN
ejpam-2332	237	2	pure	pure	PROPN
ejpam-2332	237	3	appl	appl	PROPN
ejpam-2332	237	4	.	.	PROPN
ejpam-2332	237	5	math	math	PROPN
ejpam-2332	237	6	,	,	PUNCT
ejpam-2332	237	7	8	8	NUM
ejpam-2332	237	8	(	(	PUNCT
ejpam-2332	237	9	2015	2015	NUM
ejpam-2332	237	10	)	)	PUNCT
ejpam-2332	237	11	,	,	PUNCT
ejpam-2332	237	12	153	153	NUM
ejpam-2332	237	13	-	-	SYM
ejpam-2332	237	14	171	171	NUM
ejpam-2332	237	15	161	161	NUM
ejpam-2332	237	16	si	si	NOUN
ejpam-2332	237	17	i	i	NOUN
ejpam-2332	237	18	=	=	SYM
ejpam-2332	237	19	¦	¦	PROPN
ejpam-2332	237	20	y=	y=	PROPN
ejpam-2332	237	21	(	(	PUNCT
ejpam-2332	237	22	y1	y1	PROPN
ejpam-2332	237	23	,	,	PUNCT
ejpam-2332	237	24	y2	y2	PROPN
ejpam-2332	237	25	,	,	PUNCT
ejpam-2332	237	26	.	.	PUNCT
ejpam-2332	237	27	.	.	PUNCT
ejpam-2332	238	1	.	.	PUNCT
ejpam-2332	239	1	,	,	PUNCT
ejpam-2332	239	2	yn	yn	X
ejpam-2332	239	3	)	)	PUNCT
ejpam-2332	239	4	∈	∈	PROPN
ejpam-2332	239	5	ℜ	ℜ	PROPN
ejpam-2332	239	6	n	n	NOUN
ejpam-2332	240	1	+	+	NUM
ejpam-2332	240	2	:	:	PUNCT
ejpam-2332	240	3	y	y	PROPN
ejpam-2332	240	4	j	j	PROPN
ejpam-2332	240	5	≥	≥	PROPN
ejpam-2332	240	6	0	0	NUM
ejpam-2332	240	7	;	;	PUNCT
ejpam-2332	240	8	j	j	PROPN
ejpam-2332	240	9	=	=	SYM
ejpam-2332	240	10	1,2	1,2	NUM
ejpam-2332	240	11	,	,	PUNCT
ejpam-2332	240	12	.	.	PUNCT
ejpam-2332	240	13	.	.	PUNCT
ejpam-2332	241	1	.	.	PUNCT
ejpam-2332	242	1	,	,	PUNCT
ejpam-2332	243	1	n	n	PROPN
ejpam-2332	243	2	and	and	CCONJ
ejpam-2332	243	3	n∑	n∑	PROPN
ejpam-2332	244	1	j=1	j=1	PROPN
ejpam-2332	244	2	y	y	PROPN
ejpam-2332	244	3	j	j	PROPN
ejpam-2332	244	4	=	=	NOUN
ejpam-2332	244	5	1	1	NUM
ejpam-2332	244	6	©	©	NOUN
ejpam-2332	244	7	,	,	PUNCT
ejpam-2332	244	8	where	where	SCONJ
ejpam-2332	244	9	ℜm	ℜm	NOUN
ejpam-2332	244	10	+	+	PROPN
ejpam-2332	244	11	denotes	denote	VERB
ejpam-2332	244	12	the	the	DET
ejpam-2332	244	13	m−dimensional	m−dimensional	ADJ
ejpam-2332	244	14	non	non	ADJ
ejpam-2332	244	15	negative	negative	ADJ
ejpam-2332	244	16	euclidean	euclidean	ADJ
ejpam-2332	244	17	space	space	NOUN
ejpam-2332	244	18	.	.	PUNCT
ejpam-2332	245	1	thus	thus	ADV
ejpam-2332	245	2	by	by	ADP
ejpam-2332	245	3	a	a	DET
ejpam-2332	245	4	crisp	crisp	ADJ
ejpam-2332	245	5	two	two	NUM
ejpam-2332	245	6	person	person	NOUN
ejpam-2332	245	7	zero	zero	NUM
ejpam-2332	245	8	-	-	PUNCT
ejpam-2332	245	9	sum	sum	NOUN
ejpam-2332	245	10	bi	bi	ADJ
ejpam-2332	245	11	-	-	ADJ
ejpam-2332	245	12	matrix	matrix	NOUN
ejpam-2332	245	13	game	game	NOUN
ejpam-2332	245	14	bg	bg	INTJ
ejpam-2332	245	15	we	we	PRON
ejpam-2332	245	16	mean	mean	VERB
ejpam-2332	245	17	the	the	DET
ejpam-2332	245	18	triplet	triplet	NOUN
ejpam-2332	245	19	bg	bg	NOUN
ejpam-2332	245	20	=	=	PUNCT
ejpam-2332	245	21	(	(	PUNCT
ejpam-2332	245	22	si	si	INTJ
ejpam-2332	245	23	×	×	NOUN
ejpam-2332	245	24	si	si	INTJ
ejpam-2332	246	1	i	i	PRON
ejpam-2332	246	2	,	,	PUNCT
ejpam-2332	246	3	a	a	DET
ejpam-2332	246	4	,	,	PUNCT
ejpam-2332	246	5	b	b	NOUN
ejpam-2332	246	6	)	)	PUNCT
ejpam-2332	246	7	.	.	PUNCT
ejpam-2332	247	1	since	since	SCONJ
ejpam-2332	247	2	the	the	DET
ejpam-2332	247	3	player	player	NOUN
ejpam-2332	247	4	is	be	AUX
ejpam-2332	247	5	uncertain	uncertain	ADJ
ejpam-2332	247	6	about	about	ADP
ejpam-2332	247	7	what	what	PRON
ejpam-2332	247	8	strategy	strategy	NOUN
ejpam-2332	248	1	he	he	PRON
ejpam-2332	248	2	/	/	PUNCT
ejpam-2332	248	3	she	she	PRON
ejpam-2332	248	4	will	will	AUX
ejpam-2332	248	5	choose	choose	VERB
ejpam-2332	248	6	,	,	PUNCT
ejpam-2332	248	7	he	he	PRON
ejpam-2332	248	8	/	/	PUNCT
ejpam-2332	248	9	she	she	PRON
ejpam-2332	248	10	will	will	AUX
ejpam-2332	248	11	choose	choose	VERB
ejpam-2332	248	12	a	a	DET
ejpam-2332	248	13	probability	probability	NOUN
ejpam-2332	248	14	distribution	distribution	NOUN
ejpam-2332	248	15	over	over	ADP
ejpam-2332	248	16	the	the	DET
ejpam-2332	248	17	aet	aet	NOUN
ejpam-2332	248	18	of	of	ADP
ejpam-2332	248	19	alternatives	alternative	NOUN
ejpam-2332	248	20	available	available	ADJ
ejpam-2332	248	21	to	to	ADP
ejpam-2332	248	22	him	he	PRON
ejpam-2332	248	23	/	/	SYM
ejpam-2332	248	24	her	she	PRON
ejpam-2332	248	25	or	or	CCONJ
ejpam-2332	248	26	a	a	DET
ejpam-2332	248	27	mixed	mixed	ADJ
ejpam-2332	248	28	strategy	strategy	NOUN
ejpam-2332	248	29	in	in	ADP
ejpam-2332	248	30	terms	term	NOUN
ejpam-2332	248	31	of	of	ADP
ejpam-2332	248	32	game	game	NOUN
ejpam-2332	248	33	theory	theory	NOUN
ejpam-2332	248	34	.	.	PUNCT
ejpam-2332	249	1	definition	definition	NOUN
ejpam-2332	249	2	8	8	NUM
ejpam-2332	249	3	(	(	PUNCT
ejpam-2332	249	4	expected	expect	VERB
ejpam-2332	249	5	payoff	payoff	NOUN
ejpam-2332	249	6	)	)	PUNCT
ejpam-2332	249	7	.	.	PUNCT
ejpam-2332	250	1	if	if	SCONJ
ejpam-2332	250	2	the	the	DET
ejpam-2332	250	3	mixed	mixed	ADJ
ejpam-2332	250	4	strategies	strategy	NOUN
ejpam-2332	250	5	x	x	PUNCT
ejpam-2332	250	6	and	and	CCONJ
ejpam-2332	250	7	y	y	PROPN
ejpam-2332	250	8	are	be	AUX
ejpam-2332	250	9	proposed	propose	VERB
ejpam-2332	250	10	by	by	ADP
ejpam-2332	250	11	the	the	DET
ejpam-2332	250	12	player	player	NOUN
ejpam-2332	250	13	i	i	PRON
ejpam-2332	250	14	and	and	CCONJ
ejpam-2332	250	15	player	player	NOUN
ejpam-2332	251	1	i	i	PRON
ejpam-2332	251	2	i	i	PRON
ejpam-2332	251	3	respectively	respectively	ADV
ejpam-2332	251	4	,	,	PUNCT
ejpam-2332	251	5	then	then	ADV
ejpam-2332	251	6	the	the	DET
ejpam-2332	251	7	expected	expect	VERB
ejpam-2332	251	8	pay	pay	NOUN
ejpam-2332	251	9	-	-	PUNCT
ejpam-2332	251	10	offs	off	NOUN
ejpam-2332	251	11	of	of	ADP
ejpam-2332	251	12	the	the	DET
ejpam-2332	251	13	players	player	NOUN
ejpam-2332	251	14	i	i	PRON
ejpam-2332	251	15	and	and	CCONJ
ejpam-2332	251	16	i	i	PRON
ejpam-2332	251	17	i	i	PRON
ejpam-2332	251	18	are	be	AUX
ejpam-2332	251	19	respectively	respectively	ADV
ejpam-2332	251	20	xt	xt	ADP
ejpam-2332	251	21	ay=	ay=	PROPN
ejpam-2332	251	22	m∑	m∑	NOUN
ejpam-2332	251	23	i=1	i=1	PROPN
ejpam-2332	251	24	n∑	n∑	PROPN
ejpam-2332	252	1	j=1	j=1	NOUN
ejpam-2332	252	2	x	x	X
ejpam-2332	252	3	iai	iai	VERB
ejpam-2332	252	4	j	j	PROPN
ejpam-2332	252	5	y	y	PROPN
ejpam-2332	252	6	j	j	PROPN
ejpam-2332	252	7	and	and	CCONJ
ejpam-2332	252	8	xt	xt	AUX
ejpam-2332	252	9	by=	by=	PROPN
ejpam-2332	252	10	m∑	m∑	NOUN
ejpam-2332	252	11	i=1	i=1	PROPN
ejpam-2332	252	12	n∑	n∑	PROPN
ejpam-2332	253	1	j=1	j=1	NOUN
ejpam-2332	254	1	x	x	PUNCT
ejpam-2332	254	2	i	i	PRON
ejpam-2332	254	3	bi	bi	PROPN
ejpam-2332	254	4	j	j	PROPN
ejpam-2332	254	5	y	y	PROPN
ejpam-2332	254	6	j	j	PROPN
ejpam-2332	254	7	.	.	PUNCT
ejpam-2332	255	1	definition	definition	NOUN
ejpam-2332	255	2	9	9	NUM
ejpam-2332	255	3	(	(	PUNCT
ejpam-2332	255	4	equilibrium	equilibrium	NOUN
ejpam-2332	255	5	solution	solution	NOUN
ejpam-2332	255	6	)	)	PUNCT
ejpam-2332	255	7	.	.	PUNCT
ejpam-2332	256	1	a	a	DET
ejpam-2332	256	2	pair	pair	NOUN
ejpam-2332	256	3	(	(	PUNCT
ejpam-2332	256	4	x∗,y∗	x∗,y∗	PROPN
ejpam-2332	256	5	)	)	PUNCT
ejpam-2332	256	6	∈	∈	PROPN
ejpam-2332	257	1	si	si	NOUN
ejpam-2332	257	2	×	×	NOUN
ejpam-2332	257	3	si	si	INTJ
ejpam-2332	258	1	i	i	PRON
ejpam-2332	258	2	is	be	AUX
ejpam-2332	258	3	said	say	VERB
ejpam-2332	258	4	to	to	PART
ejpam-2332	258	5	be	be	AUX
ejpam-2332	258	6	an	an	DET
ejpam-2332	258	7	equilibrium	equilibrium	NOUN
ejpam-2332	258	8	solution	solution	NOUN
ejpam-2332	258	9	of	of	ADP
ejpam-2332	258	10	the	the	DET
ejpam-2332	258	11	bi	bi	ADJ
ejpam-2332	258	12	-	-	ADJ
ejpam-2332	258	13	matrix	matrix	NOUN
ejpam-2332	258	14	game	game	NOUN
ejpam-2332	258	15	bg	bg	PROPN
ejpam-2332	258	16	if	if	SCONJ
ejpam-2332	258	17	xt	xt	PROPN
ejpam-2332	258	18	ay∗	ay∗	PROPN
ejpam-2332	258	19	≤	≤	PROPN
ejpam-2332	259	1	x∗t	x∗t	NUM
ejpam-2332	259	2	ay∗,∀x	ay∗,∀x	PROPN
ejpam-2332	259	3	∈	∈	PROPN
ejpam-2332	259	4	si	si	PROPN
ejpam-2332	259	5	and	and	CCONJ
ejpam-2332	259	6	x∗t	x∗t	NUM
ejpam-2332	259	7	by≤	by≤	PRON
ejpam-2332	259	8	x∗t	x∗t	NUM
ejpam-2332	259	9	by∗,∀y	by∗,∀y	VERB
ejpam-2332	259	10	∈	∈	PROPN
ejpam-2332	259	11	si	si	NOUN
ejpam-2332	259	12	i	i	PRON
ejpam-2332	259	13	.	.	PUNCT
ejpam-2332	260	1	x∗	x∗	PROPN
ejpam-2332	260	2	and	and	CCONJ
ejpam-2332	260	3	y∗	y∗	PROPN
ejpam-2332	260	4	are	be	AUX
ejpam-2332	260	5	also	also	ADV
ejpam-2332	260	6	called	call	VERB
ejpam-2332	260	7	the	the	DET
ejpam-2332	260	8	optimal	optimal	ADJ
ejpam-2332	260	9	strategies	strategy	NOUN
ejpam-2332	260	10	for	for	ADP
ejpam-2332	260	11	the	the	DET
ejpam-2332	260	12	player	player	NOUN
ejpam-2332	260	13	i	i	PRON
ejpam-2332	260	14	and	and	CCONJ
ejpam-2332	260	15	i	i	PRON
ejpam-2332	260	16	i	i	PRON
ejpam-2332	260	17	respectively	respectively	ADV
ejpam-2332	260	18	.	.	PUNCT
ejpam-2332	261	1	the	the	DET
ejpam-2332	261	2	pair	pair	NOUN
ejpam-2332	261	3	of	of	ADP
ejpam-2332	261	4	numbers	number	NOUN
ejpam-2332	261	5	v	v	ADP
ejpam-2332	261	6	=	=	SYM
ejpam-2332	261	7	〈	〈	PROPN
ejpam-2332	261	8	x∗t	x∗t	NUM
ejpam-2332	261	9	ay∗,x∗t	ay∗,x∗t	ADJ
ejpam-2332	261	10	by∗	by∗	NOUN
ejpam-2332	261	11	〉	〉	NOUN
ejpam-2332	261	12	is	be	AUX
ejpam-2332	261	13	said	say	VERB
ejpam-2332	261	14	to	to	PART
ejpam-2332	261	15	be	be	AUX
ejpam-2332	261	16	the	the	DET
ejpam-2332	261	17	nash	nash	ADJ
ejpam-2332	261	18	equilibrium	equilibrium	NOUN
ejpam-2332	261	19	outcome	outcome	NOUN
ejpam-2332	261	20	of	of	ADP
ejpam-2332	261	21	bg	bg	PROPN
ejpam-2332	261	22	and	and	CCONJ
ejpam-2332	261	23	the	the	DET
ejpam-2332	261	24	triplet	triplet	NOUN
ejpam-2332	261	25	(	(	PUNCT
ejpam-2332	261	26	x∗,y∗	x∗,y∗	PROPN
ejpam-2332	261	27	,	,	PUNCT
ejpam-2332	261	28	v	v	NOUN
ejpam-2332	261	29	)	)	PUNCT
ejpam-2332	261	30	is	be	AUX
ejpam-2332	261	31	called	call	VERB
ejpam-2332	261	32	the	the	DET
ejpam-2332	261	33	solution	solution	NOUN
ejpam-2332	261	34	the	the	DET
ejpam-2332	261	35	bi	bi	ADJ
ejpam-2332	261	36	-	-	ADJ
ejpam-2332	261	37	matrix	matrix	NOUN
ejpam-2332	261	38	game	game	NOUN
ejpam-2332	261	39	.	.	PUNCT
ejpam-2332	262	1	the	the	DET
ejpam-2332	262	2	following	follow	VERB
ejpam-2332	262	3	theorem	theorem	NOUN
ejpam-2332	262	4	due	due	ADP
ejpam-2332	262	5	to	to	ADP
ejpam-2332	262	6	nash	nash	NOUN
ejpam-2332	262	7	,	,	PUNCT
ejpam-2332	262	8	guarantees	guarantee	VERB
ejpam-2332	262	9	the	the	DET
ejpam-2332	262	10	existence	existence	NOUN
ejpam-2332	262	11	of	of	ADP
ejpam-2332	262	12	an	an	DET
ejpam-2332	262	13	equilibrium	equilibrium	NOUN
ejpam-2332	262	14	solution	solution	NOUN
ejpam-2332	262	15	of	of	ADP
ejpam-2332	262	16	the	the	DET
ejpam-2332	262	17	bi	bi	ADJ
ejpam-2332	262	18	-	-	ADJ
ejpam-2332	262	19	matrix	matrix	NOUN
ejpam-2332	262	20	game	game	NOUN
ejpam-2332	262	21	bg	bg	PROPN
ejpam-2332	262	22	.	.	PUNCT
ejpam-2332	262	23	theorem	theorem	PROPN
ejpam-2332	262	24	1	1	NUM
ejpam-2332	262	25	(	(	PUNCT
ejpam-2332	262	26	owen	owen	NOUN
ejpam-2332	262	27	[	[	X
ejpam-2332	262	28	23	23	NUM
ejpam-2332	262	29	]	]	PUNCT
ejpam-2332	262	30	(	(	PUNCT
ejpam-2332	262	31	nash	nash	PROPN
ejpam-2332	262	32	existence	existence	NOUN
ejpam-2332	262	33	theorem	theorem	VERB
ejpam-2332	262	34	)	)	PUNCT
ejpam-2332	262	35	)	)	PUNCT
ejpam-2332	262	36	.	.	PUNCT
ejpam-2332	263	1	every	every	DET
ejpam-2332	263	2	bi	bi	ADJ
ejpam-2332	263	3	-	-	ADJ
ejpam-2332	263	4	matrix	matrix	NOUN
ejpam-2332	263	5	game	game	NOUN
ejpam-2332	263	6	bg	bg	PROPN
ejpam-2332	263	7	has	have	VERB
ejpam-2332	263	8	at	at	ADV
ejpam-2332	263	9	least	least	ADV
ejpam-2332	263	10	one	one	NUM
ejpam-2332	263	11	equilibrium	equilibrium	NOUN
ejpam-2332	263	12	solution	solution	NOUN
ejpam-2332	263	13	.	.	PUNCT
ejpam-2332	264	1	a	a	DET
ejpam-2332	264	2	nash	nash	ADJ
ejpam-2332	264	3	equilibrium	equilibrium	NOUN
ejpam-2332	264	4	solution	solution	NOUN
ejpam-2332	264	5	of	of	ADP
ejpam-2332	264	6	the	the	DET
ejpam-2332	264	7	bi	bi	ADJ
ejpam-2332	264	8	-	-	ADJ
ejpam-2332	264	9	matrix	matrix	NOUN
ejpam-2332	264	10	game	game	NOUN
ejpam-2332	264	11	bg	bg	PROPN
ejpam-2332	264	12	can	can	AUX
ejpam-2332	264	13	be	be	AUX
ejpam-2332	264	14	obtained	obtain	VERB
ejpam-2332	264	15	by	by	ADP
ejpam-2332	264	16	solving	solve	VERB
ejpam-2332	264	17	an	an	DET
ejpam-2332	264	18	appropriate	appropriate	ADJ
ejpam-2332	264	19	quadratic	quadratic	ADJ
ejpam-2332	264	20	programming	programming	NOUN
ejpam-2332	264	21	problem	problem	NOUN
ejpam-2332	264	22	as	as	SCONJ
ejpam-2332	264	23	discussed	discuss	VERB
ejpam-2332	264	24	below	below	ADV
ejpam-2332	264	25	.	.	PUNCT
ejpam-2332	265	1	theorem	theorem	ADJ
ejpam-2332	265	2	2	2	NUM
ejpam-2332	265	3	(	(	PUNCT
ejpam-2332	265	4	mangasarian	mangasarian	NOUN
ejpam-2332	265	5	and	and	CCONJ
ejpam-2332	265	6	stone	stone	NOUN
ejpam-2332	266	1	[	[	X
ejpam-2332	266	2	14	14	NUM
ejpam-2332	266	3	]	]	PUNCT
ejpam-2332	266	4	(	(	PUNCT
ejpam-2332	266	5	equivalence	equivalence	NOUN
ejpam-2332	266	6	theorem	theorem	VERB
ejpam-2332	266	7	)	)	PUNCT
ejpam-2332	266	8	)	)	PUNCT
ejpam-2332	266	9	.	.	PUNCT
ejpam-2332	267	1	for	for	ADP
ejpam-2332	267	2	a	a	DET
ejpam-2332	267	3	given	give	VERB
ejpam-2332	267	4	bi	bi	ADJ
ejpam-2332	267	5	-	-	ADJ
ejpam-2332	267	6	matrix	matrix	NOUN
ejpam-2332	267	7	game	game	NOUN
ejpam-2332	267	8	bg	bg	NOUN
ejpam-2332	267	9	=	=	PUNCT
ejpam-2332	267	10	(	(	PUNCT
ejpam-2332	267	11	si	si	INTJ
ejpam-2332	267	12	×	×	NOUN
ejpam-2332	267	13	si	si	INTJ
ejpam-2332	267	14	i	i	PRON
ejpam-2332	267	15	,	,	PUNCT
ejpam-2332	267	16	a	a	DET
ejpam-2332	267	17	,	,	PUNCT
ejpam-2332	267	18	b	b	NOUN
ejpam-2332	267	19	)	)	PUNCT
ejpam-2332	267	20	a	a	DET
ejpam-2332	267	21	necessary	necessary	ADJ
ejpam-2332	267	22	and	and	CCONJ
ejpam-2332	267	23	sufficient	sufficient	ADJ
ejpam-2332	267	24	condition	condition	NOUN
ejpam-2332	267	25	that	that	SCONJ
ejpam-2332	267	26	(	(	PUNCT
ejpam-2332	267	27	x∗,y∗	x∗,y∗	PROPN
ejpam-2332	267	28	)	)	PUNCT
ejpam-2332	267	29	be	be	VERB
ejpam-2332	267	30	an	an	DET
ejpam-2332	267	31	equilibrium	equilibrium	NOUN
ejpam-2332	267	32	solution	solution	NOUN
ejpam-2332	267	33	of	of	ADP
ejpam-2332	267	34	bg	bg	PROPN
ejpam-2332	267	35	is	be	AUX
ejpam-2332	267	36	that	that	SCONJ
ejpam-2332	267	37	it	it	PRON
ejpam-2332	267	38	is	be	AUX
ejpam-2332	267	39	a	a	DET
ejpam-2332	267	40	solution	solution	NOUN
ejpam-2332	267	41	of	of	ADP
ejpam-2332	267	42	the	the	DET
ejpam-2332	267	43	following	follow	VERB
ejpam-2332	267	44	quadratic	quadratic	ADJ
ejpam-2332	267	45	programming	programming	NOUN
ejpam-2332	267	46	problem	problem	NOUN
ejpam-2332	267	47	(	(	PUNCT
ejpam-2332	267	48	qpp	qpp	NOUN
ejpam-2332	267	49	)	)	PUNCT
ejpam-2332	267	50	.	.	PUNCT
ejpam-2332	268	1	max	max	PROPN
ejpam-2332	268	2	xt	xt	PROPN
ejpam-2332	268	3	(	(	PUNCT
ejpam-2332	268	4	a+	a+	PUNCT
ejpam-2332	268	5	b)y−	b)y−	NOUN
ejpam-2332	268	6	p−	p−	NOUN
ejpam-2332	268	7	q	q	X
ejpam-2332	268	8	s.t	s.t	PROPN
ejpam-2332	268	9	.	.	PROPN
ejpam-2332	268	10	ay≤	ay≤	PROPN
ejpam-2332	268	11	pe	pe	PROPN
ejpam-2332	268	12	,	,	PUNCT
ejpam-2332	268	13	bt	bt	PROPN
ejpam-2332	268	14	x≤	x≤	PROPN
ejpam-2332	268	15	qe	qe	PROPN
ejpam-2332	268	16	,	,	PUNCT
ejpam-2332	268	17	x	x	PROPN
ejpam-2332	268	18	∈	∈	NOUN
ejpam-2332	268	19	si	si	X
ejpam-2332	268	20	,	,	PUNCT
ejpam-2332	268	21	y	y	PROPN
ejpam-2332	268	22	∈	∈	PROPN
ejpam-2332	268	23	si	si	X
ejpam-2332	268	24	i	i	PRON
ejpam-2332	268	25	;	;	PUNCT
ejpam-2332	268	26	p	p	X
ejpam-2332	268	27	,	,	PUNCT
ejpam-2332	268	28	q	q	PROPN
ejpam-2332	268	29	∈	∈	NOUN
ejpam-2332	268	30	ℜ.	ℜ.	PROPN
ejpam-2332	268	31	further	far	ADV
ejpam-2332	268	32	,	,	PUNCT
ejpam-2332	268	33	if	if	SCONJ
ejpam-2332	268	34	(	(	PUNCT
ejpam-2332	268	35	x∗,y∗	x∗,y∗	PROPN
ejpam-2332	268	36	,	,	PUNCT
ejpam-2332	268	37	p∗,q∗	p∗,q∗	PROPN
ejpam-2332	268	38	)	)	PUNCT
ejpam-2332	268	39	is	be	AUX
ejpam-2332	268	40	a	a	DET
ejpam-2332	268	41	solution	solution	NOUN
ejpam-2332	268	42	of	of	ADP
ejpam-2332	268	43	the	the	DET
ejpam-2332	268	44	above	above	ADJ
ejpam-2332	268	45	problem	problem	NOUN
ejpam-2332	268	46	then	then	ADV
ejpam-2332	268	47	p∗	p∗	PROPN
ejpam-2332	268	48	=	=	SYM
ejpam-2332	268	49	x∗t	x∗t	PROPN
ejpam-2332	268	50	ay∗	ay∗	PROPN
ejpam-2332	268	51	,	,	PUNCT
ejpam-2332	268	52	q∗	q∗	NOUN
ejpam-2332	268	53	=	=	SYM
ejpam-2332	268	54	x∗t	x∗t	PUNCT
ejpam-2332	268	55	by∗	by∗	NOUN
ejpam-2332	268	56	and	and	CCONJ
ejpam-2332	268	57	x∗t	x∗t	NUM
ejpam-2332	268	58	(	(	PUNCT
ejpam-2332	268	59	a+	a+	PUNCT
ejpam-2332	268	60	b)y∗	b)y∗	NOUN
ejpam-2332	269	1	−	−	NOUN
ejpam-2332	269	2	p∗	p∗	ADJ
ejpam-2332	269	3	−	−	NOUN
ejpam-2332	269	4	q∗	q∗	NOUN
ejpam-2332	269	5	=	=	SYM
ejpam-2332	269	6	0	0	NUM
ejpam-2332	269	7	m.	m.	NOUN
ejpam-2332	269	8	seikh	seikh	PROPN
ejpam-2332	269	9	,	,	PUNCT
ejpam-2332	269	10	p.	p.	PROPN
ejpam-2332	269	11	nayak	nayak	PROPN
ejpam-2332	269	12	,	,	PUNCT
ejpam-2332	269	13	m.	m.	NOUN
ejpam-2332	269	14	pal	pal	PROPN
ejpam-2332	269	15	/	/	SYM
ejpam-2332	269	16	eur	eur	PROPN
ejpam-2332	269	17	.	.	PUNCT
ejpam-2332	270	1	j.	j.	PROPN
ejpam-2332	270	2	pure	pure	PROPN
ejpam-2332	270	3	appl	appl	PROPN
ejpam-2332	270	4	.	.	PROPN
ejpam-2332	270	5	math	math	PROPN
ejpam-2332	270	6	,	,	PUNCT
ejpam-2332	270	7	8	8	NUM
ejpam-2332	270	8	(	(	PUNCT
ejpam-2332	270	9	2015	2015	NUM
ejpam-2332	270	10	)	)	PUNCT
ejpam-2332	270	11	,	,	PUNCT
ejpam-2332	270	12	153	153	NUM
ejpam-2332	270	13	-	-	SYM
ejpam-2332	270	14	171	171	NUM
ejpam-2332	270	15	162	162	NUM
ejpam-2332	270	16	4.3	4.3	NUM
ejpam-2332	270	17	.	.	PUNCT
ejpam-2332	271	1	bi	bi	ADJ
ejpam-2332	271	2	-	-	ADJ
ejpam-2332	271	3	matrix	matrix	NOUN
ejpam-2332	271	4	games	game	NOUN
ejpam-2332	271	5	with	with	ADP
ejpam-2332	271	6	pay	pay	NOUN
ejpam-2332	271	7	-	-	PUNCT
ejpam-2332	271	8	offs	off	NOUN
ejpam-2332	271	9	of	of	ADP
ejpam-2332	271	10	tifns	tifns	NOUN
ejpam-2332	271	11	let	let	VERB
ejpam-2332	271	12	si	si	PROPN
ejpam-2332	271	13	,	,	PUNCT
ejpam-2332	271	14	si	si	INTJ
ejpam-2332	271	15	i	i	PRON
ejpam-2332	271	16	be	be	VERB
ejpam-2332	271	17	the	the	DET
ejpam-2332	271	18	strategy	strategy	NOUN
ejpam-2332	271	19	spaces	space	NOUN
ejpam-2332	271	20	for	for	ADP
ejpam-2332	271	21	player	player	NOUN
ejpam-2332	271	22	i	i	PRON
ejpam-2332	271	23	and	and	CCONJ
ejpam-2332	271	24	player	player	PROPN
ejpam-2332	271	25	ii	ii	PROPN
ejpam-2332	271	26	,	,	PUNCT
ejpam-2332	271	27	respectively	respectively	ADV
ejpam-2332	271	28	as	as	SCONJ
ejpam-2332	271	29	defined	define	VERB
ejpam-2332	271	30	in	in	ADP
ejpam-2332	271	31	above	above	ADP
ejpam-2332	271	32	section	section	NOUN
ejpam-2332	271	33	.	.	PUNCT
ejpam-2332	272	1	also	also	ADV
ejpam-2332	272	2	let	let	VERB
ejpam-2332	272	3	ã	ã	PROPN
ejpam-2332	272	4	=	=	SYM
ejpam-2332	272	5	(	(	PUNCT
ejpam-2332	272	6	ãi	ãi	INTJ
ejpam-2332	272	7	j)m×n	j)m×n	PROPN
ejpam-2332	272	8	and	and	CCONJ
ejpam-2332	272	9	b̃	b̃	PROPN
ejpam-2332	272	10	=	=	PUNCT
ejpam-2332	272	11	(	(	PUNCT
ejpam-2332	272	12	b̃i	b̃i	SCONJ
ejpam-2332	272	13	j)m×n	j)m×n	PROPN
ejpam-2332	272	14	be	be	AUX
ejpam-2332	272	15	the	the	DET
ejpam-2332	272	16	pay	pay	VERB
ejpam-2332	272	17	-	-	PUNCT
ejpam-2332	272	18	off	off	ADP
ejpam-2332	272	19	matrices	matrix	NOUN
ejpam-2332	272	20	for	for	ADP
ejpam-2332	272	21	players	player	NOUN
ejpam-2332	272	22	i	i	PRON
ejpam-2332	272	23	and	and	CCONJ
ejpam-2332	272	24	ii	ii	PROPN
ejpam-2332	272	25	,	,	PUNCT
ejpam-2332	272	26	respectively	respectively	ADV
ejpam-2332	272	27	,	,	PUNCT
ejpam-2332	272	28	where	where	SCONJ
ejpam-2332	272	29	ãi	ãi	VERB
ejpam-2332	272	30	j	j	PROPN
ejpam-2332	272	31	=	=	SYM
ejpam-2332	272	32	〈	〈	PROPN
ejpam-2332	272	33	(	(	PUNCT
ejpam-2332	272	34	ai	ai	VERB
ejpam-2332	272	35	jµ	jµ	ADJ
ejpam-2332	272	36	,	,	PUNCT
ejpam-2332	272	37	ai	ai	VERB
ejpam-2332	272	38	j	j	PROPN
ejpam-2332	272	39	,	,	PUNCT
ejpam-2332	272	40	āi	āi	PROPN
ejpam-2332	272	41	jµ	jµ	PROPN
ejpam-2332	272	42	)	)	PUNCT
ejpam-2332	272	43	;	;	PUNCT
ejpam-2332	272	44	(	(	PUNCT
ejpam-2332	272	45	ai	ai	VERB
ejpam-2332	272	46	jν	jν	NOUN
ejpam-2332	272	47	,	,	PUNCT
ejpam-2332	272	48	ai	ai	VERB
ejpam-2332	272	49	j	j	PROPN
ejpam-2332	272	50	,	,	PUNCT
ejpam-2332	272	51	āi	āi	PROPN
ejpam-2332	272	52	jν	jν	NOUN
ejpam-2332	272	53	)	)	PUNCT
ejpam-2332	272	54	〉	〉	NOUN
ejpam-2332	272	55	(	(	PUNCT
ejpam-2332	272	56	i	i	NOUN
ejpam-2332	272	57	=	=	SYM
ejpam-2332	272	58	1,2	1,2	NUM
ejpam-2332	272	59	,	,	PUNCT
ejpam-2332	272	60	.	.	PUNCT
ejpam-2332	272	61	.	.	PUNCT
ejpam-2332	272	62	.	.	PUNCT
ejpam-2332	273	1	m	m	PROPN
ejpam-2332	273	2	;	;	PUNCT
ejpam-2332	273	3	j	j	PROPN
ejpam-2332	273	4	=	=	SYM
ejpam-2332	273	5	1,2	1,2	NUM
ejpam-2332	273	6	,	,	PUNCT
ejpam-2332	273	7	.	.	PUNCT
ejpam-2332	273	8	.	.	PUNCT
ejpam-2332	273	9	.	.	PUNCT
ejpam-2332	274	1	n	n	CCONJ
ejpam-2332	274	2	)	)	PUNCT
ejpam-2332	275	1	and	and	CCONJ
ejpam-2332	275	2	b̃i	b̃i	ADP
ejpam-2332	275	3	j	j	PROPN
ejpam-2332	275	4	=	=	SYM
ejpam-2332	275	5	〈	〈	PROPN
ejpam-2332	275	6	(	(	PUNCT
ejpam-2332	275	7	bi	bi	PROPN
ejpam-2332	275	8	jµ	jµ	PROPN
ejpam-2332	275	9	,	,	PUNCT
ejpam-2332	275	10	bi	bi	PROPN
ejpam-2332	275	11	j	j	PROPN
ejpam-2332	275	12	,	,	PUNCT
ejpam-2332	275	13	b̄i	b̄i	PROPN
ejpam-2332	275	14	jµ	jµ	PROPN
ejpam-2332	275	15	)	)	PUNCT
ejpam-2332	275	16	;	;	PUNCT
ejpam-2332	275	17	(	(	PUNCT
ejpam-2332	275	18	bi	bi	NOUN
ejpam-2332	275	19	jν	jν	NOUN
ejpam-2332	275	20	,	,	PUNCT
ejpam-2332	275	21	bi	bi	PROPN
ejpam-2332	275	22	j	j	PROPN
ejpam-2332	275	23	,	,	PUNCT
ejpam-2332	275	24	b̄i	b̄i	PROPN
ejpam-2332	275	25	jν	jν	NOUN
ejpam-2332	275	26	)	)	PUNCT
ejpam-2332	275	27	〉	〉	NOUN
ejpam-2332	275	28	(	(	PUNCT
ejpam-2332	275	29	i	i	NOUN
ejpam-2332	275	30	=	=	SYM
ejpam-2332	275	31	1,2	1,2	NUM
ejpam-2332	275	32	,	,	PUNCT
ejpam-2332	275	33	.	.	PUNCT
ejpam-2332	275	34	.	.	PUNCT
ejpam-2332	275	35	.	.	PUNCT
ejpam-2332	276	1	m	m	PROPN
ejpam-2332	276	2	;	;	PUNCT
ejpam-2332	276	3	j	j	PROPN
ejpam-2332	276	4	=	=	SYM
ejpam-2332	276	5	1,2	1,2	NUM
ejpam-2332	276	6	,	,	PUNCT
ejpam-2332	276	7	.	.	PUNCT
ejpam-2332	276	8	.	.	PUNCT
ejpam-2332	276	9	.	.	PUNCT
ejpam-2332	277	1	n	n	CCONJ
ejpam-2332	277	2	)	)	PUNCT
ejpam-2332	277	3	are	be	AUX
ejpam-2332	277	4	the	the	DET
ejpam-2332	277	5	tifns	tifns	NOUN
ejpam-2332	277	6	as	as	SCONJ
ejpam-2332	277	7	defined	define	VERB
ejpam-2332	277	8	in	in	ADP
ejpam-2332	277	9	2.1	2.1	NUM
ejpam-2332	277	10	.	.	PUNCT
ejpam-2332	278	1	then	then	ADV
ejpam-2332	278	2	a	a	DET
ejpam-2332	278	3	two	two	NUM
ejpam-2332	278	4	person	person	NOUN
ejpam-2332	278	5	bi	bi	ADJ
ejpam-2332	278	6	-	-	NOUN
ejpam-2332	278	7	matrix	matrix	NOUN
ejpam-2332	278	8	game	game	NOUN
ejpam-2332	278	9	with	with	ADP
ejpam-2332	278	10	pay	pay	NOUN
ejpam-2332	278	11	-	-	PUNCT
ejpam-2332	278	12	offs	off	NOUN
ejpam-2332	278	13	of	of	ADP
ejpam-2332	278	14	tifns	tifns	NOUN
ejpam-2332	278	15	is	be	AUX
ejpam-2332	278	16	defined	define	VERB
ejpam-2332	278	17	by	by	ADP
ejpam-2332	278	18	(	(	PUNCT
ejpam-2332	278	19	si	si	X
ejpam-2332	278	20	,	,	PUNCT
ejpam-2332	278	21	si	si	X
ejpam-2332	278	22	i	i	PROPN
ejpam-2332	278	23	,	,	PUNCT
ejpam-2332	278	24	ã	ã	PROPN
ejpam-2332	278	25	,	,	PUNCT
ejpam-2332	278	26	b̃	b̃	PROPN
ejpam-2332	278	27	)	)	PUNCT
ejpam-2332	278	28	.	.	PUNCT
ejpam-2332	279	1	in	in	ADP
ejpam-2332	279	2	the	the	DET
ejpam-2332	279	3	following	following	NOUN
ejpam-2332	279	4	,	,	PUNCT
ejpam-2332	279	5	we	we	PRON
ejpam-2332	279	6	shall	shall	AUX
ejpam-2332	279	7	often	often	ADV
ejpam-2332	279	8	call	call	VERB
ejpam-2332	279	9	a	a	DET
ejpam-2332	279	10	two	two	NUM
ejpam-2332	279	11	-	-	PUNCT
ejpam-2332	279	12	person	person	NOUN
ejpam-2332	279	13	bi	bi	ADJ
ejpam-2332	279	14	-	-	NOUN
ejpam-2332	279	15	matrix	matrix	NOUN
ejpam-2332	279	16	game	game	NOUN
ejpam-2332	279	17	with	with	ADP
ejpam-2332	279	18	pay	pay	NOUN
ejpam-2332	279	19	-	-	PUNCT
ejpam-2332	279	20	offs	off	NOUN
ejpam-2332	279	21	of	of	ADP
ejpam-2332	279	22	tifns	tifns	NOUN
ejpam-2332	279	23	as	as	ADP
ejpam-2332	279	24	intuitionistic	intuitionistic	ADJ
ejpam-2332	279	25	fuzzy	fuzzy	ADJ
ejpam-2332	279	26	bi	bi	ADJ
ejpam-2332	279	27	-	-	ADJ
ejpam-2332	279	28	matrix	matrix	NOUN
ejpam-2332	279	29	game	game	NOUN
ejpam-2332	279	30	,	,	PUNCT
ejpam-2332	279	31	denoted	denote	VERB
ejpam-2332	279	32	byái	byái	NOUN
ejpam-2332	279	33	fbg	fbg	PROPN
ejpam-2332	279	34	=	=	SYM
ejpam-2332	279	35	(	(	PUNCT
ejpam-2332	279	36	si	si	X
ejpam-2332	279	37	,	,	PUNCT
ejpam-2332	279	38	si	si	INTJ
ejpam-2332	279	39	i	i	PROPN
ejpam-2332	279	40	,	,	PUNCT
ejpam-2332	279	41	ã	ã	PROPN
ejpam-2332	279	42	,	,	PUNCT
ejpam-2332	279	43	b̃	b̃	PROPN
ejpam-2332	279	44	)	)	PUNCT
ejpam-2332	279	45	.	.	PUNCT
ejpam-2332	280	1	definition	definition	NOUN
ejpam-2332	280	2	10	10	NUM
ejpam-2332	280	3	(	(	PUNCT
ejpam-2332	280	4	expected	expect	VERB
ejpam-2332	280	5	pay	pay	NOUN
ejpam-2332	280	6	-	-	PUNCT
ejpam-2332	280	7	offs	off	NOUN
ejpam-2332	280	8	)	)	PUNCT
ejpam-2332	280	9	.	.	PUNCT
ejpam-2332	281	1	let	let	VERB
ejpam-2332	281	2	player	player	NOUN
ejpam-2332	281	3	i	i	PRON
ejpam-2332	281	4	chooses	choose	VERB
ejpam-2332	281	5	any	any	DET
ejpam-2332	281	6	mixed	mixed	ADJ
ejpam-2332	281	7	strategy	strategy	NOUN
ejpam-2332	281	8	x	x	X
ejpam-2332	281	9	∈	∈	NOUN
ejpam-2332	281	10	si	si	X
ejpam-2332	281	11	and	and	CCONJ
ejpam-2332	281	12	player	player	PROPN
ejpam-2332	281	13	ii	ii	PROPN
ejpam-2332	281	14	chooses	choose	VERB
ejpam-2332	281	15	any	any	DET
ejpam-2332	281	16	mixed	mixed	ADJ
ejpam-2332	281	17	strategy	strategy	NOUN
ejpam-2332	281	18	y	y	PROPN
ejpam-2332	281	19	∈	∈	PROPN
ejpam-2332	282	1	si	si	PROPN
ejpam-2332	283	1	i	i	PRON
ejpam-2332	283	2	,	,	PUNCT
ejpam-2332	283	3	then	then	ADV
ejpam-2332	283	4	the	the	DET
ejpam-2332	283	5	expected	expect	VERB
ejpam-2332	283	6	pay	pay	NOUN
ejpam-2332	283	7	-	-	PUNCT
ejpam-2332	283	8	offs	off	NOUN
ejpam-2332	283	9	for	for	ADP
ejpam-2332	283	10	player	player	NOUN
ejpam-2332	283	11	i	i	PRON
ejpam-2332	283	12	and	and	CCONJ
ejpam-2332	283	13	player	player	PROPN
ejpam-2332	283	14	ii	ii	PROPN
ejpam-2332	283	15	are	be	AUX
ejpam-2332	283	16	ẽ1(ã	ẽ1(ã	NOUN
ejpam-2332	283	17	)	)	PUNCT
ejpam-2332	283	18	=	=	PUNCT
ejpam-2332	284	1	xt	xt	VERB
ejpam-2332	285	1	ãy=	ãy=	PROPN
ejpam-2332	285	2	m∑	m∑	VERB
ejpam-2332	285	3	i=1	i=1	PROPN
ejpam-2332	285	4	n∑	n∑	PROPN
ejpam-2332	286	1	j=1	j=1	PROPN
ejpam-2332	286	2	ãi	ãi	PROPN
ejpam-2332	287	1	j	j	PROPN
ejpam-2332	287	2	x	x	VERB
ejpam-2332	288	1	i	i	PRON
ejpam-2332	288	2	y	y	PROPN
ejpam-2332	288	3	j	j	PROPN
ejpam-2332	288	4	=	=	PUNCT
ejpam-2332	288	5	¬	¬	PROPN
ejpam-2332	288	6	�	�	PROPN
ejpam-2332	288	7	m∑	m∑	NOUN
ejpam-2332	288	8	i=1	i=1	PROPN
ejpam-2332	288	9	n∑	n∑	PROPN
ejpam-2332	289	1	j=1	j=1	PROPN
ejpam-2332	289	2	ai	ai	VERB
ejpam-2332	289	3	jµx	jµx	PROPN
ejpam-2332	290	1	i	i	PRON
ejpam-2332	290	2	y	y	PROPN
ejpam-2332	290	3	j	j	PROPN
ejpam-2332	290	4	,	,	PUNCT
ejpam-2332	290	5	m∑	m∑	INTJ
ejpam-2332	290	6	i=1	i=1	PROPN
ejpam-2332	290	7	n∑	n∑	PROPN
ejpam-2332	291	1	j=1	j=1	PROPN
ejpam-2332	291	2	ai	ai	VERB
ejpam-2332	291	3	j	j	PROPN
ejpam-2332	291	4	x	x	PROPN
ejpam-2332	292	1	i	i	PRON
ejpam-2332	292	2	y	y	PROPN
ejpam-2332	292	3	j	j	PROPN
ejpam-2332	292	4	,	,	PUNCT
ejpam-2332	292	5	m∑	m∑	INTJ
ejpam-2332	292	6	i=1	i=1	PROPN
ejpam-2332	292	7	n∑	n∑	PROPN
ejpam-2332	293	1	j=1	j=1	PROPN
ejpam-2332	293	2	āi	āi	PROPN
ejpam-2332	293	3	jµx	jµx	NOUN
ejpam-2332	294	1	i	i	PROPN
ejpam-2332	294	2	y	y	PROPN
ejpam-2332	294	3	j	j	PROPN
ejpam-2332	294	4	�	�	PROPN
ejpam-2332	294	5	;	;	PUNCT
ejpam-2332	294	6	�	�	PROPN
ejpam-2332	294	7	m∑	m∑	CCONJ
ejpam-2332	294	8	i=1	i=1	PROPN
ejpam-2332	294	9	n∑	n∑	PROPN
ejpam-2332	295	1	j=1	j=1	PROPN
ejpam-2332	295	2	ai	ai	VERB
ejpam-2332	295	3	jνx	jνx	PROPN
ejpam-2332	296	1	i	i	PRON
ejpam-2332	296	2	y	y	PROPN
ejpam-2332	296	3	j	j	PROPN
ejpam-2332	296	4	,	,	PUNCT
ejpam-2332	296	5	m∑	m∑	INTJ
ejpam-2332	296	6	i=1	i=1	PROPN
ejpam-2332	296	7	n∑	n∑	PROPN
ejpam-2332	297	1	j=1	j=1	PROPN
ejpam-2332	297	2	ai	ai	VERB
ejpam-2332	297	3	j	j	PROPN
ejpam-2332	297	4	x	x	PROPN
ejpam-2332	298	1	i	i	PRON
ejpam-2332	298	2	y	y	PROPN
ejpam-2332	298	3	j	j	PROPN
ejpam-2332	298	4	,	,	PUNCT
ejpam-2332	298	5	m∑	m∑	INTJ
ejpam-2332	298	6	i=1	i=1	PROPN
ejpam-2332	298	7	n∑	n∑	PROPN
ejpam-2332	299	1	j=1	j=1	ADJ
ejpam-2332	299	2	āi	āi	NUM
ejpam-2332	299	3	jνx	jνx	PROPN
ejpam-2332	300	1	i	i	PRON
ejpam-2332	300	2	y	y	PROPN
ejpam-2332	300	3	j	j	PROPN
ejpam-2332	300	4	�	�	PROPN
ejpam-2332	300	5	¶	¶	PROPN
ejpam-2332	300	6	ẽ2(b̃	ẽ2(b̃	ADJ
ejpam-2332	300	7	)	)	PUNCT
ejpam-2332	300	8	=	=	SYM
ejpam-2332	300	9	xt	xt	X
ejpam-2332	301	1	b̃y=	b̃y=	PROPN
ejpam-2332	301	2	m∑	m∑	VERB
ejpam-2332	301	3	i=1	i=1	PROPN
ejpam-2332	301	4	n∑	n∑	PUNCT
ejpam-2332	302	1	j=1	j=1	PROPN
ejpam-2332	302	2	b̃i	b̃i	ADP
ejpam-2332	302	3	j	j	PROPN
ejpam-2332	302	4	x	x	VERB
ejpam-2332	303	1	i	i	PRON
ejpam-2332	303	2	y	y	PROPN
ejpam-2332	303	3	j	j	PROPN
ejpam-2332	303	4	=	=	PUNCT
ejpam-2332	303	5	¬	¬	PROPN
ejpam-2332	303	6	�	�	PROPN
ejpam-2332	303	7	m∑	m∑	NOUN
ejpam-2332	303	8	i=1	i=1	PROPN
ejpam-2332	303	9	n∑	n∑	PROPN
ejpam-2332	304	1	j=1	j=1	ADJ
ejpam-2332	304	2	bi	bi	NOUN
ejpam-2332	304	3	jµx	jµx	PROPN
ejpam-2332	305	1	i	i	PROPN
ejpam-2332	305	2	y	y	PROPN
ejpam-2332	305	3	j	j	PROPN
ejpam-2332	305	4	,	,	PUNCT
ejpam-2332	305	5	m∑	m∑	INTJ
ejpam-2332	305	6	i=1	i=1	PROPN
ejpam-2332	305	7	n∑	n∑	PROPN
ejpam-2332	306	1	j=1	j=1	ADJ
ejpam-2332	306	2	bi	bi	PROPN
ejpam-2332	306	3	j	j	PROPN
ejpam-2332	306	4	x	x	VERB
ejpam-2332	307	1	i	i	PRON
ejpam-2332	307	2	y	y	PROPN
ejpam-2332	307	3	j	j	PROPN
ejpam-2332	307	4	,	,	PUNCT
ejpam-2332	307	5	m∑	m∑	INTJ
ejpam-2332	307	6	i=1	i=1	PROPN
ejpam-2332	307	7	n∑	n∑	PROPN
ejpam-2332	307	8	j=1	j=1	PROPN
ejpam-2332	307	9	b̄i	b̄i	PROPN
ejpam-2332	307	10	jµx	jµx	VERB
ejpam-2332	308	1	i	i	PRON
ejpam-2332	308	2	y	y	PROPN
ejpam-2332	308	3	j	j	PROPN
ejpam-2332	308	4	�	�	PROPN
ejpam-2332	308	5	;	;	PUNCT
ejpam-2332	308	6	�	�	PROPN
ejpam-2332	308	7	m∑	m∑	CCONJ
ejpam-2332	308	8	i=1	i=1	PROPN
ejpam-2332	308	9	n∑	n∑	PROPN
ejpam-2332	309	1	j=1	j=1	ADJ
ejpam-2332	309	2	bi	bi	NOUN
ejpam-2332	309	3	jνx	jνx	PROPN
ejpam-2332	310	1	i	i	PRON
ejpam-2332	310	2	y	y	PROPN
ejpam-2332	310	3	j	j	PROPN
ejpam-2332	310	4	,	,	PUNCT
ejpam-2332	310	5	m∑	m∑	INTJ
ejpam-2332	310	6	i=1	i=1	PROPN
ejpam-2332	310	7	n∑	n∑	PROPN
ejpam-2332	311	1	j=1	j=1	ADJ
ejpam-2332	311	2	bi	bi	PROPN
ejpam-2332	311	3	j	j	PROPN
ejpam-2332	311	4	x	x	VERB
ejpam-2332	312	1	i	i	PRON
ejpam-2332	312	2	y	y	PROPN
ejpam-2332	312	3	j	j	PROPN
ejpam-2332	312	4	,	,	PUNCT
ejpam-2332	312	5	m∑	m∑	INTJ
ejpam-2332	312	6	i=1	i=1	PROPN
ejpam-2332	312	7	n∑	n∑	PROPN
ejpam-2332	312	8	j=1	j=1	PROPN
ejpam-2332	313	1	b̄i	b̄i	NOUN
ejpam-2332	313	2	jνx	jνx	VERB
ejpam-2332	313	3	i	i	PRON
ejpam-2332	313	4	y	y	PROPN
ejpam-2332	313	5	j	j	PROPN
ejpam-2332	313	6	�	�	PROPN
ejpam-2332	313	7	¶	¶	PROPN
ejpam-2332	313	8	respectively	respectively	ADV
ejpam-2332	313	9	,	,	PUNCT
ejpam-2332	313	10	which	which	PRON
ejpam-2332	313	11	are	be	AUX
ejpam-2332	313	12	tifns	tifns	ADJ
ejpam-2332	313	13	.	.	PUNCT
ejpam-2332	314	1	in	in	ADP
ejpam-2332	314	2	the	the	DET
ejpam-2332	314	3	next	next	ADJ
ejpam-2332	314	4	section	section	NOUN
ejpam-2332	314	5	,	,	PUNCT
ejpam-2332	314	6	we	we	PRON
ejpam-2332	314	7	have	have	AUX
ejpam-2332	314	8	described	describe	VERB
ejpam-2332	314	9	the	the	DET
ejpam-2332	314	10	meaning	meaning	NOUN
ejpam-2332	314	11	of	of	ADP
ejpam-2332	314	12	equilibrium	equilibrium	NOUN
ejpam-2332	314	13	solution	solution	NOUN
ejpam-2332	314	14	of	of	ADP
ejpam-2332	314	15	bi	bi	NOUN
ejpam-2332	314	16	-	-	NOUN
ejpam-2332	314	17	matrix	matrix	NOUN
ejpam-2332	314	18	ái	ái	ADJ
ejpam-2332	314	19	fbg	fbg	PROPN
ejpam-2332	314	20	.	.	PUNCT
ejpam-2332	315	1	definition	definition	NOUN
ejpam-2332	315	2	11	11	NUM
ejpam-2332	315	3	.	.	PUNCT
ejpam-2332	316	1	let	let	VERB
ejpam-2332	316	2	ũ	ũ	PROPN
ejpam-2332	316	3	and	and	CCONJ
ejpam-2332	316	4	ṽ	ṽ	PROPN
ejpam-2332	316	5	be	be	AUX
ejpam-2332	316	6	two	two	NUM
ejpam-2332	316	7	tifns	tifns	NOUN
ejpam-2332	316	8	.	.	PUNCT
ejpam-2332	317	1	then	then	ADV
ejpam-2332	317	2	(	(	PUNCT
ejpam-2332	317	3	ũ	ũ	PROPN
ejpam-2332	317	4	,	,	PUNCT
ejpam-2332	317	5	ṽ	ṽ	PROPN
ejpam-2332	317	6	)	)	PUNCT
ejpam-2332	317	7	is	be	AUX
ejpam-2332	317	8	called	call	VERB
ejpam-2332	317	9	a	a	DET
ejpam-2332	317	10	reasonable	reasonable	ADJ
ejpam-2332	317	11	solution	solution	NOUN
ejpam-2332	317	12	of	of	ADP
ejpam-2332	317	13	the	the	DET
ejpam-2332	317	14	bi	bi	ADJ
ejpam-2332	317	15	-	-	NOUN
ejpam-2332	317	16	matrix	matrix	NOUN
ejpam-2332	317	17	gameái	gameái	NOUN
ejpam-2332	317	18	fbg	fbg	NOUN
ejpam-2332	317	19	if	if	SCONJ
ejpam-2332	317	20	there	there	PRON
ejpam-2332	317	21	exists	exist	VERB
ejpam-2332	317	22	x∗	x∗	PROPN
ejpam-2332	317	23	∈	∈	PROPN
ejpam-2332	317	24	si	si	X
ejpam-2332	317	25	,	,	PUNCT
ejpam-2332	317	26	y	y	PROPN
ejpam-2332	317	27	∗	∗	X
ejpam-2332	317	28	∈	∈	PROPN
ejpam-2332	318	1	si	si	INTJ
ejpam-2332	319	1	i	i	PRON
ejpam-2332	319	2	such	such	ADJ
ejpam-2332	319	3	that	that	SCONJ
ejpam-2332	319	4	(	(	PUNCT
ejpam-2332	319	5	i	i	NOUN
ejpam-2332	319	6	)	)	PUNCT
ejpam-2332	319	7	xt	xt	ADP
ejpam-2332	319	8	ãy∗	ãy∗	PROPN
ejpam-2332	319	9	�	�	PROPN
ejpam-2332	319	10	̃p̃,q̃	̃p̃,q̃	PROPN
ejpam-2332	319	11	ũ	ũ	PROPN
ejpam-2332	319	12	,	,	PUNCT
ejpam-2332	319	13	for	for	ADP
ejpam-2332	319	14	all	all	DET
ejpam-2332	319	15	x	x	SYM
ejpam-2332	319	16	∈	∈	ADJ
ejpam-2332	319	17	si	si	X
ejpam-2332	319	18	(	(	PUNCT
ejpam-2332	319	19	ii	ii	PROPN
ejpam-2332	319	20	)	)	PUNCT
ejpam-2332	319	21	x∗t	x∗t	NUM
ejpam-2332	320	1	b̃y	b̃y	PROPN
ejpam-2332	320	2	�	�	PROPN
ejpam-2332	320	3	̃r̃,s̃	̃r̃,s̃	PROPN
ejpam-2332	320	4	ṽ	ṽ	PROPN
ejpam-2332	320	5	,	,	PUNCT
ejpam-2332	320	6	for	for	ADP
ejpam-2332	320	7	all	all	DET
ejpam-2332	320	8	y	y	PROPN
ejpam-2332	320	9	∈	∈	NOUN
ejpam-2332	320	10	si	si	X
ejpam-2332	321	1	i	i	PRON
ejpam-2332	321	2	(	(	PUNCT
ejpam-2332	321	3	iii	iii	NOUN
ejpam-2332	321	4	)	)	PUNCT
ejpam-2332	321	5	x∗t	x∗t	NUM
ejpam-2332	321	6	ãy∗	ãy∗	PROPN
ejpam-2332	321	7	�	�	PROPN
ejpam-2332	321	8	̃p̃0,q̃0	̃p̃0,q̃0	PROPN
ejpam-2332	321	9	ũ	ũ	PROPN
ejpam-2332	321	10	(	(	PUNCT
ejpam-2332	321	11	iv	iv	PROPN
ejpam-2332	321	12	)	)	PUNCT
ejpam-2332	321	13	x∗t	x∗t	PROPN
ejpam-2332	321	14	b̃y∗	b̃y∗	PROPN
ejpam-2332	321	15	�	�	PROPN
ejpam-2332	321	16	̃r̃0,s̃0	̃r̃0,s̃0	PART
ejpam-2332	321	17	ṽ.	ṽ.	PROPN
ejpam-2332	321	18	m.	m.	NOUN
ejpam-2332	321	19	seikh	seikh	NOUN
ejpam-2332	321	20	,	,	PUNCT
ejpam-2332	321	21	p.	p.	PROPN
ejpam-2332	321	22	nayak	nayak	PROPN
ejpam-2332	321	23	,	,	PUNCT
ejpam-2332	321	24	m.	m.	NOUN
ejpam-2332	321	25	pal	pal	PROPN
ejpam-2332	321	26	/	/	SYM
ejpam-2332	321	27	eur	eur	PROPN
ejpam-2332	321	28	.	.	PUNCT
ejpam-2332	322	1	j.	j.	PROPN
ejpam-2332	322	2	pure	pure	PROPN
ejpam-2332	322	3	appl	appl	PROPN
ejpam-2332	322	4	.	.	PROPN
ejpam-2332	322	5	math	math	PROPN
ejpam-2332	322	6	,	,	PUNCT
ejpam-2332	322	7	8	8	NUM
ejpam-2332	322	8	(	(	PUNCT
ejpam-2332	322	9	2015	2015	NUM
ejpam-2332	322	10	)	)	PUNCT
ejpam-2332	322	11	,	,	PUNCT
ejpam-2332	322	12	153	153	NUM
ejpam-2332	322	13	-	-	SYM
ejpam-2332	322	14	171	171	NUM
ejpam-2332	322	15	163	163	NUM
ejpam-2332	322	16	if	if	SCONJ
ejpam-2332	322	17	(	(	PUNCT
ejpam-2332	322	18	ũ	ũ	PROPN
ejpam-2332	322	19	,	,	PUNCT
ejpam-2332	322	20	ṽ	ṽ	PROPN
ejpam-2332	322	21	)	)	PUNCT
ejpam-2332	322	22	be	be	VERB
ejpam-2332	322	23	a	a	DET
ejpam-2332	322	24	reasonable	reasonable	ADJ
ejpam-2332	322	25	solution	solution	NOUN
ejpam-2332	322	26	ofái	ofái	NOUN
ejpam-2332	322	27	fbg	fbg	PROPN
ejpam-2332	322	28	then	then	ADV
ejpam-2332	322	29	ũ	ũ	PROPN
ejpam-2332	322	30	,	,	PUNCT
ejpam-2332	322	31	ṽ	ṽ	PROPN
ejpam-2332	322	32	are	be	AUX
ejpam-2332	322	33	called	call	VERB
ejpam-2332	322	34	the	the	DET
ejpam-2332	322	35	reasonable	reasonable	ADJ
ejpam-2332	322	36	values	value	NOUN
ejpam-2332	322	37	for	for	ADP
ejpam-2332	322	38	player	player	NOUN
ejpam-2332	322	39	i	i	PROPN
ejpam-2332	322	40	and	and	CCONJ
ejpam-2332	322	41	ii	ii	PROPN
ejpam-2332	322	42	,	,	PUNCT
ejpam-2332	322	43	respectively	respectively	ADV
ejpam-2332	322	44	.	.	PUNCT
ejpam-2332	323	1	definition	definition	NOUN
ejpam-2332	323	2	12	12	NUM
ejpam-2332	323	3	.	.	PUNCT
ejpam-2332	324	1	let	let	VERB
ejpam-2332	324	2	ũ	ũ	PROPN
ejpam-2332	324	3	and	and	CCONJ
ejpam-2332	324	4	ṽ	ṽ	PROPN
ejpam-2332	324	5	be	be	VERB
ejpam-2332	324	6	the	the	DET
ejpam-2332	324	7	set	set	NOUN
ejpam-2332	324	8	of	of	ADP
ejpam-2332	324	9	all	all	DET
ejpam-2332	324	10	reasonable	reasonable	ADJ
ejpam-2332	324	11	values	value	NOUN
ejpam-2332	324	12	ũ	ũ	PROPN
ejpam-2332	324	13	and	and	CCONJ
ejpam-2332	324	14	ṽ	ṽ	PROPN
ejpam-2332	324	15	for	for	ADP
ejpam-2332	324	16	player	player	NOUN
ejpam-2332	324	17	i	i	PROPN
ejpam-2332	324	18	and	and	CCONJ
ejpam-2332	324	19	ii	ii	PROPN
ejpam-2332	324	20	,	,	PUNCT
ejpam-2332	324	21	respectively	respectively	ADV
ejpam-2332	324	22	.	.	PUNCT
ejpam-2332	325	1	also	also	ADV
ejpam-2332	325	2	let	let	VERB
ejpam-2332	325	3	there	there	PRON
ejpam-2332	325	4	exist	exist	VERB
ejpam-2332	325	5	ũ∗	ũ∗	ADP
ejpam-2332	325	6	∈	∈	PROPN
ejpam-2332	325	7	ũ	ũ	PROPN
ejpam-2332	325	8	,	,	PUNCT
ejpam-2332	325	9	ṽ∗	ṽ∗	ADP
ejpam-2332	325	10	∈	∈	PROPN
ejpam-2332	325	11	ṽ	ṽ	PROPN
ejpam-2332	325	12	such	such	ADJ
ejpam-2332	325	13	that	that	SCONJ
ejpam-2332	325	14	r(ũ∗)≥	r(ũ∗)≥	PROPN
ejpam-2332	325	15	r(ũ	r(ũ	PROPN
ejpam-2332	325	16	)	)	PUNCT
ejpam-2332	325	17	,	,	PUNCT
ejpam-2332	325	18	∀ũ	∀ũ	NOUN
ejpam-2332	325	19	∈	∈	PROPN
ejpam-2332	325	20	ũ	ũ	PROPN
ejpam-2332	325	21	and	and	CCONJ
ejpam-2332	325	22	r(ṽ∗)≥	r(ṽ∗)≥	ADJ
ejpam-2332	325	23	r(ṽ	r(ṽ	NOUN
ejpam-2332	325	24	)	)	PUNCT
ejpam-2332	325	25	,	,	PUNCT
ejpam-2332	325	26	∀ṽ	∀ṽ	PROPN
ejpam-2332	325	27	∈	∈	PROPN
ejpam-2332	325	28	ṽ	ṽ	PROPN
ejpam-2332	325	29	,	,	PUNCT
ejpam-2332	325	30	where	where	SCONJ
ejpam-2332	325	31	r	r	NOUN
ejpam-2332	325	32	is	be	AUX
ejpam-2332	325	33	the	the	DET
ejpam-2332	325	34	ranking	rank	VERB
ejpam-2332	325	35	function	function	NOUN
ejpam-2332	325	36	defined	define	VERB
ejpam-2332	325	37	in	in	ADP
ejpam-2332	325	38	section	section	NOUN
ejpam-2332	325	39	2	2	NUM
ejpam-2332	325	40	.	.	PUNCT
ejpam-2332	326	1	then	then	ADV
ejpam-2332	326	2	the	the	DET
ejpam-2332	326	3	pair	pair	NOUN
ejpam-2332	326	4	(	(	PUNCT
ejpam-2332	326	5	x∗,y∗	x∗,y∗	PROPN
ejpam-2332	326	6	)	)	PUNCT
ejpam-2332	326	7	is	be	AUX
ejpam-2332	326	8	called	call	VERB
ejpam-2332	326	9	an	an	DET
ejpam-2332	326	10	equilibrium	equilibrium	NOUN
ejpam-2332	326	11	point	point	NOUN
ejpam-2332	326	12	of	of	ADP
ejpam-2332	326	13	the	the	DET
ejpam-2332	326	14	gameái	gameái	ADJ
ejpam-2332	326	15	fbg	fbg	NOUN
ejpam-2332	326	16	and	and	CCONJ
ejpam-2332	326	17	x∗	x∗	PROPN
ejpam-2332	326	18	,	,	PUNCT
ejpam-2332	326	19	y∗	y∗	ADV
ejpam-2332	326	20	are	be	AUX
ejpam-2332	326	21	called	call	VERB
ejpam-2332	326	22	nash	nash	NOUN
ejpam-2332	326	23	equilibrium	equilibrium	NOUN
ejpam-2332	326	24	strategies	strategy	NOUN
ejpam-2332	326	25	of	of	ADP
ejpam-2332	326	26	player	player	NOUN
ejpam-2332	326	27	i	i	PROPN
ejpam-2332	326	28	and	and	CCONJ
ejpam-2332	326	29	ii	ii	PROPN
ejpam-2332	326	30	,	,	PUNCT
ejpam-2332	326	31	respectively	respectively	ADV
ejpam-2332	326	32	.	.	PUNCT
ejpam-2332	327	1	also	also	ADV
ejpam-2332	327	2	ũ∗	ũ∗	X
ejpam-2332	327	3	=	=	SYM
ejpam-2332	327	4	xt	xt	X
ejpam-2332	327	5	ãy	ãy	NOUN
ejpam-2332	327	6	and	and	CCONJ
ejpam-2332	327	7	ṽ∗	ṽ∗	PROPN
ejpam-2332	327	8	=	=	SYM
ejpam-2332	327	9	xt	xt	PROPN
ejpam-2332	328	1	b̃y	b̃y	PROPN
ejpam-2332	328	2	are	be	AUX
ejpam-2332	328	3	called	call	VERB
ejpam-2332	328	4	the	the	DET
ejpam-2332	328	5	nash	nash	ADJ
ejpam-2332	328	6	equilibrium	equilibrium	NOUN
ejpam-2332	328	7	values	value	NOUN
ejpam-2332	328	8	of	of	ADP
ejpam-2332	328	9	the	the	DET
ejpam-2332	328	10	gameái	gameái	PROPN
ejpam-2332	328	11	fbg	fbg	NOUN
ejpam-2332	328	12	for	for	ADP
ejpam-2332	328	13	player	player	NOUN
ejpam-2332	328	14	i	i	PROPN
ejpam-2332	328	15	and	and	CCONJ
ejpam-2332	328	16	ii	ii	PROPN
ejpam-2332	328	17	,	,	PUNCT
ejpam-2332	328	18	respectively	respectively	ADV
ejpam-2332	328	19	,	,	PUNCT
ejpam-2332	328	20	and	and	CCONJ
ejpam-2332	328	21	(	(	PUNCT
ejpam-2332	328	22	x∗,y∗	x∗,y∗	PROPN
ejpam-2332	328	23	,	,	PUNCT
ejpam-2332	328	24	ũ∗	ũ∗	PROPN
ejpam-2332	328	25	,	,	PUNCT
ejpam-2332	328	26	ṽ∗	ṽ∗	PROPN
ejpam-2332	328	27	)	)	PUNCT
ejpam-2332	328	28	is	be	AUX
ejpam-2332	328	29	called	call	VERB
ejpam-2332	328	30	the	the	DET
ejpam-2332	328	31	nash	nash	ADJ
ejpam-2332	328	32	equilibrium	equilibrium	NOUN
ejpam-2332	328	33	solution	solution	NOUN
ejpam-2332	328	34	of	of	ADP
ejpam-2332	328	35	the	the	DET
ejpam-2332	328	36	bi	bi	ADJ
ejpam-2332	328	37	-	-	NOUN
ejpam-2332	328	38	matrix	matrix	NOUN
ejpam-2332	328	39	gameái	gameái	NOUN
ejpam-2332	328	40	fbg	fbg	NOUN
ejpam-2332	328	41	.	.	PUNCT
ejpam-2332	329	1	by	by	ADP
ejpam-2332	329	2	using	use	VERB
ejpam-2332	329	3	the	the	DET
ejpam-2332	329	4	above	above	ADJ
ejpam-2332	329	5	definitions	definition	NOUN
ejpam-2332	329	6	we	we	PRON
ejpam-2332	329	7	can	can	AUX
ejpam-2332	329	8	now	now	ADV
ejpam-2332	329	9	construct	construct	VERB
ejpam-2332	329	10	the	the	DET
ejpam-2332	329	11	following	follow	VERB
ejpam-2332	329	12	i	i	PROPN
ejpam-2332	329	13	-	-	PUNCT
ejpam-2332	329	14	fuzzy	fuzzy	ADJ
ejpam-2332	329	15	non	non	ADJ
ejpam-2332	329	16	-	-	ADJ
ejpam-2332	329	17	linear	linear	ADJ
ejpam-2332	329	18	programming	programming	NOUN
ejpam-2332	329	19	problem	problem	NOUN
ejpam-2332	329	20	as	as	ADP
ejpam-2332	329	21	max	max	PROPN
ejpam-2332	329	22	{	{	PUNCT
ejpam-2332	329	23	ũ+	ũ+	PROPN
ejpam-2332	329	24	ṽ	ṽ	PROPN
ejpam-2332	329	25	}	}	PUNCT
ejpam-2332	329	26	subject	subject	NOUN
ejpam-2332	329	27	to	to	ADP
ejpam-2332	329	28	xt	xt	PROPN
ejpam-2332	329	29	ãy	ãy	NOUN
ejpam-2332	329	30	�	�	PROPN
ejpam-2332	329	31	̃p̃,q̃	̃p̃,q̃	PROPN
ejpam-2332	329	32	ũ	ũ	PROPN
ejpam-2332	329	33	,	,	PUNCT
ejpam-2332	329	34	for	for	ADP
ejpam-2332	329	35	all	all	PRON
ejpam-2332	329	36	x	x	SYM
ejpam-2332	329	37	∈	∈	ADV
ejpam-2332	329	38	si	si	X
ejpam-2332	329	39	,	,	PUNCT
ejpam-2332	329	40	xt	xt	PROPN
ejpam-2332	329	41	b̃y	b̃y	PROPN
ejpam-2332	329	42	�	�	PROPN
ejpam-2332	329	43	̃r̃,s̃	̃r̃,s̃	PROPN
ejpam-2332	329	44	ṽ	ṽ	PROPN
ejpam-2332	329	45	,	,	PUNCT
ejpam-2332	329	46	for	for	ADP
ejpam-2332	329	47	all	all	DET
ejpam-2332	329	48	y	y	PROPN
ejpam-2332	329	49	∈	∈	NOUN
ejpam-2332	329	50	si	si	X
ejpam-2332	330	1	i	i	PRON
ejpam-2332	330	2	,	,	PUNCT
ejpam-2332	330	3	xt	xt	ADP
ejpam-2332	330	4	ãy	ãy	PROPN
ejpam-2332	330	5	�	�	PROPN
ejpam-2332	330	6	̃p̃0,q̃0	̃p̃0,q̃0	NUM
ejpam-2332	330	7	ũ	ũ	PROPN
ejpam-2332	330	8	,	,	PUNCT
ejpam-2332	330	9	xt	xt	ADP
ejpam-2332	330	10	b̃y	b̃y	PROPN
ejpam-2332	330	11	�	�	PROPN
ejpam-2332	330	12	̃r̃0,s̃0	̃r̃0,s̃0	PROPN
ejpam-2332	330	13	ṽ	ṽ	PROPN
ejpam-2332	330	14	,	,	PUNCT
ejpam-2332	330	15	x	x	SYM
ejpam-2332	330	16	∈	∈	NOUN
ejpam-2332	330	17	si	si	X
ejpam-2332	330	18	,	,	PUNCT
ejpam-2332	330	19	y	y	PROPN
ejpam-2332	330	20	∈	∈	PROPN
ejpam-2332	331	1	si	si	X
ejpam-2332	331	2	i	i	PRON
ejpam-2332	331	3	,	,	PUNCT
ejpam-2332	331	4	ũ	ũ	PROPN
ejpam-2332	331	5	,	,	PUNCT
ejpam-2332	331	6	ṽ	ṽ	PROPN
ejpam-2332	331	7	∈	∈	PROPN
ejpam-2332	331	8	f	f	X
ejpam-2332	331	9	(	(	PUNCT
ejpam-2332	331	10	ℜ	ℜ	PROPN
ejpam-2332	331	11	)	)	PUNCT
ejpam-2332	331	12	(	(	PUNCT
ejpam-2332	331	13	11	11	NUM
ejpam-2332	331	14	)	)	PUNCT
ejpam-2332	331	15	since	since	SCONJ
ejpam-2332	331	16	si	si	PROPN
ejpam-2332	331	17	and	and	CCONJ
ejpam-2332	331	18	si	si	INTJ
ejpam-2332	331	19	i	i	PRON
ejpam-2332	331	20	are	be	AUX
ejpam-2332	331	21	convex	convex	ADJ
ejpam-2332	331	22	polytopes	polytope	NOUN
ejpam-2332	331	23	,	,	PUNCT
ejpam-2332	331	24	it	it	PRON
ejpam-2332	331	25	is	be	AUX
ejpam-2332	331	26	sufficient	sufficient	ADJ
ejpam-2332	331	27	to	to	PART
ejpam-2332	331	28	consider	consider	VERB
ejpam-2332	331	29	only	only	ADV
ejpam-2332	331	30	the	the	DET
ejpam-2332	331	31	extreme	extreme	ADJ
ejpam-2332	331	32	points	point	NOUN
ejpam-2332	331	33	(	(	PUNCT
ejpam-2332	331	34	i.e.	i.e.	X
ejpam-2332	331	35	pure	pure	ADJ
ejpam-2332	331	36	strategies	strategy	NOUN
ejpam-2332	331	37	)	)	PUNCT
ejpam-2332	331	38	of	of	ADP
ejpam-2332	331	39	si	si	PROPN
ejpam-2332	331	40	and	and	CCONJ
ejpam-2332	331	41	si	si	INTJ
ejpam-2332	331	42	i	i	PROPN
ejpam-2332	331	43	.	.	PUNCT
ejpam-2332	332	1	this	this	DET
ejpam-2332	332	2	observation	observation	NOUN
ejpam-2332	332	3	leads	lead	VERB
ejpam-2332	332	4	to	to	ADP
ejpam-2332	332	5	the	the	DET
ejpam-2332	332	6	following	follow	VERB
ejpam-2332	332	7	i	i	NOUN
ejpam-2332	332	8	-	-	PUNCT
ejpam-2332	332	9	fuzzy	fuzzy	ADJ
ejpam-2332	332	10	non	non	ADJ
ejpam-2332	332	11	-	-	ADJ
ejpam-2332	332	12	linear	linear	ADJ
ejpam-2332	332	13	programming	programming	NOUN
ejpam-2332	332	14	problem	problem	NOUN
ejpam-2332	332	15	as	as	ADP
ejpam-2332	332	16	max	max	PROPN
ejpam-2332	332	17	{	{	PUNCT
ejpam-2332	332	18	ũ+	ũ+	PROPN
ejpam-2332	332	19	ṽ	ṽ	PROPN
ejpam-2332	332	20	}	}	PUNCT
ejpam-2332	332	21	subject	subject	NOUN
ejpam-2332	332	22	to	to	ADP
ejpam-2332	332	23	ãiy	ãiy	PROPN
ejpam-2332	332	24	�	�	PROPN
ejpam-2332	332	25	̃p̃,q̃	̃p̃,q̃	PROPN
ejpam-2332	332	26	ũ	ũ	PROPN
ejpam-2332	332	27	(	(	PUNCT
ejpam-2332	332	28	i	i	NOUN
ejpam-2332	332	29	=	=	SYM
ejpam-2332	332	30	1,2	1,2	NUM
ejpam-2332	332	31	,	,	PUNCT
ejpam-2332	332	32	.	.	PUNCT
ejpam-2332	332	33	.	.	PUNCT
ejpam-2332	333	1	.	.	PUNCT
ejpam-2332	334	1	,	,	PUNCT
ejpam-2332	334	2	m	m	PROPN
ejpam-2332	334	3	)	)	PUNCT
ejpam-2332	334	4	,	,	PUNCT
ejpam-2332	334	5	xt	xt	PUNCT
ejpam-2332	335	1	b̃	b̃	PROPN
ejpam-2332	335	2	j	j	PROPN
ejpam-2332	335	3	�	�	PROPN
ejpam-2332	335	4	̃r̃,s̃	̃r̃,s̃	PROPN
ejpam-2332	335	5	ṽ	ṽ	PROPN
ejpam-2332	335	6	(	(	PUNCT
ejpam-2332	335	7	j	j	PROPN
ejpam-2332	335	8	=	=	SYM
ejpam-2332	335	9	1,2	1,2	NUM
ejpam-2332	335	10	,	,	PUNCT
ejpam-2332	335	11	.	.	PUNCT
ejpam-2332	335	12	.	.	PUNCT
ejpam-2332	336	1	.	.	PUNCT
ejpam-2332	336	2	,	,	PUNCT
ejpam-2332	336	3	n	n	CCONJ
ejpam-2332	336	4	)	)	PUNCT
ejpam-2332	336	5	,	,	PUNCT
ejpam-2332	337	1	xt	xt	ADP
ejpam-2332	337	2	ãy	ãy	PROPN
ejpam-2332	337	3	�	�	PROPN
ejpam-2332	337	4	̃p̃0,q̃0	̃p̃0,q̃0	NUM
ejpam-2332	337	5	ũ	ũ	PROPN
ejpam-2332	337	6	,	,	PUNCT
ejpam-2332	337	7	xt	xt	ADP
ejpam-2332	337	8	b̃y	b̃y	PROPN
ejpam-2332	337	9	�	�	PROPN
ejpam-2332	337	10	̃r̃0,s̃0	̃r̃0,s̃0	PROPN
ejpam-2332	337	11	ṽ	ṽ	PROPN
ejpam-2332	337	12	,	,	PUNCT
ejpam-2332	337	13	x	x	SYM
ejpam-2332	337	14	∈	∈	NOUN
ejpam-2332	337	15	si	si	X
ejpam-2332	337	16	,	,	PUNCT
ejpam-2332	337	17	y	y	PROPN
ejpam-2332	337	18	∈	∈	PROPN
ejpam-2332	338	1	si	si	X
ejpam-2332	338	2	i	i	PRON
ejpam-2332	338	3	,	,	PUNCT
ejpam-2332	338	4	ũ	ũ	PROPN
ejpam-2332	338	5	,	,	PUNCT
ejpam-2332	338	6	ṽ	ṽ	PROPN
ejpam-2332	338	7	∈	∈	PROPN
ejpam-2332	338	8	f	f	X
ejpam-2332	338	9	(	(	PUNCT
ejpam-2332	338	10	ℜ	ℜ	PROPN
ejpam-2332	338	11	)	)	PUNCT
ejpam-2332	338	12	(	(	PUNCT
ejpam-2332	338	13	12	12	NUM
ejpam-2332	338	14	)	)	PUNCT
ejpam-2332	338	15	here	here	ADV
ejpam-2332	338	16	ãi	ãi	VERB
ejpam-2332	339	1	(	(	PUNCT
ejpam-2332	339	2	i	i	NOUN
ejpam-2332	339	3	=	=	SYM
ejpam-2332	339	4	1,2	1,2	NUM
ejpam-2332	339	5	,	,	PUNCT
ejpam-2332	339	6	.	.	PUNCT
ejpam-2332	339	7	.	.	PUNCT
ejpam-2332	340	1	.	.	PUNCT
ejpam-2332	341	1	,	,	PUNCT
ejpam-2332	341	2	m	m	NOUN
ejpam-2332	341	3	)	)	PUNCT
ejpam-2332	341	4	denotes	denote	VERB
ejpam-2332	341	5	the	the	DET
ejpam-2332	341	6	i	i	PROPN
ejpam-2332	341	7	th	th	X
ejpam-2332	341	8	row	row	NOUN
ejpam-2332	341	9	of	of	ADP
ejpam-2332	341	10	the	the	DET
ejpam-2332	341	11	pay	pay	VERB
ejpam-2332	341	12	-	-	PUNCT
ejpam-2332	341	13	off	off	ADP
ejpam-2332	341	14	matrix	matrix	NOUN
ejpam-2332	341	15	ã	ã	PROPN
ejpam-2332	341	16	and	and	CCONJ
ejpam-2332	342	1	b̃	b̃	PROPN
ejpam-2332	342	2	j	j	PROPN
ejpam-2332	342	3	(	(	PUNCT
ejpam-2332	342	4	j	j	PROPN
ejpam-2332	342	5	=	=	SYM
ejpam-2332	342	6	1,2	1,2	NUM
ejpam-2332	342	7	,	,	PUNCT
ejpam-2332	342	8	.	.	PUNCT
ejpam-2332	342	9	.	.	PUNCT
ejpam-2332	343	1	.	.	PUNCT
ejpam-2332	344	1	,	,	PUNCT
ejpam-2332	345	1	n	n	CCONJ
ejpam-2332	345	2	)	)	PUNCT
ejpam-2332	346	1	represents	represent	VERB
ejpam-2332	346	2	the	the	DET
ejpam-2332	346	3	j	j	PROPN
ejpam-2332	346	4	th	th	X
ejpam-2332	346	5	column	column	NOUN
ejpam-2332	346	6	of	of	ADP
ejpam-2332	346	7	b̃.	b̃.	NOUN
ejpam-2332	346	8	now	now	ADV
ejpam-2332	346	9	by	by	ADP
ejpam-2332	346	10	using	use	VERB
ejpam-2332	346	11	the	the	DET
ejpam-2332	346	12	resolution	resolution	NOUN
ejpam-2332	346	13	procedure	procedure	NOUN
ejpam-2332	346	14	for	for	ADP
ejpam-2332	346	15	the	the	DET
ejpam-2332	346	16	double	double	ADJ
ejpam-2332	346	17	i	i	NOUN
ejpam-2332	346	18	-	-	PUNCT
ejpam-2332	346	19	fuzzy	fuzzy	ADJ
ejpam-2332	346	20	constraints	constraint	NOUN
ejpam-2332	346	21	described	describe	VERB
ejpam-2332	346	22	in	in	ADP
ejpam-2332	346	23	section	section	NOUN
ejpam-2332	346	24	3	3	NUM
ejpam-2332	346	25	,	,	PUNCT
ejpam-2332	346	26	we	we	PRON
ejpam-2332	346	27	obtain	obtain	VERB
ejpam-2332	346	28	the	the	DET
ejpam-2332	346	29	following	follow	VERB
ejpam-2332	346	30	i	i	NOUN
ejpam-2332	346	31	-	-	PUNCT
ejpam-2332	346	32	fuzzy	fuzzy	ADJ
ejpam-2332	346	33	non	non	ADJ
ejpam-2332	346	34	-	-	ADJ
ejpam-2332	346	35	linear	linear	ADJ
ejpam-2332	346	36	programming	programming	NOUN
ejpam-2332	346	37	problem	problem	NOUN
ejpam-2332	346	38	as	as	ADP
ejpam-2332	346	39	max	max	PROPN
ejpam-2332	346	40	{	{	PUNCT
ejpam-2332	346	41	ũ+	ũ+	PROPN
ejpam-2332	346	42	ṽ	ṽ	PROPN
ejpam-2332	346	43	}	}	PUNCT
ejpam-2332	346	44	subject	subject	NOUN
ejpam-2332	346	45	to	to	ADP
ejpam-2332	346	46	ãiy	ãiy	PROPN
ejpam-2332	346	47	�	�	PROPN
ejpam-2332	346	48	̃	̃	PROPN
ejpam-2332	346	49	ũ+	ũ+	NOUN
ejpam-2332	346	50	(	(	PUNCT
ejpam-2332	346	51	1−	1−	NUM
ejpam-2332	346	52	ξ)p̃i	ξ)p̃i	NUM
ejpam-2332	346	53	(	(	PUNCT
ejpam-2332	346	54	i	i	NOUN
ejpam-2332	346	55	=	=	SYM
ejpam-2332	346	56	1,2	1,2	NUM
ejpam-2332	346	57	,	,	PUNCT
ejpam-2332	346	58	.	.	PUNCT
ejpam-2332	346	59	.	.	PUNCT
ejpam-2332	347	1	.	.	PUNCT
ejpam-2332	348	1	,	,	PUNCT
ejpam-2332	348	2	m	m	PROPN
ejpam-2332	348	3	)	)	PUNCT
ejpam-2332	348	4	,	,	PUNCT
ejpam-2332	348	5	ãiy	ãiy	PROPN
ejpam-2332	348	6	�	�	PROPN
ejpam-2332	348	7	̃	̃	PROPN
ejpam-2332	348	8	(	(	PUNCT
ejpam-2332	348	9	ũ+	ũ+	PROPN
ejpam-2332	348	10	p̃i)−	p̃i)−	PROPN
ejpam-2332	348	11	(	(	PUNCT
ejpam-2332	348	12	1−η)q̃i	1−η)q̃i	NUM
ejpam-2332	348	13	(	(	PUNCT
ejpam-2332	348	14	i	i	NOUN
ejpam-2332	348	15	=	=	SYM
ejpam-2332	348	16	1,2	1,2	NUM
ejpam-2332	348	17	,	,	PUNCT
ejpam-2332	348	18	.	.	PUNCT
ejpam-2332	348	19	.	.	PUNCT
ejpam-2332	348	20	.	.	PUNCT
ejpam-2332	349	1	,	,	PUNCT
ejpam-2332	349	2	m	m	PROPN
ejpam-2332	349	3	)	)	PUNCT
ejpam-2332	349	4	,	,	PUNCT
ejpam-2332	349	5	m.	m.	NOUN
ejpam-2332	349	6	seikh	seikh	PROPN
ejpam-2332	349	7	,	,	PUNCT
ejpam-2332	349	8	p.	p.	PROPN
ejpam-2332	349	9	nayak	nayak	PROPN
ejpam-2332	349	10	,	,	PUNCT
ejpam-2332	349	11	m.	m.	NOUN
ejpam-2332	349	12	pal	pal	PROPN
ejpam-2332	349	13	/	/	SYM
ejpam-2332	349	14	eur	eur	PROPN
ejpam-2332	349	15	.	.	PUNCT
ejpam-2332	350	1	j.	j.	PROPN
ejpam-2332	350	2	pure	pure	PROPN
ejpam-2332	350	3	appl	appl	PROPN
ejpam-2332	350	4	.	.	PROPN
ejpam-2332	350	5	math	math	PROPN
ejpam-2332	350	6	,	,	PUNCT
ejpam-2332	350	7	8	8	NUM
ejpam-2332	350	8	(	(	PUNCT
ejpam-2332	350	9	2015	2015	NUM
ejpam-2332	350	10	)	)	PUNCT
ejpam-2332	350	11	,	,	PUNCT
ejpam-2332	350	12	153	153	NUM
ejpam-2332	350	13	-	-	SYM
ejpam-2332	350	14	171	171	NUM
ejpam-2332	350	15	164	164	NUM
ejpam-2332	350	16	xt	xt	ADP
ejpam-2332	351	1	b̃	b̃	PROPN
ejpam-2332	351	2	j	j	PROPN
ejpam-2332	351	3	�	�	PROPN
ejpam-2332	351	4	̃	̃	PROPN
ejpam-2332	351	5	ṽ	ṽ	PROPN
ejpam-2332	351	6	+	+	CCONJ
ejpam-2332	351	7	(	(	PUNCT
ejpam-2332	351	8	1−	1−	NUM
ejpam-2332	351	9	γ)r̃	γ)r̃	NUM
ejpam-2332	351	10	j	j	PROPN
ejpam-2332	351	11	(	(	PUNCT
ejpam-2332	351	12	j	j	PROPN
ejpam-2332	351	13	=	=	SYM
ejpam-2332	351	14	1,2	1,2	NUM
ejpam-2332	351	15	,	,	PUNCT
ejpam-2332	351	16	.	.	PUNCT
ejpam-2332	351	17	.	.	PUNCT
ejpam-2332	351	18	.	.	PUNCT
ejpam-2332	351	19	,	,	PUNCT
ejpam-2332	351	20	n	n	CCONJ
ejpam-2332	351	21	)	)	PUNCT
ejpam-2332	351	22	,	,	PUNCT
ejpam-2332	351	23	xt	xt	PUNCT
ejpam-2332	352	1	b̃	b̃	PROPN
ejpam-2332	352	2	j	j	PROPN
ejpam-2332	352	3	�	�	PROPN
ejpam-2332	352	4	̃	̃	PROPN
ejpam-2332	352	5	(	(	PUNCT
ejpam-2332	352	6	ṽ	ṽ	PROPN
ejpam-2332	352	7	+	+	CCONJ
ejpam-2332	352	8	r̃	r̃	PROPN
ejpam-2332	352	9	j)−	j)−	PROPN
ejpam-2332	352	10	(	(	PUNCT
ejpam-2332	352	11	1−δ)s̃	1−δ)s̃	NUM
ejpam-2332	352	12	j	j	X
ejpam-2332	352	13	(	(	PUNCT
ejpam-2332	352	14	j	j	PROPN
ejpam-2332	352	15	=	=	SYM
ejpam-2332	352	16	1,2	1,2	NUM
ejpam-2332	352	17	,	,	PUNCT
ejpam-2332	352	18	.	.	PUNCT
ejpam-2332	352	19	.	.	PUNCT
ejpam-2332	352	20	.	.	PUNCT
ejpam-2332	352	21	,	,	PUNCT
ejpam-2332	352	22	n	n	CCONJ
ejpam-2332	352	23	)	)	PUNCT
ejpam-2332	352	24	,	,	PUNCT
ejpam-2332	352	25	xt	xt	ADP
ejpam-2332	352	26	ãy	ãy	NOUN
ejpam-2332	352	27	�	�	NOUN
ejpam-2332	352	28	̃	̃	NOUN
ejpam-2332	352	29	ũ−	ũ−	NOUN
ejpam-2332	352	30	(	(	PUNCT
ejpam-2332	352	31	1−	1−	NUM
ejpam-2332	352	32	ξ)p̃0	ξ)p̃0	PROPN
ejpam-2332	352	33	,	,	PUNCT
ejpam-2332	352	34	(	(	PUNCT
ejpam-2332	352	35	13	13	NUM
ejpam-2332	352	36	)	)	PUNCT
ejpam-2332	352	37	xt	xt	ADP
ejpam-2332	353	1	ãy	ãy	NOUN
ejpam-2332	353	2	�	�	NOUN
ejpam-2332	353	3	̃	̃	NOUN
ejpam-2332	353	4	(	(	PUNCT
ejpam-2332	353	5	ũ−	ũ−	NOUN
ejpam-2332	353	6	p̃0	p̃0	PROPN
ejpam-2332	353	7	)	)	PUNCT
ejpam-2332	354	1	+	+	CCONJ
ejpam-2332	354	2	(	(	PUNCT
ejpam-2332	354	3	1−η)q̃0	1−η)q̃0	NUM
ejpam-2332	354	4	,	,	PUNCT
ejpam-2332	354	5	xt	xt	X
ejpam-2332	354	6	b̃y	b̃y	PROPN
ejpam-2332	354	7	�	�	PROPN
ejpam-2332	354	8	̃	̃	PROPN
ejpam-2332	354	9	ṽ	ṽ	PROPN
ejpam-2332	354	10	−	−	PROPN
ejpam-2332	354	11	(	(	PUNCT
ejpam-2332	354	12	1−	1−	NUM
ejpam-2332	354	13	γ)r̃0	γ)r̃0	NOUN
ejpam-2332	354	14	,	,	PUNCT
ejpam-2332	354	15	xt	xt	X
ejpam-2332	354	16	b̃y	b̃y	PROPN
ejpam-2332	354	17	�	�	PROPN
ejpam-2332	354	18	̃	̃	PROPN
ejpam-2332	354	19	(	(	PUNCT
ejpam-2332	354	20	ṽ	ṽ	PROPN
ejpam-2332	354	21	−	−	PROPN
ejpam-2332	354	22	r̃0	r̃0	PROPN
ejpam-2332	354	23	)	)	PUNCT
ejpam-2332	354	24	+	+	CCONJ
ejpam-2332	354	25	(	(	PUNCT
ejpam-2332	354	26	1−δ)s̃0	1−δ)s̃0	NUM
ejpam-2332	354	27	,	,	PUNCT
ejpam-2332	354	28	x	x	SYM
ejpam-2332	354	29	∈	∈	NOUN
ejpam-2332	354	30	si	si	X
ejpam-2332	354	31	,	,	PUNCT
ejpam-2332	354	32	y	y	PROPN
ejpam-2332	354	33	∈	∈	PROPN
ejpam-2332	355	1	si	si	X
ejpam-2332	355	2	i	i	PRON
ejpam-2332	355	3	,	,	PUNCT
ejpam-2332	355	4	0≤	0≤	PROPN
ejpam-2332	356	1	ξ≤	ξ≤	PROPN
ejpam-2332	356	2	1,0≤	1,0≤	NUM
ejpam-2332	356	3	η≤	η≤	ADP
ejpam-2332	356	4	1	1	NUM
ejpam-2332	356	5	0≤	0≤	NUM
ejpam-2332	356	6	γ≤	γ≤	NUM
ejpam-2332	356	7	1,0≤	1,0≤	NUM
ejpam-2332	356	8	δ	δ	PROPN
ejpam-2332	356	9	≤	≤	ADV
ejpam-2332	356	10	1	1	NUM
ejpam-2332	356	11	here	here	ADV
ejpam-2332	356	12	�	�	PROPN
ejpam-2332	356	13	̃	̃	PROPN
ejpam-2332	356	14	and	and	CCONJ
ejpam-2332	356	15	�	�	NOUN
ejpam-2332	356	16	̃	̃	NOUN
ejpam-2332	356	17	are	be	AUX
ejpam-2332	356	18	the	the	DET
ejpam-2332	356	19	relations	relation	NOUN
ejpam-2332	356	20	between	between	ADP
ejpam-2332	356	21	tifns	tifns	PROPN
ejpam-2332	356	22	,	,	PUNCT
ejpam-2332	356	23	which	which	PRON
ejpam-2332	356	24	preserve	preserve	VERB
ejpam-2332	356	25	the	the	DET
ejpam-2332	356	26	ranking	ranking	NOUN
ejpam-2332	356	27	when	when	SCONJ
ejpam-2332	356	28	i	i	PRON
ejpam-2332	356	29	-	-	PUNCT
ejpam-2332	356	30	fuzzy	fuzzy	ADJ
ejpam-2332	356	31	numbers	number	NOUN
ejpam-2332	356	32	are	be	AUX
ejpam-2332	356	33	multiplied	multiply	VERB
ejpam-2332	356	34	by	by	ADP
ejpam-2332	356	35	positive	positive	ADJ
ejpam-2332	356	36	scalar	scalar	NOUN
ejpam-2332	356	37	.	.	PUNCT
ejpam-2332	357	1	now	now	ADV
ejpam-2332	357	2	by	by	ADP
ejpam-2332	357	3	utilizing	utilize	VERB
ejpam-2332	357	4	the	the	DET
ejpam-2332	357	5	ranking	rank	VERB
ejpam-2332	357	6	function	function	NOUN
ejpam-2332	357	7	r(defined	r(define	VERB
ejpam-2332	357	8	in	in	ADP
ejpam-2332	357	9	section	section	NOUN
ejpam-2332	357	10	2	2	NUM
ejpam-2332	357	11	,	,	PUNCT
ejpam-2332	357	12	definition	definition	NOUN
ejpam-2332	357	13	6	6	NUM
ejpam-2332	357	14	)	)	PUNCT
ejpam-2332	357	15	,	,	PUNCT
ejpam-2332	357	16	the	the	DET
ejpam-2332	357	17	above	above	ADJ
ejpam-2332	357	18	problem	problem	NOUN
ejpam-2332	357	19	can	can	AUX
ejpam-2332	357	20	be	be	AUX
ejpam-2332	357	21	transformed	transform	VERB
ejpam-2332	357	22	into	into	ADP
ejpam-2332	357	23	crisp	crisp	ADJ
ejpam-2332	357	24	equivalent	equivalent	ADJ
ejpam-2332	357	25	non	non	ADJ
ejpam-2332	357	26	-	-	ADJ
ejpam-2332	357	27	linear	linear	ADJ
ejpam-2332	357	28	programming	programming	NOUN
ejpam-2332	357	29	problem	problem	NOUN
ejpam-2332	357	30	as	as	SCONJ
ejpam-2332	357	31	follows	follow	VERB
ejpam-2332	357	32	:	:	PUNCT
ejpam-2332	357	33	max	max	PROPN
ejpam-2332	357	34	{	{	PUNCT
ejpam-2332	357	35	r(ũ	r(ũ	PROPN
ejpam-2332	357	36	)	)	PUNCT
ejpam-2332	358	1	+	+	NUM
ejpam-2332	358	2	r(ṽ	r(ṽ	NOUN
ejpam-2332	358	3	)	)	PUNCT
ejpam-2332	358	4	}	}	PUNCT
ejpam-2332	358	5	subject	subject	ADJ
ejpam-2332	358	6	to	to	ADP
ejpam-2332	358	7	n∑	n∑	PROPN
ejpam-2332	358	8	j=1	j=1	PROPN
ejpam-2332	358	9	r(ãi	r(ãi	PUNCT
ejpam-2332	359	1	j)y	j)y	ADJ
ejpam-2332	359	2	j	j	PROPN
ejpam-2332	359	3	≤	≤	NUM
ejpam-2332	359	4	r(ũ	r(ũ	NOUN
ejpam-2332	359	5	)	)	PUNCT
ejpam-2332	360	1	+	+	CCONJ
ejpam-2332	360	2	(	(	PUNCT
ejpam-2332	360	3	1−	1−	NUM
ejpam-2332	360	4	ξ)r(p̃i	ξ)r(p̃i	NOUN
ejpam-2332	360	5	)	)	PUNCT
ejpam-2332	361	1	(	(	PUNCT
ejpam-2332	361	2	i	i	NOUN
ejpam-2332	361	3	=	=	SYM
ejpam-2332	361	4	1,2	1,2	NUM
ejpam-2332	361	5	,	,	PUNCT
ejpam-2332	361	6	.	.	PUNCT
ejpam-2332	361	7	.	.	PUNCT
ejpam-2332	361	8	.	.	PUNCT
ejpam-2332	362	1	,	,	PUNCT
ejpam-2332	362	2	m	m	PROPN
ejpam-2332	362	3	)	)	PUNCT
ejpam-2332	362	4	,	,	PUNCT
ejpam-2332	362	5	n∑	n∑	NOUN
ejpam-2332	362	6	j=1	j=1	PROPN
ejpam-2332	362	7	r(ãi	r(ãi	PUNCT
ejpam-2332	363	1	j)y	j)y	ADJ
ejpam-2332	363	2	j	j	PROPN
ejpam-2332	363	3	≤	≤	NUM
ejpam-2332	363	4	r(ũ	r(ũ	NOUN
ejpam-2332	363	5	)	)	PUNCT
ejpam-2332	364	1	+	+	CCONJ
ejpam-2332	364	2	r(p̃i)−	r(p̃i)−	NOUN
ejpam-2332	364	3	(	(	PUNCT
ejpam-2332	364	4	1−η)r(q̃i	1−η)r(q̃i	NUM
ejpam-2332	364	5	)	)	PUNCT
ejpam-2332	364	6	(	(	PUNCT
ejpam-2332	364	7	i	i	NOUN
ejpam-2332	364	8	=	=	SYM
ejpam-2332	364	9	1,2	1,2	NUM
ejpam-2332	364	10	,	,	PUNCT
ejpam-2332	364	11	.	.	PUNCT
ejpam-2332	364	12	.	.	PUNCT
ejpam-2332	364	13	.	.	PUNCT
ejpam-2332	364	14	,	,	PUNCT
ejpam-2332	364	15	m	m	PROPN
ejpam-2332	364	16	)	)	PUNCT
ejpam-2332	364	17	,	,	PUNCT
ejpam-2332	364	18	m∑	m∑	CCONJ
ejpam-2332	364	19	i=1	i=1	PRON
ejpam-2332	364	20	r	r	NOUN
ejpam-2332	364	21	(	(	PUNCT
ejpam-2332	364	22	b̃i	b̃i	X
ejpam-2332	364	23	j)x	j)x	X
ejpam-2332	364	24	i	i	PRON
ejpam-2332	364	25	≤	≤	ADJ
ejpam-2332	364	26	r(ṽ	r(ṽ	NOUN
ejpam-2332	364	27	)	)	PUNCT
ejpam-2332	365	1	+	+	CCONJ
ejpam-2332	365	2	(	(	PUNCT
ejpam-2332	365	3	1−	1−	NUM
ejpam-2332	365	4	γ)r(r̃	γ)r(r̃	PROPN
ejpam-2332	365	5	j	j	PROPN
ejpam-2332	365	6	)	)	PUNCT
ejpam-2332	365	7	(	(	PUNCT
ejpam-2332	365	8	j	j	PROPN
ejpam-2332	365	9	=	=	SYM
ejpam-2332	365	10	1,2	1,2	NUM
ejpam-2332	365	11	,	,	PUNCT
ejpam-2332	365	12	.	.	PUNCT
ejpam-2332	365	13	.	.	PUNCT
ejpam-2332	366	1	.	.	PUNCT
ejpam-2332	366	2	,	,	PUNCT
ejpam-2332	367	1	n	n	CCONJ
ejpam-2332	367	2	)	)	PUNCT
ejpam-2332	368	1	,	,	PUNCT
ejpam-2332	368	2	m∑	m∑	CCONJ
ejpam-2332	368	3	i=1	i=1	PRON
ejpam-2332	369	1	r	r	NOUN
ejpam-2332	369	2	(	(	PUNCT
ejpam-2332	369	3	b̃i	b̃i	X
ejpam-2332	369	4	j)x	j)x	X
ejpam-2332	369	5	i	i	PRON
ejpam-2332	369	6	≤	≤	ADJ
ejpam-2332	369	7	r(ṽ	r(ṽ	NOUN
ejpam-2332	369	8	)	)	PUNCT
ejpam-2332	370	1	+	+	CCONJ
ejpam-2332	370	2	r(r̃	r(r̃	PROPN
ejpam-2332	370	3	j)−	j)−	PROPN
ejpam-2332	370	4	(	(	PUNCT
ejpam-2332	370	5	1−	1−	NUM
ejpam-2332	370	6	δ)r(s̃	δ)r(s̃	PROPN
ejpam-2332	370	7	j	j	PROPN
ejpam-2332	370	8	)	)	PUNCT
ejpam-2332	370	9	(	(	PUNCT
ejpam-2332	370	10	j	j	PROPN
ejpam-2332	370	11	=	=	SYM
ejpam-2332	370	12	1,2	1,2	NUM
ejpam-2332	370	13	,	,	PUNCT
ejpam-2332	370	14	.	.	PUNCT
ejpam-2332	370	15	.	.	PUNCT
ejpam-2332	370	16	.	.	PUNCT
ejpam-2332	370	17	,	,	PUNCT
ejpam-2332	370	18	n	n	CCONJ
ejpam-2332	370	19	)	)	PUNCT
ejpam-2332	370	20	,	,	PUNCT
ejpam-2332	370	21	m∑	m∑	INTJ
ejpam-2332	370	22	i=1	i=1	PROPN
ejpam-2332	370	23	n∑	n∑	PROPN
ejpam-2332	370	24	j=1	j=1	PROPN
ejpam-2332	370	25	r(ãi	r(ãi	PUNCT
ejpam-2332	370	26	j)x	j)x	NOUN
ejpam-2332	371	1	i	i	PRON
ejpam-2332	371	2	y	y	PROPN
ejpam-2332	371	3	j	j	PROPN
ejpam-2332	371	4	≥	≥	X
ejpam-2332	371	5	r(ũ)−	r(ũ)−	NOUN
ejpam-2332	371	6	(	(	PUNCT
ejpam-2332	371	7	1−	1−	NUM
ejpam-2332	371	8	ξ)r(p̃0	ξ)r(p̃0	NOUN
ejpam-2332	371	9	)	)	PUNCT
ejpam-2332	371	10	,	,	PUNCT
ejpam-2332	371	11	(	(	PUNCT
ejpam-2332	371	12	14	14	NUM
ejpam-2332	371	13	)	)	PUNCT
ejpam-2332	371	14	m∑	m∑	CCONJ
ejpam-2332	371	15	i=1	i=1	PROPN
ejpam-2332	371	16	n∑	n∑	PROPN
ejpam-2332	372	1	j=1	j=1	PROPN
ejpam-2332	372	2	r(ãi	r(ãi	PUNCT
ejpam-2332	373	1	j)x	j)x	NOUN
ejpam-2332	374	1	i	i	PRON
ejpam-2332	374	2	y	y	PROPN
ejpam-2332	374	3	j	j	PROPN
ejpam-2332	374	4	≥	≥	PROPN
ejpam-2332	374	5	r(ũ)−	r(ũ)−	PROPN
ejpam-2332	374	6	r(p̃0	r(p̃0	PROPN
ejpam-2332	374	7	)	)	PUNCT
ejpam-2332	375	1	+	+	CCONJ
ejpam-2332	375	2	(	(	PUNCT
ejpam-2332	375	3	1−η)r(q̃0	1−η)r(q̃0	X
ejpam-2332	375	4	)	)	PUNCT
ejpam-2332	375	5	,	,	PUNCT
ejpam-2332	375	6	m∑	m∑	INTJ
ejpam-2332	376	1	i=1	i=1	PROPN
ejpam-2332	376	2	n∑	n∑	PROPN
ejpam-2332	377	1	j=1	j=1	NOUN
ejpam-2332	377	2	r	r	NOUN
ejpam-2332	377	3	(	(	PUNCT
ejpam-2332	377	4	b̃i	b̃i	X
ejpam-2332	377	5	j)x	j)x	PROPN
ejpam-2332	378	1	i	i	PRON
ejpam-2332	379	1	y	y	PROPN
ejpam-2332	379	2	j	j	PROPN
ejpam-2332	379	3	≥	≥	PROPN
ejpam-2332	379	4	r(ṽ)−	r(ṽ)−	NOUN
ejpam-2332	379	5	(	(	PUNCT
ejpam-2332	379	6	1−	1−	NUM
ejpam-2332	379	7	γ)r(r̃0	γ)r(r̃0	NOUN
ejpam-2332	379	8	)	)	PUNCT
ejpam-2332	379	9	,	,	PUNCT
ejpam-2332	379	10	m∑	m∑	INTJ
ejpam-2332	379	11	i=1	i=1	PROPN
ejpam-2332	379	12	n∑	n∑	PROPN
ejpam-2332	380	1	j=1	j=1	NOUN
ejpam-2332	380	2	r	r	NOUN
ejpam-2332	380	3	(	(	PUNCT
ejpam-2332	380	4	b̃i	b̃i	X
ejpam-2332	380	5	j)x	j)x	PROPN
ejpam-2332	381	1	i	i	PRON
ejpam-2332	382	1	y	y	PROPN
ejpam-2332	382	2	j	j	PROPN
ejpam-2332	382	3	≥	≥	PROPN
ejpam-2332	382	4	r(ṽ)−	r(ṽ)−	NOUN
ejpam-2332	382	5	r(r̃0	r(r̃0	NOUN
ejpam-2332	382	6	)	)	PUNCT
ejpam-2332	383	1	+	+	CCONJ
ejpam-2332	383	2	(	(	PUNCT
ejpam-2332	383	3	1−δ)r(s̃0	1−δ)r(s̃0	NUM
ejpam-2332	383	4	)	)	PUNCT
ejpam-2332	383	5	,	,	PUNCT
ejpam-2332	383	6	m∑	m∑	INTJ
ejpam-2332	383	7	i=1	i=1	PROPN
ejpam-2332	383	8	x	x	PUNCT
ejpam-2332	384	1	i	i	NOUN
ejpam-2332	384	2	=	=	NOUN
ejpam-2332	384	3	1	1	NUM
ejpam-2332	384	4	,	,	PUNCT
ejpam-2332	384	5	n∑	n∑	NOUN
ejpam-2332	384	6	j=1	j=1	NOUN
ejpam-2332	384	7	y	y	PROPN
ejpam-2332	384	8	j	j	PROPN
ejpam-2332	384	9	=	=	SYM
ejpam-2332	384	10	1	1	NUM
ejpam-2332	384	11	,	,	PUNCT
ejpam-2332	384	12	0≤	0≤	NOUN
ejpam-2332	384	13	ξ≤	ξ≤	PROPN
ejpam-2332	384	14	1,0≤	1,0≤	NUM
ejpam-2332	384	15	η	η	PROPN
ejpam-2332	384	16	≤	≤	PROPN
ejpam-2332	384	17	1	1	NUM
ejpam-2332	384	18	,	,	PUNCT
ejpam-2332	384	19	m.	m.	NOUN
ejpam-2332	384	20	seikh	seikh	PROPN
ejpam-2332	384	21	,	,	PUNCT
ejpam-2332	384	22	p.	p.	PROPN
ejpam-2332	384	23	nayak	nayak	PROPN
ejpam-2332	384	24	,	,	PUNCT
ejpam-2332	384	25	m.	m.	NOUN
ejpam-2332	384	26	pal	pal	PROPN
ejpam-2332	384	27	/	/	SYM
ejpam-2332	384	28	eur	eur	PROPN
ejpam-2332	384	29	.	.	PUNCT
ejpam-2332	385	1	j.	j.	PROPN
ejpam-2332	385	2	pure	pure	PROPN
ejpam-2332	385	3	appl	appl	PROPN
ejpam-2332	385	4	.	.	PROPN
ejpam-2332	385	5	math	math	PROPN
ejpam-2332	385	6	,	,	PUNCT
ejpam-2332	385	7	8	8	NUM
ejpam-2332	385	8	(	(	PUNCT
ejpam-2332	385	9	2015	2015	NUM
ejpam-2332	385	10	)	)	PUNCT
ejpam-2332	385	11	,	,	PUNCT
ejpam-2332	385	12	153	153	NUM
ejpam-2332	385	13	-	-	SYM
ejpam-2332	385	14	171	171	NUM
ejpam-2332	385	15	165	165	NUM
ejpam-2332	385	16	0≤	0≤	NUM
ejpam-2332	385	17	γ≤	γ≤	NUM
ejpam-2332	385	18	1,0≤	1,0≤	NUM
ejpam-2332	385	19	δ	δ	PROPN
ejpam-2332	385	20	≤	≤	ADV
ejpam-2332	385	21	1	1	NUM
ejpam-2332	385	22	.	.	PUNCT
ejpam-2332	386	1	thus	thus	ADV
ejpam-2332	386	2	from	from	ADP
ejpam-2332	386	3	above	above	ADP
ejpam-2332	386	4	discussion	discussion	NOUN
ejpam-2332	386	5	we	we	PRON
ejpam-2332	386	6	observed	observe	VERB
ejpam-2332	386	7	that	that	SCONJ
ejpam-2332	386	8	for	for	ADP
ejpam-2332	386	9	solving	solve	VERB
ejpam-2332	386	10	a	a	DET
ejpam-2332	386	11	i	i	NOUN
ejpam-2332	386	12	-	-	PUNCT
ejpam-2332	386	13	fuzzy	fuzzy	ADJ
ejpam-2332	386	14	bi	bi	ADJ
ejpam-2332	386	15	-	-	NOUN
ejpam-2332	386	16	matrix	matrix	NOUN
ejpam-2332	386	17	gameái	gameái	NOUN
ejpam-2332	386	18	fbg	fbg	NOUN
ejpam-2332	386	19	we	we	PRON
ejpam-2332	386	20	have	have	VERB
ejpam-2332	386	21	to	to	PART
ejpam-2332	386	22	solve	solve	VERB
ejpam-2332	386	23	the	the	DET
ejpam-2332	386	24	crisp	crisp	ADJ
ejpam-2332	386	25	non	non	ADJ
ejpam-2332	386	26	-	-	ADJ
ejpam-2332	386	27	linear	linear	ADJ
ejpam-2332	386	28	programming	programming	NOUN
ejpam-2332	386	29	problem	problem	NOUN
ejpam-2332	386	30	(	(	PUNCT
ejpam-2332	386	31	14	14	NUM
ejpam-2332	386	32	)	)	PUNCT
ejpam-2332	386	33	.	.	PUNCT
ejpam-2332	387	1	therefore	therefore	ADV
ejpam-2332	387	2	,	,	PUNCT
ejpam-2332	387	3	if	if	SCONJ
ejpam-2332	387	4	(	(	PUNCT
ejpam-2332	387	5	x∗,y∗,r(ũ∗),r(ṽ∗	x∗,y∗,r(ũ∗),r(ṽ∗	NOUN
ejpam-2332	387	6	)	)	PUNCT
ejpam-2332	387	7	)	)	PUNCT
ejpam-2332	387	8	be	be	AUX
ejpam-2332	387	9	an	an	DET
ejpam-2332	387	10	optimal	optimal	ADJ
ejpam-2332	387	11	solution	solution	NOUN
ejpam-2332	387	12	of	of	ADP
ejpam-2332	387	13	the	the	DET
ejpam-2332	387	14	crisp	crisp	ADJ
ejpam-2332	387	15	non	non	ADJ
ejpam-2332	387	16	-	-	ADJ
ejpam-2332	387	17	linear	linear	ADJ
ejpam-2332	387	18	programming	programming	NOUN
ejpam-2332	387	19	problem	problem	NOUN
ejpam-2332	387	20	(	(	PUNCT
ejpam-2332	387	21	14	14	NUM
ejpam-2332	387	22	)	)	PUNCT
ejpam-2332	387	23	,	,	PUNCT
ejpam-2332	387	24	then	then	ADV
ejpam-2332	387	25	(	(	PUNCT
ejpam-2332	387	26	x∗,y∗	x∗,y∗	PROPN
ejpam-2332	387	27	)	)	PUNCT
ejpam-2332	387	28	is	be	AUX
ejpam-2332	387	29	the	the	DET
ejpam-2332	387	30	nash	nash	ADJ
ejpam-2332	387	31	equilibrium	equilibrium	NOUN
ejpam-2332	387	32	point	point	NOUN
ejpam-2332	387	33	of	of	ADP
ejpam-2332	387	34	the	the	DET
ejpam-2332	387	35	gameái	gameái	ADJ
ejpam-2332	387	36	fbg	fbg	NOUN
ejpam-2332	387	37	.	.	PUNCT
ejpam-2332	388	1	also	also	ADV
ejpam-2332	388	2	,	,	PUNCT
ejpam-2332	388	3	the	the	DET
ejpam-2332	388	4	players	player	NOUN
ejpam-2332	388	5	can	can	AUX
ejpam-2332	388	6	take	take	VERB
ejpam-2332	388	7	the	the	DET
ejpam-2332	388	8	values	value	NOUN
ejpam-2332	388	9	ũ	ũ	PROPN
ejpam-2332	388	10	and	and	CCONJ
ejpam-2332	388	11	ṽ	ṽ	PROPN
ejpam-2332	388	12	for	for	ADP
ejpam-2332	388	13	which	which	PRON
ejpam-2332	388	14	r(ũ	r(ũ	NOUN
ejpam-2332	388	15	)	)	PUNCT
ejpam-2332	388	16	and	and	CCONJ
ejpam-2332	388	17	r(ṽ	r(ṽ	NOUN
ejpam-2332	388	18	)	)	PUNCT
ejpam-2332	388	19	are	be	AUX
ejpam-2332	388	20	close	close	ADJ
ejpam-2332	388	21	to	to	PART
ejpam-2332	388	22	r(ũ∗	r(ũ∗	VERB
ejpam-2332	388	23	)	)	PUNCT
ejpam-2332	388	24	and	and	CCONJ
ejpam-2332	388	25	r(ṽ∗	r(ṽ∗	NOUN
ejpam-2332	388	26	)	)	PUNCT
ejpam-2332	388	27	,	,	PUNCT
ejpam-2332	388	28	respectively	respectively	ADV
ejpam-2332	388	29	.	.	PUNCT
ejpam-2332	389	1	the	the	DET
ejpam-2332	389	2	above	above	ADJ
ejpam-2332	389	3	discussion	discussion	NOUN
ejpam-2332	389	4	can	can	AUX
ejpam-2332	389	5	be	be	AUX
ejpam-2332	389	6	summarized	summarize	VERB
ejpam-2332	389	7	in	in	ADP
ejpam-2332	389	8	the	the	DET
ejpam-2332	389	9	following	follow	VERB
ejpam-2332	389	10	theorem	theorem	PROPN
ejpam-2332	389	11	.	.	PUNCT
ejpam-2332	389	12	theorem	theorem	NOUN
ejpam-2332	389	13	3	3	NUM
ejpam-2332	389	14	.	.	PUNCT
ejpam-2332	390	1	the	the	DET
ejpam-2332	390	2	i	i	NOUN
ejpam-2332	390	3	-	-	PUNCT
ejpam-2332	390	4	fuzzy	fuzzy	ADJ
ejpam-2332	390	5	bi	bi	ADJ
ejpam-2332	390	6	-	-	ADJ
ejpam-2332	390	7	matrix	matrix	NOUN
ejpam-2332	390	8	gameái	gameái	NOUN
ejpam-2332	390	9	fbg	fbg	PROPN
ejpam-2332	390	10	described	describe	VERB
ejpam-2332	390	11	byái	byái	NOUN
ejpam-2332	390	12	fbg	fbg	PROPN
ejpam-2332	390	13	=	=	SYM
ejpam-2332	390	14	(	(	PUNCT
ejpam-2332	390	15	si	si	X
ejpam-2332	390	16	,	,	PUNCT
ejpam-2332	390	17	si	si	INTJ
ejpam-2332	391	1	i	i	PROPN
ejpam-2332	391	2	,	,	PUNCT
ejpam-2332	391	3	ã	ã	PROPN
ejpam-2332	391	4	,	,	PUNCT
ejpam-2332	391	5	b̃	b̃	PROPN
ejpam-2332	391	6	)	)	PUNCT
ejpam-2332	391	7	is	be	AUX
ejpam-2332	391	8	equivalent	equivalent	ADJ
ejpam-2332	391	9	to	to	ADP
ejpam-2332	391	10	the	the	DET
ejpam-2332	391	11	crisp	crisp	ADJ
ejpam-2332	391	12	non	non	ADJ
ejpam-2332	391	13	-	-	ADJ
ejpam-2332	391	14	linear	linear	ADJ
ejpam-2332	391	15	programming	programming	NOUN
ejpam-2332	391	16	problem	problem	NOUN
ejpam-2332	391	17	(	(	PUNCT
ejpam-2332	391	18	14	14	NUM
ejpam-2332	391	19	)	)	PUNCT
ejpam-2332	391	20	,	,	PUNCT
ejpam-2332	391	21	which	which	PRON
ejpam-2332	391	22	can	can	AUX
ejpam-2332	391	23	be	be	AUX
ejpam-2332	391	24	easily	easily	ADV
ejpam-2332	391	25	solved	solve	VERB
ejpam-2332	391	26	by	by	ADP
ejpam-2332	391	27	ordinary	ordinary	ADJ
ejpam-2332	391	28	simplex	simplex	NOUN
ejpam-2332	391	29	method	method	NOUN
ejpam-2332	391	30	.	.	PUNCT
ejpam-2332	392	1	remark	remark	NOUN
ejpam-2332	392	2	1	1	NUM
ejpam-2332	392	3	.	.	PUNCT
ejpam-2332	393	1	it	it	PRON
ejpam-2332	393	2	may	may	AUX
ejpam-2332	393	3	be	be	AUX
ejpam-2332	393	4	noted	note	VERB
ejpam-2332	393	5	that	that	SCONJ
ejpam-2332	393	6	when	when	SCONJ
ejpam-2332	393	7	p̃i	p̃i	PROPN
ejpam-2332	393	8	=	=	PUNCT
ejpam-2332	393	9	q̃i	q̃i	VERB
ejpam-2332	393	10	,	,	PUNCT
ejpam-2332	393	11	r̃	r̃	PROPN
ejpam-2332	393	12	j	j	NOUN
ejpam-2332	393	13	=	=	SYM
ejpam-2332	393	14	s̃	s̃	PROPN
ejpam-2332	393	15	j	j	PROPN
ejpam-2332	393	16	,	,	PUNCT
ejpam-2332	393	17	p̃0	p̃0	PROPN
ejpam-2332	393	18	=	=	SYM
ejpam-2332	393	19	q̃0	q̃0	PROPN
ejpam-2332	393	20	,	,	PUNCT
ejpam-2332	393	21	r̃0	r̃0	PROPN
ejpam-2332	393	22	=	=	SYM
ejpam-2332	393	23	s̃0	s̃0	PROPN
ejpam-2332	393	24	,	,	PUNCT
ejpam-2332	393	25	η	η	NOUN
ejpam-2332	393	26	=	=	PROPN
ejpam-2332	393	27	1	1	NUM
ejpam-2332	393	28	−	−	PROPN
ejpam-2332	393	29	ξ	ξ	PROPN
ejpam-2332	393	30	and	and	CCONJ
ejpam-2332	393	31	δ	δ	PROPN
ejpam-2332	393	32	=	=	SYM
ejpam-2332	393	33	1−	1−	NUM
ejpam-2332	393	34	γ	γ	X
ejpam-2332	393	35	,	,	PUNCT
ejpam-2332	393	36	the	the	DET
ejpam-2332	393	37	i	i	NOUN
ejpam-2332	393	38	-	-	PUNCT
ejpam-2332	393	39	fuzzy	fuzzy	ADJ
ejpam-2332	393	40	bi	bi	ADJ
ejpam-2332	393	41	-	-	ADJ
ejpam-2332	393	42	matrix	matrix	NOUN
ejpam-2332	393	43	gameái	gameái	NOUN
ejpam-2332	393	44	fbg	fbg	NOUN
ejpam-2332	393	45	reduces	reduce	VERB
ejpam-2332	393	46	to	to	ADP
ejpam-2332	393	47	the	the	DET
ejpam-2332	393	48	fuzzy	fuzzy	ADJ
ejpam-2332	393	49	bi	bi	ADJ
ejpam-2332	393	50	-	-	ADJ
ejpam-2332	393	51	matrix	matrix	NOUN
ejpam-2332	393	52	game	game	NOUN
ejpam-2332	393	53	bgfp	bgfp	NOUN
ejpam-2332	393	54	studied	study	VERB
ejpam-2332	393	55	by	by	ADP
ejpam-2332	393	56	vidyottama	vidyottama	NOUN
ejpam-2332	393	57	et	et	PROPN
ejpam-2332	393	58	al	al	PROPN
ejpam-2332	393	59	.	.	PUNCT
ejpam-2332	394	1	[	[	X
ejpam-2332	394	2	32	32	NUM
ejpam-2332	394	3	]	]	PUNCT
ejpam-2332	394	4	.	.	PUNCT
ejpam-2332	395	1	further	far	ADV
ejpam-2332	395	2	,	,	PUNCT
ejpam-2332	395	3	the	the	DET
ejpam-2332	395	4	i	i	NOUN
ejpam-2332	395	5	-	-	PUNCT
ejpam-2332	395	6	fuzzy	fuzzy	ADJ
ejpam-2332	395	7	non	non	ADJ
ejpam-2332	395	8	-	-	ADJ
ejpam-2332	395	9	linear	linear	ADJ
ejpam-2332	395	10	programming	programming	NOUN
ejpam-2332	395	11	problem	problem	NOUN
ejpam-2332	395	12	(	(	PUNCT
ejpam-2332	395	13	13	13	NUM
ejpam-2332	395	14	)	)	PUNCT
ejpam-2332	395	15	reduced	reduce	VERB
ejpam-2332	395	16	to	to	ADP
ejpam-2332	395	17	fuzzy	fuzzy	ADJ
ejpam-2332	395	18	non	non	ADJ
ejpam-2332	395	19	-	-	ADJ
ejpam-2332	395	20	linear	linear	ADJ
ejpam-2332	395	21	programming	programming	NOUN
ejpam-2332	395	22	problem	problem	NOUN
ejpam-2332	395	23	of	of	ADP
ejpam-2332	395	24	vidyottama	vidyottama	NOUN
ejpam-2332	395	25	et	et	PROPN
ejpam-2332	395	26	al	al	PROPN
ejpam-2332	395	27	.	.	PUNCT
ejpam-2332	396	1	[	[	X
ejpam-2332	396	2	32	32	NUM
ejpam-2332	396	3	]	]	PUNCT
ejpam-2332	396	4	as	as	ADP
ejpam-2332	396	5	max	max	PROPN
ejpam-2332	396	6	{	{	PUNCT
ejpam-2332	396	7	ũ+	ũ+	PROPN
ejpam-2332	396	8	ṽ	ṽ	PROPN
ejpam-2332	396	9	}	}	PUNCT
ejpam-2332	396	10	subject	subject	NOUN
ejpam-2332	396	11	to	to	ADP
ejpam-2332	396	12	ãiy	ãiy	PROPN
ejpam-2332	396	13	�	�	PROPN
ejpam-2332	396	14	f	f	PROPN
ejpam-2332	396	15	ũ+	ũ+	PROPN
ejpam-2332	396	16	(	(	PUNCT
ejpam-2332	396	17	1−	1−	NUM
ejpam-2332	396	18	ξ)p̃i	ξ)p̃i	NUM
ejpam-2332	396	19	(	(	PUNCT
ejpam-2332	396	20	i	i	NOUN
ejpam-2332	396	21	=	=	SYM
ejpam-2332	396	22	1,2	1,2	NUM
ejpam-2332	396	23	,	,	PUNCT
ejpam-2332	396	24	.	.	PUNCT
ejpam-2332	396	25	.	.	PUNCT
ejpam-2332	396	26	.	.	PUNCT
ejpam-2332	397	1	,	,	PUNCT
ejpam-2332	397	2	m	m	PROPN
ejpam-2332	397	3	)	)	PUNCT
ejpam-2332	397	4	,	,	PUNCT
ejpam-2332	397	5	xt	xt	PUNCT
ejpam-2332	398	1	b̃	b̃	PROPN
ejpam-2332	398	2	j	j	PROPN
ejpam-2332	398	3	�	�	PROPN
ejpam-2332	398	4	f	f	PROPN
ejpam-2332	398	5	ṽ	ṽ	PROPN
ejpam-2332	398	6	+	+	CCONJ
ejpam-2332	398	7	(	(	PUNCT
ejpam-2332	398	8	1−	1−	NUM
ejpam-2332	398	9	γ)q̃	γ)q̃	NOUN
ejpam-2332	398	10	j	j	PROPN
ejpam-2332	398	11	(	(	PUNCT
ejpam-2332	398	12	j	j	PROPN
ejpam-2332	398	13	=	=	SYM
ejpam-2332	398	14	1,2	1,2	NUM
ejpam-2332	398	15	,	,	PUNCT
ejpam-2332	398	16	.	.	PUNCT
ejpam-2332	398	17	.	.	PUNCT
ejpam-2332	398	18	.	.	PUNCT
ejpam-2332	398	19	,	,	PUNCT
ejpam-2332	398	20	n	n	CCONJ
ejpam-2332	398	21	)	)	PUNCT
ejpam-2332	398	22	,	,	PUNCT
ejpam-2332	398	23	xt	xt	ADP
ejpam-2332	398	24	ãy	ãy	PROPN
ejpam-2332	398	25	�	�	NOUN
ejpam-2332	398	26	f	f	PROPN
ejpam-2332	398	27	ũ−	ũ−	NOUN
ejpam-2332	398	28	(	(	PUNCT
ejpam-2332	398	29	1−	1−	NUM
ejpam-2332	398	30	ξ)p̃0	ξ)p̃0	PROPN
ejpam-2332	398	31	,	,	PUNCT
ejpam-2332	398	32	(	(	PUNCT
ejpam-2332	398	33	15	15	NUM
ejpam-2332	398	34	)	)	PUNCT
ejpam-2332	398	35	xt	xt	ADP
ejpam-2332	399	1	b̃y	b̃y	PROPN
ejpam-2332	399	2	�	�	PROPN
ejpam-2332	399	3	f	f	PROPN
ejpam-2332	399	4	ṽ	ṽ	PROPN
ejpam-2332	399	5	−	−	PROPN
ejpam-2332	399	6	(	(	PUNCT
ejpam-2332	399	7	1−	1−	NUM
ejpam-2332	399	8	γ)r̃0	γ)r̃0	NOUN
ejpam-2332	399	9	,	,	PUNCT
ejpam-2332	399	10	x	x	SYM
ejpam-2332	399	11	∈	∈	NOUN
ejpam-2332	399	12	si	si	X
ejpam-2332	399	13	,	,	PUNCT
ejpam-2332	399	14	y	y	PROPN
ejpam-2332	399	15	∈	∈	PROPN
ejpam-2332	399	16	si	si	X
ejpam-2332	399	17	i	i	PRON
ejpam-2332	399	18	,	,	PUNCT
ejpam-2332	399	19	0≤	0≤	PROPN
ejpam-2332	399	20	ξ≤	ξ≤	PROPN
ejpam-2332	399	21	1,0≤	1,0≤	NUM
ejpam-2332	399	22	γ≤	γ≤	NUM
ejpam-2332	399	23	1	1	NUM
ejpam-2332	399	24	ũ	ũ	PROPN
ejpam-2332	399	25	,	,	PUNCT
ejpam-2332	399	26	ṽ	ṽ	PROPN
ejpam-2332	399	27	∈	∈	PROPN
ejpam-2332	399	28	n	n	CCONJ
ejpam-2332	399	29	(	(	PUNCT
ejpam-2332	399	30	ℜ	ℜ	PROPN
ejpam-2332	399	31	)	)	PUNCT
ejpam-2332	399	32	where	where	SCONJ
ejpam-2332	399	33	n	n	CCONJ
ejpam-2332	399	34	(	(	PUNCT
ejpam-2332	399	35	ℜ	ℜ	PROPN
ejpam-2332	399	36	)	)	PUNCT
ejpam-2332	399	37	is	be	AUX
ejpam-2332	399	38	the	the	DET
ejpam-2332	399	39	set	set	NOUN
ejpam-2332	399	40	of	of	ADP
ejpam-2332	399	41	all	all	DET
ejpam-2332	399	42	fuzzy	fuzzy	ADJ
ejpam-2332	399	43	numbers	number	NOUN
ejpam-2332	399	44	.	.	PUNCT
ejpam-2332	400	1	the	the	DET
ejpam-2332	400	2	relations	relation	NOUN
ejpam-2332	400	3	�	�	PROPN
ejpam-2332	400	4	f	f	PROPN
ejpam-2332	400	5	and	and	CCONJ
ejpam-2332	400	6	�	�	PROPN
ejpam-2332	400	7	f	f	PROPN
ejpam-2332	400	8	are	be	AUX
ejpam-2332	400	9	the	the	DET
ejpam-2332	400	10	relations	relation	NOUN
ejpam-2332	400	11	between	between	ADP
ejpam-2332	400	12	fuzzy	fuzzy	ADJ
ejpam-2332	400	13	numbers	number	NOUN
ejpam-2332	400	14	.	.	PUNCT
ejpam-2332	401	1	therefore	therefore	ADV
ejpam-2332	401	2	,	,	PUNCT
ejpam-2332	401	3	i	i	NOUN
ejpam-2332	401	4	-	-	PUNCT
ejpam-2332	401	5	fuzzy	fuzzy	ADJ
ejpam-2332	401	6	non	non	ADJ
ejpam-2332	401	7	-	-	ADJ
ejpam-2332	401	8	linear	linear	ADJ
ejpam-2332	401	9	programming	programming	NOUN
ejpam-2332	401	10	problem	problem	NOUN
ejpam-2332	401	11	(	(	PUNCT
ejpam-2332	401	12	14	14	NUM
ejpam-2332	401	13	)	)	PUNCT
ejpam-2332	401	14	is	be	AUX
ejpam-2332	401	15	a	a	DET
ejpam-2332	401	16	generalization	generalization	NOUN
ejpam-2332	401	17	of	of	ADP
ejpam-2332	401	18	fuzzy	fuzzy	ADJ
ejpam-2332	401	19	non	non	ADJ
ejpam-2332	401	20	-	-	ADJ
ejpam-2332	401	21	linear	linear	ADJ
ejpam-2332	401	22	programming	programming	NOUN
ejpam-2332	401	23	problem	problem	NOUN
ejpam-2332	401	24	(	(	PUNCT
ejpam-2332	401	25	15	15	NUM
ejpam-2332	401	26	)	)	PUNCT
ejpam-2332	401	27	.	.	PUNCT
ejpam-2332	402	1	remark	remark	PROPN
ejpam-2332	402	2	2	2	NUM
ejpam-2332	402	3	.	.	PUNCT
ejpam-2332	403	1	in	in	ADP
ejpam-2332	403	2	general	general	ADJ
ejpam-2332	403	3	,	,	PUNCT
ejpam-2332	403	4	it	it	PRON
ejpam-2332	403	5	is	be	AUX
ejpam-2332	403	6	very	very	ADV
ejpam-2332	403	7	much	much	ADV
ejpam-2332	403	8	difficult	difficult	ADJ
ejpam-2332	403	9	to	to	PART
ejpam-2332	403	10	obtain	obtain	VERB
ejpam-2332	403	11	the	the	DET
ejpam-2332	403	12	exact	exact	ADJ
ejpam-2332	403	13	membership	membership	NOUN
ejpam-2332	403	14	and	and	CCONJ
ejpam-2332	403	15	non	non	ADJ
ejpam-2332	403	16	-	-	ADJ
ejpam-2332	403	17	membership	membership	ADJ
ejpam-2332	403	18	functions	function	NOUN
ejpam-2332	403	19	for	for	ADP
ejpam-2332	403	20	ũ∗	ũ∗	PRON
ejpam-2332	403	21	and	and	CCONJ
ejpam-2332	403	22	ṽ∗	ṽ∗	PROPN
ejpam-2332	403	23	as	as	SCONJ
ejpam-2332	403	24	there	there	PRON
ejpam-2332	403	25	are	be	VERB
ejpam-2332	403	26	several	several	ADJ
ejpam-2332	403	27	number	number	NOUN
ejpam-2332	403	28	of	of	ADP
ejpam-2332	403	29	parameters	parameter	NOUN
ejpam-2332	403	30	involved	involve	VERB
ejpam-2332	403	31	in	in	ADP
ejpam-2332	403	32	their	their	PRON
ejpam-2332	403	33	representation	representation	NOUN
ejpam-2332	403	34	.	.	PUNCT
ejpam-2332	404	1	for	for	ADP
ejpam-2332	404	2	example	example	NOUN
ejpam-2332	404	3	,	,	PUNCT
ejpam-2332	404	4	if	if	SCONJ
ejpam-2332	404	5	ũ=	ũ=	NUM
ejpam-2332	404	6	〈	〈	NOUN
ejpam-2332	404	7	(	(	PUNCT
ejpam-2332	404	8	uµ,u	uµ,u	PROPN
ejpam-2332	404	9	,	,	PUNCT
ejpam-2332	404	10	ūµ	ūµ	PROPN
ejpam-2332	404	11	)	)	PUNCT
ejpam-2332	404	12	;	;	PUNCT
ejpam-2332	404	13	(	(	PUNCT
ejpam-2332	404	14	uν	uν	PROPN
ejpam-2332	404	15	,	,	PUNCT
ejpam-2332	404	16	u	u	NOUN
ejpam-2332	404	17	,	,	PUNCT
ejpam-2332	404	18	ūν	ūν	ADJ
ejpam-2332	404	19	)	)	PUNCT
ejpam-2332	404	20	〉	〉	NOUN
ejpam-2332	404	21	be	be	VERB
ejpam-2332	404	22	a	a	DET
ejpam-2332	404	23	tifn	tifn	NOUN
ejpam-2332	404	24	then	then	ADV
ejpam-2332	404	25	to	to	PART
ejpam-2332	404	26	determine	determine	VERB
ejpam-2332	404	27	ũ	ũ	PROPN
ejpam-2332	404	28	completely	completely	ADV
ejpam-2332	404	29	we	we	PRON
ejpam-2332	404	30	need	need	VERB
ejpam-2332	404	31	all	all	PRON
ejpam-2332	404	32	of	of	ADP
ejpam-2332	404	33	these	these	DET
ejpam-2332	404	34	variables	variable	NOUN
ejpam-2332	404	35	.	.	PUNCT
ejpam-2332	405	1	thus	thus	ADV
ejpam-2332	405	2	,	,	PUNCT
ejpam-2332	405	3	from	from	ADP
ejpam-2332	405	4	computational	computational	ADJ
ejpam-2332	405	5	point	point	NOUN
ejpam-2332	405	6	of	of	ADP
ejpam-2332	405	7	view	view	NOUN
ejpam-2332	405	8	we	we	PRON
ejpam-2332	405	9	take	take	VERB
ejpam-2332	405	10	r(ũ	r(ũ	NOUN
ejpam-2332	405	11	)	)	PUNCT
ejpam-2332	405	12	and	and	CCONJ
ejpam-2332	405	13	r(ṽ	r(ṽ	NOUN
ejpam-2332	405	14	)	)	PUNCT
ejpam-2332	405	15	as	as	ADP
ejpam-2332	405	16	real	real	ADJ
ejpam-2332	405	17	variables	variable	NOUN
ejpam-2332	405	18	u	u	NOUN
ejpam-2332	405	19	and	and	CCONJ
ejpam-2332	405	20	v	v	VERB
ejpam-2332	405	21	and	and	CCONJ
ejpam-2332	405	22	modify	modify	VERB
ejpam-2332	405	23	the	the	DET
ejpam-2332	405	24	non	non	ADJ
ejpam-2332	405	25	-	-	ADJ
ejpam-2332	405	26	linear	linear	ADJ
ejpam-2332	405	27	programming	programming	NOUN
ejpam-2332	405	28	problem	problem	NOUN
ejpam-2332	405	29	(	(	PUNCT
ejpam-2332	405	30	14	14	NUM
ejpam-2332	405	31	)	)	PUNCT
ejpam-2332	405	32	as	as	SCONJ
ejpam-2332	405	33	follows	follow	VERB
ejpam-2332	405	34	max	max	PROPN
ejpam-2332	405	35	{	{	PUNCT
ejpam-2332	405	36	u+	u+	PROPN
ejpam-2332	405	37	v	v	PART
ejpam-2332	405	38	}	}	PUNCT
ejpam-2332	405	39	subject	subject	NOUN
ejpam-2332	405	40	to	to	ADP
ejpam-2332	405	41	n∑	n∑	PROPN
ejpam-2332	405	42	j=1	j=1	PROPN
ejpam-2332	405	43	r(ãi	r(ãi	PUNCT
ejpam-2332	406	1	j)y	j)y	NOUN
ejpam-2332	406	2	j	j	PROPN
ejpam-2332	406	3	≤	≤	X
ejpam-2332	406	4	u+	u+	NUM
ejpam-2332	406	5	(	(	PUNCT
ejpam-2332	406	6	1−	1−	NUM
ejpam-2332	406	7	ξ)r(p̃i	ξ)r(p̃i	NOUN
ejpam-2332	406	8	)	)	PUNCT
ejpam-2332	406	9	(	(	PUNCT
ejpam-2332	406	10	i	i	NOUN
ejpam-2332	406	11	=	=	SYM
ejpam-2332	406	12	1,2	1,2	NUM
ejpam-2332	406	13	,	,	PUNCT
ejpam-2332	406	14	.	.	PUNCT
ejpam-2332	406	15	.	.	PUNCT
ejpam-2332	406	16	.	.	PUNCT
ejpam-2332	407	1	,	,	PUNCT
ejpam-2332	407	2	m	m	PROPN
ejpam-2332	407	3	)	)	PUNCT
ejpam-2332	407	4	,	,	PUNCT
ejpam-2332	407	5	n∑	n∑	NOUN
ejpam-2332	407	6	j=1	j=1	PROPN
ejpam-2332	407	7	r(ãi	r(ãi	PUNCT
ejpam-2332	408	1	j)y	j)y	NOUN
ejpam-2332	408	2	j	j	PROPN
ejpam-2332	408	3	≤	≤	NUM
ejpam-2332	408	4	u+	u+	NUM
ejpam-2332	408	5	r(p̃i)−	r(p̃i)−	PRON
ejpam-2332	408	6	(	(	PUNCT
ejpam-2332	408	7	1−η)r(q̃i	1−η)r(q̃i	NUM
ejpam-2332	408	8	)	)	PUNCT
ejpam-2332	408	9	(	(	PUNCT
ejpam-2332	408	10	i	i	NOUN
ejpam-2332	408	11	=	=	SYM
ejpam-2332	408	12	1,2	1,2	NUM
ejpam-2332	408	13	,	,	PUNCT
ejpam-2332	408	14	.	.	PUNCT
ejpam-2332	408	15	.	.	PUNCT
ejpam-2332	408	16	.	.	PUNCT
ejpam-2332	409	1	,	,	PUNCT
ejpam-2332	409	2	m	m	PROPN
ejpam-2332	409	3	)	)	PUNCT
ejpam-2332	409	4	,	,	PUNCT
ejpam-2332	409	5	m.	m.	NOUN
ejpam-2332	409	6	seikh	seikh	PROPN
ejpam-2332	409	7	,	,	PUNCT
ejpam-2332	409	8	p.	p.	PROPN
ejpam-2332	409	9	nayak	nayak	PROPN
ejpam-2332	409	10	,	,	PUNCT
ejpam-2332	409	11	m.	m.	NOUN
ejpam-2332	409	12	pal	pal	PROPN
ejpam-2332	409	13	/	/	SYM
ejpam-2332	409	14	eur	eur	PROPN
ejpam-2332	409	15	.	.	PUNCT
ejpam-2332	410	1	j.	j.	PROPN
ejpam-2332	410	2	pure	pure	PROPN
ejpam-2332	410	3	appl	appl	PROPN
ejpam-2332	410	4	.	.	PROPN
ejpam-2332	410	5	math	math	PROPN
ejpam-2332	410	6	,	,	PUNCT
ejpam-2332	410	7	8	8	NUM
ejpam-2332	410	8	(	(	PUNCT
ejpam-2332	410	9	2015	2015	NUM
ejpam-2332	410	10	)	)	PUNCT
ejpam-2332	410	11	,	,	PUNCT
ejpam-2332	410	12	153	153	NUM
ejpam-2332	410	13	-	-	SYM
ejpam-2332	410	14	171	171	NUM
ejpam-2332	410	15	166	166	NUM
ejpam-2332	411	1	m∑	m∑	NOUN
ejpam-2332	411	2	i=1	i=1	PRON
ejpam-2332	412	1	r	r	PROPN
ejpam-2332	412	2	(	(	PUNCT
ejpam-2332	412	3	b̃i	b̃i	X
ejpam-2332	412	4	j)x	j)x	X
ejpam-2332	413	1	i	i	PRON
ejpam-2332	413	2	≤	≤	ADV
ejpam-2332	413	3	v	v	ADP
ejpam-2332	413	4	+	+	CCONJ
ejpam-2332	413	5	(	(	PUNCT
ejpam-2332	413	6	1−	1−	NUM
ejpam-2332	413	7	γ)r(r̃	γ)r(r̃	PROPN
ejpam-2332	413	8	j	j	PROPN
ejpam-2332	413	9	)	)	PUNCT
ejpam-2332	413	10	(	(	PUNCT
ejpam-2332	413	11	j	j	PROPN
ejpam-2332	413	12	=	=	SYM
ejpam-2332	413	13	1,2	1,2	NUM
ejpam-2332	413	14	,	,	PUNCT
ejpam-2332	413	15	.	.	PUNCT
ejpam-2332	413	16	.	.	PUNCT
ejpam-2332	413	17	.	.	PUNCT
ejpam-2332	413	18	,	,	PUNCT
ejpam-2332	413	19	n	n	CCONJ
ejpam-2332	413	20	)	)	PUNCT
ejpam-2332	413	21	,	,	PUNCT
ejpam-2332	413	22	m∑	m∑	CCONJ
ejpam-2332	413	23	i=1	i=1	PRON
ejpam-2332	414	1	r	r	NOUN
ejpam-2332	414	2	(	(	PUNCT
ejpam-2332	414	3	b̃i	b̃i	X
ejpam-2332	414	4	j)x	j)x	X
ejpam-2332	415	1	i	i	PRON
ejpam-2332	415	2	≤	≤	X
ejpam-2332	415	3	v	v	ADP
ejpam-2332	415	4	+	+	CCONJ
ejpam-2332	415	5	r(r̃	r(r̃	PROPN
ejpam-2332	415	6	j)−	j)−	PROPN
ejpam-2332	415	7	(	(	PUNCT
ejpam-2332	415	8	1−δ)r(s̃	1−δ)r(s̃	NUM
ejpam-2332	415	9	j	j	NOUN
ejpam-2332	415	10	)	)	PUNCT
ejpam-2332	415	11	(	(	PUNCT
ejpam-2332	415	12	j	j	PROPN
ejpam-2332	415	13	=	=	SYM
ejpam-2332	415	14	1,2	1,2	NUM
ejpam-2332	415	15	,	,	PUNCT
ejpam-2332	415	16	.	.	PUNCT
ejpam-2332	415	17	.	.	PUNCT
ejpam-2332	416	1	.	.	PUNCT
ejpam-2332	416	2	,	,	PUNCT
ejpam-2332	417	1	n	n	CCONJ
ejpam-2332	417	2	)	)	PUNCT
ejpam-2332	418	1	,	,	PUNCT
ejpam-2332	418	2	m∑	m∑	INTJ
ejpam-2332	418	3	i=1	i=1	PROPN
ejpam-2332	418	4	n∑	n∑	PROPN
ejpam-2332	418	5	j=1	j=1	PROPN
ejpam-2332	418	6	r(ãi	r(ãi	PUNCT
ejpam-2332	419	1	j)x	j)x	NOUN
ejpam-2332	420	1	i	i	PRON
ejpam-2332	420	2	y	y	PROPN
ejpam-2332	420	3	j	j	PROPN
ejpam-2332	420	4	≥	≥	PROPN
ejpam-2332	420	5	u−	u−	PROPN
ejpam-2332	420	6	(	(	PUNCT
ejpam-2332	420	7	1−	1−	NUM
ejpam-2332	420	8	ξ)r(p̃0	ξ)r(p̃0	NOUN
ejpam-2332	420	9	)	)	PUNCT
ejpam-2332	420	10	,	,	PUNCT
ejpam-2332	420	11	(	(	PUNCT
ejpam-2332	420	12	16	16	NUM
ejpam-2332	420	13	)	)	PUNCT
ejpam-2332	420	14	m∑	m∑	CCONJ
ejpam-2332	420	15	i=1	i=1	PROPN
ejpam-2332	420	16	n∑	n∑	PROPN
ejpam-2332	421	1	j=1	j=1	PROPN
ejpam-2332	421	2	r(ãi	r(ãi	PUNCT
ejpam-2332	422	1	j)x	j)x	NOUN
ejpam-2332	423	1	i	i	PRON
ejpam-2332	423	2	y	y	PROPN
ejpam-2332	423	3	j	j	PROPN
ejpam-2332	423	4	≥	≥	PROPN
ejpam-2332	423	5	u−	u−	PROPN
ejpam-2332	423	6	r(p̃0	r(p̃0	NOUN
ejpam-2332	423	7	)	)	PUNCT
ejpam-2332	424	1	+	+	CCONJ
ejpam-2332	424	2	(	(	PUNCT
ejpam-2332	424	3	1−η)r(q̃0	1−η)r(q̃0	X
ejpam-2332	424	4	)	)	PUNCT
ejpam-2332	424	5	,	,	PUNCT
ejpam-2332	424	6	m∑	m∑	INTJ
ejpam-2332	425	1	i=1	i=1	PROPN
ejpam-2332	425	2	n∑	n∑	PROPN
ejpam-2332	426	1	j=1	j=1	NOUN
ejpam-2332	426	2	r	r	NOUN
ejpam-2332	426	3	(	(	PUNCT
ejpam-2332	426	4	b̃i	b̃i	X
ejpam-2332	426	5	j)x	j)x	PROPN
ejpam-2332	427	1	i	i	PRON
ejpam-2332	428	1	y	y	PROPN
ejpam-2332	428	2	j	j	PROPN
ejpam-2332	428	3	≥	≥	NUM
ejpam-2332	428	4	v	v	ADP
ejpam-2332	428	5	−	−	PROPN
ejpam-2332	428	6	(	(	PUNCT
ejpam-2332	428	7	1−	1−	NUM
ejpam-2332	428	8	γ)r(r̃0	γ)r(r̃0	NOUN
ejpam-2332	428	9	)	)	PUNCT
ejpam-2332	428	10	,	,	PUNCT
ejpam-2332	428	11	m∑	m∑	INTJ
ejpam-2332	429	1	i=1	i=1	PROPN
ejpam-2332	429	2	n∑	n∑	PROPN
ejpam-2332	430	1	j=1	j=1	NOUN
ejpam-2332	430	2	r	r	NOUN
ejpam-2332	430	3	(	(	PUNCT
ejpam-2332	430	4	b̃i	b̃i	X
ejpam-2332	430	5	j)x	j)x	PROPN
ejpam-2332	431	1	i	i	PRON
ejpam-2332	432	1	y	y	PROPN
ejpam-2332	432	2	j	j	PROPN
ejpam-2332	432	3	≥	≥	NUM
ejpam-2332	432	4	v	v	ADP
ejpam-2332	432	5	−	−	PROPN
ejpam-2332	432	6	r(r̃0	r(r̃0	NOUN
ejpam-2332	432	7	)	)	PUNCT
ejpam-2332	432	8	+	+	CCONJ
ejpam-2332	432	9	(	(	PUNCT
ejpam-2332	432	10	1−	1−	NUM
ejpam-2332	432	11	δ)r(s̃0	δ)r(s̃0	NOUN
ejpam-2332	432	12	)	)	PUNCT
ejpam-2332	432	13	,	,	PUNCT
ejpam-2332	432	14	m∑	m∑	CCONJ
ejpam-2332	432	15	i=1	i=1	PROPN
ejpam-2332	433	1	x	x	PUNCT
ejpam-2332	433	2	i	i	NOUN
ejpam-2332	433	3	=	=	NOUN
ejpam-2332	433	4	1	1	NUM
ejpam-2332	433	5	,	,	PUNCT
ejpam-2332	433	6	n∑	n∑	NOUN
ejpam-2332	433	7	j=1	j=1	NOUN
ejpam-2332	434	1	y	y	PROPN
ejpam-2332	434	2	j	j	PROPN
ejpam-2332	434	3	=	=	SYM
ejpam-2332	434	4	1	1	NUM
ejpam-2332	434	5	,	,	PUNCT
ejpam-2332	434	6	0≤	0≤	NOUN
ejpam-2332	434	7	ξ≤	ξ≤	PROPN
ejpam-2332	434	8	1,0≤	1,0≤	NUM
ejpam-2332	434	9	η	η	PROPN
ejpam-2332	434	10	≤	≤	PROPN
ejpam-2332	434	11	1	1	NUM
ejpam-2332	434	12	,	,	PUNCT
ejpam-2332	434	13	0≤	0≤	NUM
ejpam-2332	434	14	γ≤	γ≤	NUM
ejpam-2332	434	15	1,0≤	1,0≤	NUM
ejpam-2332	434	16	δ	δ	PROPN
ejpam-2332	434	17	≤	≤	ADV
ejpam-2332	434	18	1	1	NUM
ejpam-2332	434	19	.	.	PUNCT
ejpam-2332	435	1	in	in	ADP
ejpam-2332	435	2	this	this	DET
ejpam-2332	435	3	situation	situation	NOUN
ejpam-2332	435	4	,	,	PUNCT
ejpam-2332	435	5	we	we	PRON
ejpam-2332	435	6	shall	shall	AUX
ejpam-2332	435	7	get	get	VERB
ejpam-2332	435	8	only	only	ADV
ejpam-2332	435	9	the	the	DET
ejpam-2332	435	10	numerical	numerical	ADJ
ejpam-2332	435	11	values	value	NOUN
ejpam-2332	435	12	u∗	u∗	VERB
ejpam-2332	435	13	and	and	CCONJ
ejpam-2332	435	14	v∗	v∗	ADJ
ejpam-2332	435	15	instead	instead	ADV
ejpam-2332	435	16	of	of	ADP
ejpam-2332	435	17	ũ∗	ũ∗	X
ejpam-2332	435	18	and	and	CCONJ
ejpam-2332	435	19	ṽ∗	ṽ∗	PROPN
ejpam-2332	435	20	,	,	PUNCT
ejpam-2332	435	21	respectively	respectively	ADV
ejpam-2332	435	22	for	for	ADP
ejpam-2332	435	23	player	player	NOUN
ejpam-2332	435	24	i	i	PROPN
ejpam-2332	435	25	and	and	CCONJ
ejpam-2332	435	26	ii	ii	PROPN
ejpam-2332	435	27	.	.	PUNCT
ejpam-2332	436	1	therefore	therefore	ADV
ejpam-2332	436	2	,	,	PUNCT
ejpam-2332	436	3	we	we	PRON
ejpam-2332	436	4	are	be	AUX
ejpam-2332	436	5	not	not	PART
ejpam-2332	436	6	able	able	ADJ
ejpam-2332	436	7	to	to	PART
ejpam-2332	436	8	get	get	VERB
ejpam-2332	436	9	exact	exact	ADJ
ejpam-2332	436	10	membership	membership	NOUN
ejpam-2332	436	11	and	and	CCONJ
ejpam-2332	436	12	non	non	ADJ
ejpam-2332	436	13	-	-	ADJ
ejpam-2332	436	14	membership	membership	ADJ
ejpam-2332	436	15	values	value	NOUN
ejpam-2332	436	16	for	for	ADP
ejpam-2332	436	17	ũ∗	ũ∗	PRON
ejpam-2332	436	18	and	and	CCONJ
ejpam-2332	436	19	ṽ∗	ṽ∗	PROPN
ejpam-2332	436	20	which	which	PRON
ejpam-2332	436	21	are	be	AUX
ejpam-2332	436	22	very	very	ADV
ejpam-2332	436	23	much	much	ADV
ejpam-2332	436	24	desirable	desirable	ADJ
ejpam-2332	436	25	and	and	CCONJ
ejpam-2332	436	26	be	be	AUX
ejpam-2332	436	27	satisfied	satisfied	ADJ
ejpam-2332	436	28	with	with	ADP
ejpam-2332	436	29	u∗	u∗	NOUN
ejpam-2332	436	30	and	and	CCONJ
ejpam-2332	436	31	v∗	v∗	PROPN
ejpam-2332	436	32	that	that	PRON
ejpam-2332	436	33	are	be	AUX
ejpam-2332	436	34	close	close	ADJ
ejpam-2332	436	35	to	to	ADP
ejpam-2332	436	36	the	the	DET
ejpam-2332	436	37	actual	actual	ADJ
ejpam-2332	436	38	i	i	NOUN
ejpam-2332	436	39	-	-	PUNCT
ejpam-2332	436	40	fuzzy	fuzzy	ADJ
ejpam-2332	436	41	values	value	NOUN
ejpam-2332	436	42	for	for	ADP
ejpam-2332	436	43	the	the	DET
ejpam-2332	436	44	player	player	NOUN
ejpam-2332	436	45	i	i	PROPN
ejpam-2332	436	46	and	and	CCONJ
ejpam-2332	436	47	ii	ii	PROPN
ejpam-2332	436	48	,	,	PUNCT
ejpam-2332	436	49	respective	respective	ADJ
ejpam-2332	436	50	.	.	PUNCT
ejpam-2332	437	1	5	5	X
ejpam-2332	437	2	.	.	X
ejpam-2332	437	3	an	an	DET
ejpam-2332	437	4	application	application	NOUN
ejpam-2332	437	5	to	to	ADP
ejpam-2332	437	6	media	medium	NOUN
ejpam-2332	437	7	industry	industry	NOUN
ejpam-2332	437	8	in	in	ADP
ejpam-2332	437	9	this	this	DET
ejpam-2332	437	10	section	section	NOUN
ejpam-2332	437	11	,	,	PUNCT
ejpam-2332	437	12	decision	decision	NOUN
ejpam-2332	437	13	making	make	VERB
ejpam-2332	437	14	problem	problem	NOUN
ejpam-2332	437	15	in	in	ADP
ejpam-2332	437	16	media	medium	NOUN
ejpam-2332	437	17	industry	industry	NOUN
ejpam-2332	437	18	is	be	AUX
ejpam-2332	437	19	considered	consider	VERB
ejpam-2332	437	20	to	to	PART
ejpam-2332	437	21	show	show	VERB
ejpam-2332	437	22	the	the	DET
ejpam-2332	437	23	validity	validity	NOUN
ejpam-2332	437	24	and	and	CCONJ
ejpam-2332	437	25	applicability	applicability	NOUN
ejpam-2332	437	26	of	of	ADP
ejpam-2332	437	27	the	the	DET
ejpam-2332	437	28	proposed	propose	VERB
ejpam-2332	437	29	methodology	methodology	NOUN
ejpam-2332	437	30	in	in	ADP
ejpam-2332	437	31	real	real	ADJ
ejpam-2332	437	32	life	life	NOUN
ejpam-2332	437	33	problem	problem	NOUN
ejpam-2332	437	34	.	.	PUNCT
ejpam-2332	438	1	let	let	VERB
ejpam-2332	438	2	us	we	PRON
ejpam-2332	438	3	consider	consider	VERB
ejpam-2332	438	4	two	two	NUM
ejpam-2332	438	5	major	major	ADJ
ejpam-2332	438	6	tv	tv	NOUN
ejpam-2332	438	7	station	station	NOUN
ejpam-2332	438	8	companies	company	NOUN
ejpam-2332	438	9	t1	t1	VERB
ejpam-2332	438	10	and	and	CCONJ
ejpam-2332	438	11	t2	t2	NOUN
ejpam-2332	438	12	aiming	aim	VERB
ejpam-2332	438	13	to	to	PART
ejpam-2332	438	14	enhance	enhance	VERB
ejpam-2332	438	15	trps	trps	PROPN
ejpam-2332	438	16	by	by	ADP
ejpam-2332	438	17	increasing	increase	VERB
ejpam-2332	438	18	their	their	PRON
ejpam-2332	438	19	number	number	NOUN
ejpam-2332	438	20	of	of	ADP
ejpam-2332	438	21	viewers	viewer	NOUN
ejpam-2332	438	22	.	.	PUNCT
ejpam-2332	439	1	assume	assume	VERB
ejpam-2332	439	2	that	that	SCONJ
ejpam-2332	439	3	management	management	NOUN
ejpam-2332	439	4	of	of	ADP
ejpam-2332	439	5	both	both	CCONJ
ejpam-2332	439	6	the	the	DET
ejpam-2332	439	7	companies	company	NOUN
ejpam-2332	439	8	are	be	AUX
ejpam-2332	439	9	rational	rational	ADJ
ejpam-2332	439	10	i.e.	i.e.	ADV
ejpam-2332	439	11	,	,	PUNCT
ejpam-2332	439	12	they	they	PRON
ejpam-2332	439	13	will	will	AUX
ejpam-2332	439	14	choose	choose	VERB
ejpam-2332	439	15	optimal	optimal	ADJ
ejpam-2332	439	16	strategies	strategy	NOUN
ejpam-2332	439	17	to	to	PART
ejpam-2332	439	18	maximize	maximize	VERB
ejpam-2332	439	19	their	their	PRON
ejpam-2332	439	20	own	own	ADJ
ejpam-2332	439	21	trps	trps	PROPN
ejpam-2332	439	22	without	without	ADP
ejpam-2332	439	23	co	co	NOUN
ejpam-2332	439	24	-	-	NOUN
ejpam-2332	439	25	operation	operation	NOUN
ejpam-2332	439	26	.	.	PUNCT
ejpam-2332	440	1	let	let	VERB
ejpam-2332	440	2	the	the	DET
ejpam-2332	440	3	manager	manager	NOUN
ejpam-2332	440	4	of	of	ADP
ejpam-2332	440	5	tv	tv	NOUN
ejpam-2332	440	6	stations	station	NOUN
ejpam-2332	440	7	t1	t1	VERB
ejpam-2332	440	8	and	and	CCONJ
ejpam-2332	440	9	t2	t2	NOUN
ejpam-2332	440	10	make	make	VERB
ejpam-2332	440	11	decision	decision	NOUN
ejpam-2332	440	12	to	to	PART
ejpam-2332	440	13	show	show	VERB
ejpam-2332	440	14	what	what	PRON
ejpam-2332	440	15	kind	kind	NOUN
ejpam-2332	440	16	of	of	ADP
ejpam-2332	440	17	tv	tv	NOUN
ejpam-2332	440	18	program	program	NOUN
ejpam-2332	440	19	to	to	PART
ejpam-2332	440	20	broadcast	broadcast	VERB
ejpam-2332	440	21	every	every	DET
ejpam-2332	440	22	day	day	NOUN
ejpam-2332	440	23	at	at	ADP
ejpam-2332	440	24	the	the	DET
ejpam-2332	440	25	peak	peak	NOUN
ejpam-2332	440	26	watching	watch	VERB
ejpam-2332	440	27	hours	hour	NOUN
ejpam-2332	440	28	(	(	PUNCT
ejpam-2332	440	29	6	6	NUM
ejpam-2332	440	30	p.m.-10	p.m.-10	NOUN
ejpam-2332	440	31	p.m.	p.m.	NUM
ejpam-2332	440	32	)	)	PUNCT
ejpam-2332	440	33	.	.	PUNCT
ejpam-2332	441	1	they	they	PRON
ejpam-2332	441	2	choose	choose	VERB
ejpam-2332	441	3	two	two	NUM
ejpam-2332	441	4	options	option	NOUN
ejpam-2332	441	5	called	call	VERB
ejpam-2332	441	6	strategies	strategy	NOUN
ejpam-2332	441	7	-	-	PUNCT
ejpam-2332	441	8	tv	tv	NOUN
ejpam-2332	441	9	serials	serial	NOUN
ejpam-2332	441	10	(	(	PUNCT
ejpam-2332	441	11	strategy	strategy	NOUN
ejpam-2332	441	12	ε1	ε1	PROPN
ejpam-2332	441	13	)	)	PUNCT
ejpam-2332	441	14	and	and	CCONJ
ejpam-2332	441	15	reality	reality	NOUN
ejpam-2332	441	16	show	show	NOUN
ejpam-2332	441	17	(	(	PUNCT
ejpam-2332	441	18	strategy	strategy	NOUN
ejpam-2332	441	19	ε2	ε2	NOUN
ejpam-2332	441	20	)	)	PUNCT
ejpam-2332	441	21	.	.	PUNCT
ejpam-2332	442	1	the	the	DET
ejpam-2332	442	2	above	above	ADJ
ejpam-2332	442	3	problem	problem	NOUN
ejpam-2332	442	4	may	may	AUX
ejpam-2332	442	5	be	be	AUX
ejpam-2332	442	6	regarded	regard	VERB
ejpam-2332	442	7	as	as	ADP
ejpam-2332	442	8	a	a	DET
ejpam-2332	442	9	bi	bi	ADJ
ejpam-2332	442	10	-	-	ADJ
ejpam-2332	442	11	matrix	matrix	NOUN
ejpam-2332	442	12	game	game	NOUN
ejpam-2332	442	13	.	.	PUNCT
ejpam-2332	443	1	namely	namely	ADV
ejpam-2332	443	2	,	,	PUNCT
ejpam-2332	443	3	the	the	DET
ejpam-2332	443	4	tv	tv	NOUN
ejpam-2332	443	5	station	station	NOUN
ejpam-2332	443	6	companies	company	NOUN
ejpam-2332	443	7	t1	t1	VERB
ejpam-2332	443	8	and	and	CCONJ
ejpam-2332	443	9	t2	t2	PROPN
ejpam-2332	443	10	are	be	AUX
ejpam-2332	443	11	regarded	regard	VERB
ejpam-2332	443	12	as	as	ADP
ejpam-2332	443	13	players	player	NOUN
ejpam-2332	443	14	i	i	PRON
ejpam-2332	443	15	and	and	CCONJ
ejpam-2332	443	16	ii	ii	PROPN
ejpam-2332	443	17	,	,	PUNCT
ejpam-2332	443	18	respectively	respectively	ADV
ejpam-2332	443	19	.	.	PUNCT
ejpam-2332	444	1	they	they	PRON
ejpam-2332	444	2	may	may	AUX
ejpam-2332	444	3	use	use	VERB
ejpam-2332	444	4	strategies	strategy	NOUN
ejpam-2332	444	5	ε1	ε1	NOUN
ejpam-2332	444	6	and	and	CCONJ
ejpam-2332	444	7	ε2	ε2	ADJ
ejpam-2332	444	8	.	.	PUNCT
ejpam-2332	445	1	due	due	ADP
ejpam-2332	445	2	to	to	ADP
ejpam-2332	445	3	a	a	DET
ejpam-2332	445	4	lack	lack	NOUN
ejpam-2332	445	5	of	of	ADP
ejpam-2332	445	6	information	information	NOUN
ejpam-2332	445	7	or	or	CCONJ
ejpam-2332	445	8	imprecision	imprecision	NOUN
ejpam-2332	445	9	of	of	ADP
ejpam-2332	445	10	the	the	DET
ejpam-2332	445	11	available	available	ADJ
ejpam-2332	445	12	information	information	NOUN
ejpam-2332	445	13	,	,	PUNCT
ejpam-2332	445	14	the	the	DET
ejpam-2332	445	15	managers	manager	NOUN
ejpam-2332	445	16	of	of	ADP
ejpam-2332	445	17	two	two	NUM
ejpam-2332	445	18	companies	company	NOUN
ejpam-2332	445	19	usually	usually	ADV
ejpam-2332	445	20	are	be	AUX
ejpam-2332	445	21	not	not	PART
ejpam-2332	445	22	able	able	ADJ
ejpam-2332	445	23	to	to	PART
ejpam-2332	445	24	forecast	forecast	VERB
ejpam-2332	445	25	the	the	DET
ejpam-2332	445	26	number	number	NOUN
ejpam-2332	445	27	of	of	ADP
ejpam-2332	445	28	viewers	viewer	NOUN
ejpam-2332	445	29	exactly	exactly	ADV
ejpam-2332	445	30	.	.	PUNCT
ejpam-2332	446	1	they	they	PRON
ejpam-2332	446	2	estimate	estimate	VERB
ejpam-2332	446	3	the	the	DET
ejpam-2332	446	4	same	same	ADJ
ejpam-2332	446	5	with	with	ADP
ejpam-2332	446	6	a	a	DET
ejpam-2332	446	7	certain	certain	ADJ
ejpam-2332	446	8	confidence	confidence	NOUN
ejpam-2332	446	9	degree	degree	NOUN
ejpam-2332	446	10	,	,	PUNCT
ejpam-2332	446	11	but	but	CCONJ
ejpam-2332	446	12	it	it	PRON
ejpam-2332	446	13	is	be	AUX
ejpam-2332	446	14	possible	possible	ADJ
ejpam-2332	446	15	that	that	SCONJ
ejpam-2332	446	16	they	they	PRON
ejpam-2332	446	17	are	be	AUX
ejpam-2332	446	18	not	not	PART
ejpam-2332	446	19	so	so	ADV
ejpam-2332	446	20	sure	sure	ADJ
ejpam-2332	446	21	about	about	ADP
ejpam-2332	446	22	it	it	PRON
ejpam-2332	446	23	.	.	PUNCT
ejpam-2332	447	1	thus	thus	ADV
ejpam-2332	447	2	,	,	PUNCT
ejpam-2332	447	3	there	there	PRON
ejpam-2332	447	4	may	may	AUX
ejpam-2332	447	5	survive	survive	VERB
ejpam-2332	447	6	a	a	DET
ejpam-2332	447	7	hesitation	hesitation	NOUN
ejpam-2332	447	8	degree	degree	NOUN
ejpam-2332	447	9	.	.	PUNCT
ejpam-2332	448	1	in	in	ADP
ejpam-2332	448	2	order	order	NOUN
ejpam-2332	448	3	to	to	PART
ejpam-2332	448	4	deal	deal	VERB
ejpam-2332	448	5	with	with	ADP
ejpam-2332	448	6	uncertainty	uncertainty	NOUN
ejpam-2332	448	7	,	,	PUNCT
ejpam-2332	448	8	tifns	tifns	PROPN
ejpam-2332	448	9	are	be	AUX
ejpam-2332	448	10	used	use	VERB
ejpam-2332	448	11	to	to	PART
ejpam-2332	448	12	express	express	VERB
ejpam-2332	448	13	the	the	DET
ejpam-2332	448	14	m.	m.	NOUN
ejpam-2332	448	15	seikh	seikh	NOUN
ejpam-2332	448	16	,	,	PUNCT
ejpam-2332	448	17	p.	p.	PROPN
ejpam-2332	448	18	nayak	nayak	PROPN
ejpam-2332	448	19	,	,	PUNCT
ejpam-2332	448	20	m.	m.	NOUN
ejpam-2332	448	21	pal	pal	PROPN
ejpam-2332	448	22	/	/	SYM
ejpam-2332	448	23	eur	eur	PROPN
ejpam-2332	448	24	.	.	PUNCT
ejpam-2332	449	1	j.	j.	PROPN
ejpam-2332	449	2	pure	pure	PROPN
ejpam-2332	449	3	appl	appl	PROPN
ejpam-2332	449	4	.	.	PROPN
ejpam-2332	449	5	math	math	PROPN
ejpam-2332	449	6	,	,	PUNCT
ejpam-2332	449	7	8	8	NUM
ejpam-2332	449	8	(	(	PUNCT
ejpam-2332	449	9	2015	2015	NUM
ejpam-2332	449	10	)	)	PUNCT
ejpam-2332	449	11	,	,	PUNCT
ejpam-2332	449	12	153	153	NUM
ejpam-2332	449	13	-	-	SYM
ejpam-2332	449	14	171	171	NUM
ejpam-2332	449	15	167	167	NUM
ejpam-2332	449	16	number	number	NOUN
ejpam-2332	449	17	of	of	ADP
ejpam-2332	449	18	viewers	viewer	NOUN
ejpam-2332	449	19	for	for	ADP
ejpam-2332	449	20	a	a	DET
ejpam-2332	449	21	particular	particular	ADJ
ejpam-2332	449	22	tv	tv	NOUN
ejpam-2332	449	23	station	station	NOUN
ejpam-2332	449	24	for	for	ADP
ejpam-2332	449	25	a	a	DET
ejpam-2332	449	26	specified	specified	ADJ
ejpam-2332	449	27	time	time	NOUN
ejpam-2332	449	28	period	period	NOUN
ejpam-2332	449	29	.	.	PUNCT
ejpam-2332	450	1	let	let	VERB
ejpam-2332	450	2	there	there	PRON
ejpam-2332	450	3	are	be	VERB
ejpam-2332	450	4	about	about	ADV
ejpam-2332	450	5	20	20	NUM
ejpam-2332	450	6	million	million	NUM
ejpam-2332	450	7	of	of	ADP
ejpam-2332	450	8	viewers	viewer	NOUN
ejpam-2332	450	9	.	.	PUNCT
ejpam-2332	451	1	the	the	DET
ejpam-2332	451	2	marketing	marketing	NOUN
ejpam-2332	451	3	research	research	NOUN
ejpam-2332	451	4	department	department	NOUN
ejpam-2332	451	5	of	of	ADP
ejpam-2332	451	6	both	both	CCONJ
ejpam-2332	451	7	the	the	DET
ejpam-2332	451	8	companies	company	NOUN
ejpam-2332	451	9	supplied	supply	VERB
ejpam-2332	451	10	the	the	DET
ejpam-2332	451	11	following	follow	VERB
ejpam-2332	451	12	pay	pay	VERB
ejpam-2332	451	13	-	-	PUNCT
ejpam-2332	451	14	off	off	ADP
ejpam-2332	451	15	matrices	matrix	NOUN
ejpam-2332	451	16	.	.	PUNCT
ejpam-2332	452	1	ã=	ã=	PROPN
ejpam-2332	452	2	tv	tv	NOUN
ejpam-2332	452	3	serials	serial	NOUN
ejpam-2332	452	4	reality	reality	NOUN
ejpam-2332	452	5	show	show	NOUN
ejpam-2332	452	6			PROPN
ejpam-2332	452	7			NOUN
ejpam-2332	452	8	tv	tv	NOUN
ejpam-2332	452	9	serials	serial	NOUN
ejpam-2332	452	10	reality	reality	NOUN
ejpam-2332	452	11	show	show	VERB
ejpam-2332	452	12	〈	〈	PROPN
ejpam-2332	452	13	(	(	PUNCT
ejpam-2332	452	14	7,8,9	7,8,9	NOUN
ejpam-2332	452	15	)	)	PUNCT
ejpam-2332	452	16	;	;	PUNCT
ejpam-2332	452	17	(	(	PUNCT
ejpam-2332	452	18	6.5,8,9.5	6.5,8,9.5	X
ejpam-2332	452	19	)	)	PUNCT
ejpam-2332	452	20	〉	〉	NOUN
ejpam-2332	452	21	〈	〈	PROPN
ejpam-2332	452	22	(	(	PUNCT
ejpam-2332	452	23	10.5,12,13	10.5,12,13	NUM
ejpam-2332	452	24	)	)	PUNCT
ejpam-2332	452	25	;	;	PUNCT
ejpam-2332	452	26	(	(	PUNCT
ejpam-2332	452	27	10,12,14	10,12,14	ADV
ejpam-2332	452	28	)	)	PUNCT
ejpam-2332	452	29	〉	〉	NOUN
ejpam-2332	452	30	〈	〈	PROPN
ejpam-2332	452	31	(	(	PUNCT
ejpam-2332	452	32	9.5,10,10.5	9.5,10,10.5	NUM
ejpam-2332	452	33	)	)	PUNCT
ejpam-2332	452	34	;	;	PUNCT
ejpam-2332	452	35	(	(	PUNCT
ejpam-2332	452	36	9,10,11	9,10,11	X
ejpam-2332	452	37	)	)	PUNCT
ejpam-2332	452	38	〉	〉	NOUN
ejpam-2332	452	39	〈	〈	PROPN
ejpam-2332	452	40	(	(	PUNCT
ejpam-2332	452	41	4.5,6,7	4.5,6,7	NOUN
ejpam-2332	452	42	)	)	PUNCT
ejpam-2332	452	43	;	;	PUNCT
ejpam-2332	452	44	(	(	PUNCT
ejpam-2332	452	45	4,6,7.5	4,6,7.5	X
ejpam-2332	452	46	)	)	PUNCT
ejpam-2332	452	47	〉	〉	NOUN
ejpam-2332	452	48			PROPN
ejpam-2332	452	49			PROPN
ejpam-2332	452	50	b̃	b̃	PROPN
ejpam-2332	452	51	=	=	NOUN
ejpam-2332	452	52	tv	tv	NOUN
ejpam-2332	452	53	serials	serial	NOUN
ejpam-2332	452	54	reality	reality	NOUN
ejpam-2332	452	55	show	show	NOUN
ejpam-2332	452	56			PROPN
ejpam-2332	452	57			NOUN
ejpam-2332	452	58	tv	tv	NOUN
ejpam-2332	452	59	serials	serial	NOUN
ejpam-2332	452	60	reality	reality	NOUN
ejpam-2332	452	61	show	show	VERB
ejpam-2332	452	62	〈	〈	PROPN
ejpam-2332	452	63	(	(	PUNCT
ejpam-2332	452	64	7,8,9	7,8,9	NOUN
ejpam-2332	452	65	)	)	PUNCT
ejpam-2332	452	66	;	;	PUNCT
ejpam-2332	452	67	(	(	PUNCT
ejpam-2332	452	68	6.5,8,9.5	6.5,8,9.5	X
ejpam-2332	452	69	)	)	PUNCT
ejpam-2332	452	70	〉	〉	NOUN
ejpam-2332	452	71	〈	〈	PROPN
ejpam-2332	452	72	(	(	PUNCT
ejpam-2332	452	73	4.5,6,7	4.5,6,7	NOUN
ejpam-2332	452	74	)	)	PUNCT
ejpam-2332	452	75	;	;	PUNCT
ejpam-2332	452	76	(	(	PUNCT
ejpam-2332	452	77	4,6,7.5	4,6,7.5	NUM
ejpam-2332	452	78	)	)	PUNCT
ejpam-2332	452	79	〉	〉	NOUN
ejpam-2332	452	80	〈	〈	PROPN
ejpam-2332	452	81	(	(	PUNCT
ejpam-2332	452	82	4.5,6,7	4.5,6,7	NOUN
ejpam-2332	452	83	)	)	PUNCT
ejpam-2332	452	84	;	;	PUNCT
ejpam-2332	452	85	(	(	PUNCT
ejpam-2332	452	86	4,6,7.5	4,6,7.5	NUM
ejpam-2332	452	87	)	)	PUNCT
ejpam-2332	452	88	〉	〉	NOUN
ejpam-2332	452	89	〈	〈	PROPN
ejpam-2332	452	90	(	(	PUNCT
ejpam-2332	452	91	9.5,10,10.5	9.5,10,10.5	NUM
ejpam-2332	452	92	)	)	PUNCT
ejpam-2332	452	93	;	;	PUNCT
ejpam-2332	452	94	(	(	PUNCT
ejpam-2332	452	95	9,10,11	9,10,11	X
ejpam-2332	452	96	)	)	PUNCT
ejpam-2332	452	97	〉	〉	NOUN
ejpam-2332	452	98			PROPN
ejpam-2332	452	99			PROPN
ejpam-2332	452	100	the	the	DET
ejpam-2332	452	101	entries	entry	NOUN
ejpam-2332	452	102	of	of	ADP
ejpam-2332	452	103	these	these	DET
ejpam-2332	452	104	matrices	matrix	NOUN
ejpam-2332	452	105	are	be	AUX
ejpam-2332	452	106	tifns	tifns	NOUN
ejpam-2332	452	107	in	in	ADP
ejpam-2332	452	108	millions	million	NOUN
ejpam-2332	452	109	of	of	ADP
ejpam-2332	452	110	viewers	viewer	NOUN
ejpam-2332	452	111	who	who	PRON
ejpam-2332	452	112	would	would	AUX
ejpam-2332	452	113	watch	watch	VERB
ejpam-2332	452	114	tv	tv	NOUN
ejpam-2332	452	115	station	station	NOUN
ejpam-2332	452	116	t1	t1	NOUN
ejpam-2332	452	117	or	or	CCONJ
ejpam-2332	452	118	tv	tv	NOUN
ejpam-2332	452	119	station	station	NOUN
ejpam-2332	452	120	t2	t2	PROPN
ejpam-2332	452	121	respectively	respectively	ADV
ejpam-2332	452	122	,	,	PUNCT
ejpam-2332	452	123	at	at	ADP
ejpam-2332	452	124	the	the	DET
ejpam-2332	452	125	specified	specified	ADJ
ejpam-2332	452	126	time	time	NOUN
ejpam-2332	452	127	.	.	PUNCT
ejpam-2332	453	1	other	other	ADJ
ejpam-2332	453	2	viewers	viewer	NOUN
ejpam-2332	453	3	may	may	AUX
ejpam-2332	453	4	watch	watch	VERB
ejpam-2332	453	5	other	other	ADJ
ejpam-2332	453	6	minor	minor	ADJ
ejpam-2332	453	7	tv	tv	NOUN
ejpam-2332	453	8	stations	station	NOUN
ejpam-2332	453	9	.	.	PUNCT
ejpam-2332	454	1	here	here	ADV
ejpam-2332	454	2	〈	〈	PROPN
ejpam-2332	454	3	(	(	PUNCT
ejpam-2332	454	4	7,8,9	7,8,9	NOUN
ejpam-2332	454	5	)	)	PUNCT
ejpam-2332	454	6	;	;	PUNCT
ejpam-2332	454	7	(	(	PUNCT
ejpam-2332	454	8	6.5,8,9.5	6.5,8,9.5	X
ejpam-2332	454	9	)	)	PUNCT
ejpam-2332	454	10	〉	〉	NOUN
ejpam-2332	454	11	in	in	ADP
ejpam-2332	454	12	the	the	DET
ejpam-2332	454	13	matrix	matrix	NOUN
ejpam-2332	454	14	ã	ã	PROPN
ejpam-2332	454	15	is	be	AUX
ejpam-2332	454	16	an	an	DET
ejpam-2332	454	17	tifn	tifn	NOUN
ejpam-2332	454	18	,	,	PUNCT
ejpam-2332	454	19	which	which	PRON
ejpam-2332	454	20	indicates	indicate	VERB
ejpam-2332	454	21	that	that	SCONJ
ejpam-2332	454	22	expected	expect	VERB
ejpam-2332	454	23	number	number	NOUN
ejpam-2332	454	24	of	of	ADP
ejpam-2332	454	25	viewers	viewer	NOUN
ejpam-2332	454	26	in	in	ADP
ejpam-2332	454	27	favour	favour	NOUN
ejpam-2332	454	28	of	of	ADP
ejpam-2332	454	29	tv	tv	NOUN
ejpam-2332	454	30	station	station	NOUN
ejpam-2332	454	31	t1	t1	NOUN
ejpam-2332	454	32	is	be	AUX
ejpam-2332	454	33	“	"	PUNCT
ejpam-2332	454	34	about	about	ADV
ejpam-2332	454	35	8	8	NUM
ejpam-2332	454	36	million	million	NUM
ejpam-2332	454	37	”	"	PUNCT
ejpam-2332	454	38	when	when	SCONJ
ejpam-2332	454	39	both	both	CCONJ
ejpam-2332	454	40	the	the	DET
ejpam-2332	454	41	companies	company	NOUN
ejpam-2332	454	42	t1	t1	VERB
ejpam-2332	454	43	and	and	CCONJ
ejpam-2332	454	44	t2	t2	NOUN
ejpam-2332	454	45	use	use	VERB
ejpam-2332	454	46	the	the	DET
ejpam-2332	454	47	strategy	strategy	NOUN
ejpam-2332	454	48	ε1	ε1	PROPN
ejpam-2332	454	49	(	(	PUNCT
ejpam-2332	454	50	tv	tv	NOUN
ejpam-2332	454	51	serials	serial	NOUN
ejpam-2332	454	52	)	)	PUNCT
ejpam-2332	454	53	simultaneously	simultaneously	ADV
ejpam-2332	454	54	.	.	PUNCT
ejpam-2332	455	1	other	other	ADJ
ejpam-2332	455	2	elements	element	NOUN
ejpam-2332	455	3	(	(	PUNCT
ejpam-2332	455	4	i.e.	i.e.	X
ejpam-2332	455	5	,	,	PUNCT
ejpam-2332	455	6	tifns	tifns	NOUN
ejpam-2332	455	7	)	)	PUNCT
ejpam-2332	455	8	in	in	ADP
ejpam-2332	455	9	the	the	DET
ejpam-2332	455	10	matrices	matrix	NOUN
ejpam-2332	455	11	ã	ã	PROPN
ejpam-2332	455	12	and	and	CCONJ
ejpam-2332	455	13	b̃	b̃	PROPN
ejpam-2332	455	14	are	be	AUX
ejpam-2332	455	15	explained	explain	VERB
ejpam-2332	455	16	similarly	similarly	ADV
ejpam-2332	455	17	.	.	PUNCT
ejpam-2332	456	1	we	we	PRON
ejpam-2332	456	2	assume	assume	VERB
ejpam-2332	456	3	that	that	SCONJ
ejpam-2332	456	4	the	the	DET
ejpam-2332	456	5	player	player	NOUN
ejpam-2332	456	6	i	i	PRON
ejpam-2332	456	7	and	and	CCONJ
ejpam-2332	456	8	ii	ii	PROPN
ejpam-2332	456	9	have	have	VERB
ejpam-2332	456	10	the	the	DET
ejpam-2332	456	11	tolerances	tolerance	NOUN
ejpam-2332	456	12	p̃1	p̃1	PROPN
ejpam-2332	456	13	=	=	NOUN
ejpam-2332	456	14	p̃2	p̃2	NOUN
ejpam-2332	456	15	=	=	SYM
ejpam-2332	456	16	p̃0	p̃0	PROPN
ejpam-2332	456	17	=	=	SYM
ejpam-2332	456	18	〈	〈	PROPN
ejpam-2332	456	19	(	(	PUNCT
ejpam-2332	456	20	0.08,0.10,0.11	0.08,0.10,0.11	NOUN
ejpam-2332	456	21	)	)	PUNCT
ejpam-2332	456	22	;	;	PUNCT
ejpam-2332	456	23	(	(	PUNCT
ejpam-2332	456	24	0.06,0.10,0.12	0.06,0.10,0.12	X
ejpam-2332	456	25	)	)	PUNCT
ejpam-2332	456	26	〉	〉	NOUN
ejpam-2332	456	27	,	,	PUNCT
ejpam-2332	456	28	q̃1	q̃1	PROPN
ejpam-2332	456	29	=	=	NOUN
ejpam-2332	456	30	q̃2	q̃2	NOUN
ejpam-2332	456	31	=	=	SYM
ejpam-2332	456	32	q̃0	q̃0	NOUN
ejpam-2332	456	33	=	=	PUNCT
ejpam-2332	456	34	〈	〈	PROPN
ejpam-2332	456	35	(	(	PUNCT
ejpam-2332	456	36	0.13,0.15,0.17	0.13,0.15,0.17	NOUN
ejpam-2332	456	37	)	)	PUNCT
ejpam-2332	456	38	;	;	PUNCT
ejpam-2332	456	39	(	(	PUNCT
ejpam-2332	456	40	0.12,0.15,0.18	0.12,0.15,0.18	NOUN
ejpam-2332	456	41	)	)	PUNCT
ejpam-2332	456	42	〉	〉	NOUN
ejpam-2332	456	43	,	,	PUNCT
ejpam-2332	456	44	r̃1	r̃1	NOUN
ejpam-2332	456	45	=	=	SYM
ejpam-2332	456	46	r̃2	r̃2	PROPN
ejpam-2332	456	47	=	=	SYM
ejpam-2332	456	48	r̃0	r̃0	PROPN
ejpam-2332	456	49	=	=	PUNCT
ejpam-2332	456	50	〈	〈	PROPN
ejpam-2332	456	51	(	(	PUNCT
ejpam-2332	456	52	0.10,0.12,0.13	0.10,0.12,0.13	NUM
ejpam-2332	456	53	)	)	PUNCT
ejpam-2332	456	54	;	;	PUNCT
ejpam-2332	456	55	(	(	PUNCT
ejpam-2332	456	56	0.9,0.12,0.14	0.9,0.12,0.14	NOUN
ejpam-2332	456	57	)	)	PUNCT
ejpam-2332	456	58	〉	〉	NOUN
ejpam-2332	456	59	,	,	PUNCT
ejpam-2332	456	60	s̃1	s̃1	PROPN
ejpam-2332	456	61	=	=	SYM
ejpam-2332	456	62	s̃2	s̃2	X
ejpam-2332	456	63	=	=	SYM
ejpam-2332	456	64	s̃0	s̃0	PROPN
ejpam-2332	456	65	=	=	SYM
ejpam-2332	456	66	〈	〈	PROPN
ejpam-2332	456	67	(	(	PUNCT
ejpam-2332	456	68	0.12,0.15,0.16	0.12,0.15,0.16	NOUN
ejpam-2332	456	69	)	)	PUNCT
ejpam-2332	456	70	;	;	PUNCT
ejpam-2332	456	71	(	(	PUNCT
ejpam-2332	456	72	0.10,0.15,0.17	0.10,0.15,0.17	NOUN
ejpam-2332	456	73	)	)	PUNCT
ejpam-2332	456	74	〉	〉	NOUN
ejpam-2332	456	75	,	,	PUNCT
ejpam-2332	456	76	respectively	respectively	ADV
ejpam-2332	456	77	.	.	PUNCT
ejpam-2332	457	1	the	the	DET
ejpam-2332	457	2	crisp	crisp	ADJ
ejpam-2332	457	3	equivalent	equivalent	NOUN
ejpam-2332	457	4	of	of	ADP
ejpam-2332	457	5	the	the	DET
ejpam-2332	457	6	tifns	tifns	NOUN
ejpam-2332	457	7	ãi	ãi	PROPN
ejpam-2332	457	8	j	j	PROPN
ejpam-2332	457	9	=	=	SYM
ejpam-2332	457	10	〈	〈	PROPN
ejpam-2332	457	11	(	(	PUNCT
ejpam-2332	457	12	ai	ai	VERB
ejpam-2332	457	13	jµ	jµ	ADJ
ejpam-2332	457	14	,	,	PUNCT
ejpam-2332	457	15	ai	ai	VERB
ejpam-2332	457	16	j	j	PROPN
ejpam-2332	457	17	,	,	PUNCT
ejpam-2332	457	18	āi	āi	PROPN
ejpam-2332	457	19	jµ	jµ	PROPN
ejpam-2332	457	20	)	)	PUNCT
ejpam-2332	457	21	;	;	PUNCT
ejpam-2332	457	22	(	(	PUNCT
ejpam-2332	457	23	ai	ai	VERB
ejpam-2332	457	24	jν	jν	NOUN
ejpam-2332	457	25	,	,	PUNCT
ejpam-2332	457	26	ai	ai	VERB
ejpam-2332	457	27	j	j	PROPN
ejpam-2332	457	28	,	,	PUNCT
ejpam-2332	457	29	āi	āi	PROPN
ejpam-2332	457	30	jν	jν	NOUN
ejpam-2332	457	31	)	)	PUNCT
ejpam-2332	457	32	〉	〉	NOUN
ejpam-2332	457	33	(	(	PUNCT
ejpam-2332	457	34	i	i	NOUN
ejpam-2332	457	35	=	=	SYM
ejpam-2332	457	36	1,2	1,2	NUM
ejpam-2332	457	37	;	;	PUNCT
ejpam-2332	457	38	j	j	PROPN
ejpam-2332	457	39	=	=	SYM
ejpam-2332	457	40	1,2	1,2	NUM
ejpam-2332	457	41	)	)	PUNCT
ejpam-2332	457	42	can	can	AUX
ejpam-2332	457	43	be	be	AUX
ejpam-2332	457	44	obtained	obtain	VERB
ejpam-2332	457	45	by	by	ADP
ejpam-2332	457	46	using	use	VERB
ejpam-2332	457	47	the	the	DET
ejpam-2332	457	48	ranking	rank	VERB
ejpam-2332	457	49	function	function	NOUN
ejpam-2332	457	50	defined	define	VERB
ejpam-2332	457	51	in	in	ADP
ejpam-2332	457	52	section	section	NOUN
ejpam-2332	457	53	2	2	NUM
ejpam-2332	457	54	as	as	SCONJ
ejpam-2332	457	55	follows	follow	VERB
ejpam-2332	457	56	r(ãi	r(ãi	PROPN
ejpam-2332	457	57	j	j	NOUN
ejpam-2332	457	58	)	)	PUNCT
ejpam-2332	458	1	=	=	NOUN
ejpam-2332	458	2	v	v	NOUN
ejpam-2332	458	3	(	(	PUNCT
ejpam-2332	458	4	ãi	ãi	PROPN
ejpam-2332	458	5	j	j	PROPN
ejpam-2332	458	6	,	,	PUNCT
ejpam-2332	458	7	1	1	NUM
ejpam-2332	458	8	2	2	NUM
ejpam-2332	458	9	)	)	PUNCT
ejpam-2332	458	10	−	−	PROPN
ejpam-2332	459	1	a(ãi	a(ãi	PROPN
ejpam-2332	459	2	j	j	PROPN
ejpam-2332	459	3	,	,	PUNCT
ejpam-2332	459	4	1	1	NUM
ejpam-2332	459	5	2	2	NUM
ejpam-2332	459	6	)	)	PUNCT
ejpam-2332	459	7	=	=	PUNCT
ejpam-2332	459	8	gν(ãi	gν(ãi	PROPN
ejpam-2332	459	9	j	j	PROPN
ejpam-2332	459	10	)	)	PUNCT
ejpam-2332	460	1	+	+	CCONJ
ejpam-2332	460	2	gµ(ãi	gµ(ãi	PROPN
ejpam-2332	460	3	j	j	NOUN
ejpam-2332	460	4	)	)	PUNCT
ejpam-2332	460	5	2	2	NUM
ejpam-2332	460	6	−	−	PROPN
ejpam-2332	460	7	hµ(ãi	hµ(ãi	ADV
ejpam-2332	460	8	j	j	PROPN
ejpam-2332	460	9	)	)	PUNCT
ejpam-2332	461	1	+	+	CCONJ
ejpam-2332	461	2	hν(ãi	hν(ãi	X
ejpam-2332	461	3	j	j	NOUN
ejpam-2332	461	4	)	)	PUNCT
ejpam-2332	461	5	2	2	NUM
ejpam-2332	462	1	=	=	SYM
ejpam-2332	462	2	(	(	PUNCT
ejpam-2332	462	3	ai	ai	VERB
ejpam-2332	462	4	jν	jν	NOUN
ejpam-2332	462	5	+	+	CCONJ
ejpam-2332	462	6	4ai	4ai	ADJ
ejpam-2332	462	7	j	j	PROPN
ejpam-2332	463	1	+	+	CCONJ
ejpam-2332	463	2	āi	āi	NUM
ejpam-2332	463	3	jν	jν	NOUN
ejpam-2332	463	4	)	)	PUNCT
ejpam-2332	464	1	+	+	CCONJ
ejpam-2332	464	2	(	(	PUNCT
ejpam-2332	464	3	ai	ai	VERB
ejpam-2332	464	4	jµ	jµ	PRON
ejpam-2332	465	1	+	+	NUM
ejpam-2332	465	2	4ai	4ai	ADJ
ejpam-2332	465	3	j	j	PROPN
ejpam-2332	465	4	+	+	CCONJ
ejpam-2332	465	5	āi	āi	PROPN
ejpam-2332	465	6	jµ	jµ	PROPN
ejpam-2332	465	7	)	)	PUNCT
ejpam-2332	465	8	12	12	NUM
ejpam-2332	465	9	−	−	PROPN
ejpam-2332	465	10	(	(	PUNCT
ejpam-2332	465	11	āi	āi	VERB
ejpam-2332	465	12	jµ	jµ	PRON
ejpam-2332	465	13	−	−	PROPN
ejpam-2332	465	14	ai	ai	INTJ
ejpam-2332	465	15	jµ	jµ	PROPN
ejpam-2332	465	16	)	)	PUNCT
ejpam-2332	466	1	+	+	CCONJ
ejpam-2332	466	2	(	(	PUNCT
ejpam-2332	466	3	āi	āi	NUM
ejpam-2332	466	4	jν	jν	NOUN
ejpam-2332	466	5	−	−	NOUN
ejpam-2332	466	6	ai	ai	VERB
ejpam-2332	466	7	jν	jν	NOUN
ejpam-2332	466	8	)	)	PUNCT
ejpam-2332	466	9	6	6	NUM
ejpam-2332	467	1	=	=	SYM
ejpam-2332	467	2	8(ai	8(ai	NUM
ejpam-2332	467	3	jµ	jµ	INTJ
ejpam-2332	468	1	+	+	CCONJ
ejpam-2332	468	2	ai	ai	VERB
ejpam-2332	468	3	j	j	PROPN
ejpam-2332	468	4	+	+	ADP
ejpam-2332	468	5	ai	ai	VERB
ejpam-2332	468	6	jν)−	jν)−	ADJ
ejpam-2332	468	7	(	(	PUNCT
ejpam-2332	468	8	āi	āi	VERB
ejpam-2332	468	9	jµ	jµ	PROPN
ejpam-2332	469	1	+	+	CCONJ
ejpam-2332	469	2	āi	āi	NUM
ejpam-2332	469	3	jν	jν	NOUN
ejpam-2332	469	4	)	)	PUNCT
ejpam-2332	469	5	12	12	NUM
ejpam-2332	469	6	therefore	therefore	ADV
ejpam-2332	469	7	,	,	PUNCT
ejpam-2332	469	8	r(ã11	r(ã11	PROPN
ejpam-2332	469	9	)	)	PUNCT
ejpam-2332	469	10	=	=	PUNCT
ejpam-2332	470	1	12.79	12.79	NUM
ejpam-2332	470	2	,	,	PUNCT
ejpam-2332	470	3	r(ã12	r(ã12	NOUN
ejpam-2332	470	4	)	)	PUNCT
ejpam-2332	470	5	=	=	SYM
ejpam-2332	470	6	19.42	19.42	NUM
ejpam-2332	470	7	,	,	PUNCT
ejpam-2332	470	8	r(ã21	r(ã21	PROPN
ejpam-2332	470	9	)	)	PUNCT
ejpam-2332	470	10	=	=	SYM
ejpam-2332	470	11	17.21	17.21	NUM
ejpam-2332	470	12	,	,	PUNCT
ejpam-2332	470	13	r(ã22	r(ã22	NOUN
ejpam-2332	470	14	)	)	PUNCT
ejpam-2332	470	15	=	=	SYM
ejpam-2332	470	16	8.46	8.46	NUM
ejpam-2332	470	17	.	.	PUNCT
ejpam-2332	471	1	similarly	similarly	ADV
ejpam-2332	471	2	,	,	PUNCT
ejpam-2332	471	3	r	r	NOUN
ejpam-2332	471	4	(	(	PUNCT
ejpam-2332	471	5	b̃11	b̃11	NOUN
ejpam-2332	471	6	)	)	PUNCT
ejpam-2332	471	7	=	=	SYM
ejpam-2332	471	8	12.79	12.79	NUM
ejpam-2332	471	9	,	,	PUNCT
ejpam-2332	471	10	r	r	NOUN
ejpam-2332	471	11	(	(	PUNCT
ejpam-2332	471	12	b̃12	b̃12	NUM
ejpam-2332	471	13	)	)	PUNCT
ejpam-2332	471	14	=	=	SYM
ejpam-2332	471	15	8.46	8.46	NUM
ejpam-2332	471	16	,	,	PUNCT
ejpam-2332	471	17	r	r	NOUN
ejpam-2332	471	18	(	(	PUNCT
ejpam-2332	471	19	b̃21	b̃21	NOUN
ejpam-2332	471	20	)	)	PUNCT
ejpam-2332	471	21	=	=	SYM
ejpam-2332	471	22	8.46	8.46	NUM
ejpam-2332	471	23	,	,	PUNCT
ejpam-2332	471	24	r	r	X
ejpam-2332	471	25	(	(	PUNCT
ejpam-2332	471	26	b̃22	b̃22	ADJ
ejpam-2332	471	27	)	)	PUNCT
ejpam-2332	471	28	=	=	SYM
ejpam-2332	471	29	17.21	17.21	NUM
ejpam-2332	471	30	.	.	PUNCT
ejpam-2332	472	1	also	also	ADV
ejpam-2332	472	2	,	,	PUNCT
ejpam-2332	472	3	r(p̃0	r(p̃0	NOUN
ejpam-2332	472	4	)	)	PUNCT
ejpam-2332	472	5	=	=	SYM
ejpam-2332	473	1	0.14	0.14	NUM
ejpam-2332	473	2	,	,	PUNCT
ejpam-2332	473	3	r(q̃0	r(q̃0	NOUN
ejpam-2332	473	4	)	)	PUNCT
ejpam-2332	474	1	=	=	SYM
ejpam-2332	474	2	0.24	0.24	NUM
ejpam-2332	474	3	,	,	PUNCT
ejpam-2332	474	4	r(r̃0	r(r̃0	NOUN
ejpam-2332	474	5	)	)	PUNCT
ejpam-2332	474	6	=	=	SYM
ejpam-2332	474	7	0.18	0.18	NUM
ejpam-2332	474	8	,	,	PUNCT
ejpam-2332	474	9	r(s̃0	r(s̃0	NOUN
ejpam-2332	474	10	)	)	PUNCT
ejpam-2332	474	11	=	=	SYM
ejpam-2332	475	1	0.22	0.22	NUM
ejpam-2332	475	2	.	.	PUNCT
ejpam-2332	475	3	m.	m.	NOUN
ejpam-2332	475	4	seikh	seikh	PROPN
ejpam-2332	475	5	,	,	PUNCT
ejpam-2332	475	6	p.	p.	PROPN
ejpam-2332	475	7	nayak	nayak	PROPN
ejpam-2332	475	8	,	,	PUNCT
ejpam-2332	475	9	m.	m.	NOUN
ejpam-2332	475	10	pal	pal	PROPN
ejpam-2332	475	11	/	/	SYM
ejpam-2332	475	12	eur	eur	PROPN
ejpam-2332	475	13	.	.	PUNCT
ejpam-2332	476	1	j.	j.	PROPN
ejpam-2332	476	2	pure	pure	PROPN
ejpam-2332	476	3	appl	appl	PROPN
ejpam-2332	476	4	.	.	PROPN
ejpam-2332	476	5	math	math	PROPN
ejpam-2332	476	6	,	,	PUNCT
ejpam-2332	476	7	8	8	NUM
ejpam-2332	476	8	(	(	PUNCT
ejpam-2332	476	9	2015	2015	NUM
ejpam-2332	476	10	)	)	PUNCT
ejpam-2332	476	11	,	,	PUNCT
ejpam-2332	476	12	153	153	NUM
ejpam-2332	476	13	-	-	SYM
ejpam-2332	476	14	171	171	NUM
ejpam-2332	476	15	168	168	NUM
ejpam-2332	476	16	thus	thus	ADV
ejpam-2332	476	17	according	accord	VERB
ejpam-2332	476	18	to	to	ADP
ejpam-2332	476	19	equation	equation	NOUN
ejpam-2332	476	20	(	(	PUNCT
ejpam-2332	476	21	16	16	NUM
ejpam-2332	476	22	)	)	PUNCT
ejpam-2332	476	23	the	the	DET
ejpam-2332	476	24	non	non	ADJ
ejpam-2332	476	25	-	-	ADJ
ejpam-2332	476	26	linear	linear	ADJ
ejpam-2332	476	27	programming	programming	NOUN
ejpam-2332	476	28	models	model	NOUN
ejpam-2332	476	29	can	can	AUX
ejpam-2332	476	30	be	be	AUX
ejpam-2332	476	31	written	write	VERB
ejpam-2332	476	32	as	as	ADP
ejpam-2332	476	33	:	:	PUNCT
ejpam-2332	476	34	max	max	PROPN
ejpam-2332	476	35	{	{	PUNCT
ejpam-2332	476	36	u+	u+	NOUN
ejpam-2332	476	37	v	v	PART
ejpam-2332	476	38	}	}	PUNCT
ejpam-2332	476	39	subject	subject	ADJ
ejpam-2332	476	40	to	to	ADP
ejpam-2332	476	41	12.79y1	12.79y1	NUM
ejpam-2332	476	42	+	+	CCONJ
ejpam-2332	476	43	19.42y2	19.42y2	NUM
ejpam-2332	476	44	≤	≤	NUM
ejpam-2332	476	45	u+	u+	NUM
ejpam-2332	476	46	0.14(1−	0.14(1−	NUM
ejpam-2332	476	47	ξ	ξ	NOUN
ejpam-2332	476	48	)	)	PUNCT
ejpam-2332	476	49	17.21y1	17.21y1	NUM
ejpam-2332	477	1	+	+	CCONJ
ejpam-2332	477	2	8.46y2	8.46y2	PROPN
ejpam-2332	477	3	≤	≤	NOUN
ejpam-2332	477	4	u+	u+	NUM
ejpam-2332	477	5	0.14(1−	0.14(1−	NUM
ejpam-2332	477	6	ξ	ξ	NOUN
ejpam-2332	477	7	)	)	PUNCT
ejpam-2332	477	8	12.79y1	12.79y1	NUM
ejpam-2332	478	1	+	+	CCONJ
ejpam-2332	478	2	19.42y2	19.42y2	NUM
ejpam-2332	478	3	≤	≤	NUM
ejpam-2332	478	4	u+	u+	NUM
ejpam-2332	478	5	0.14−	0.14−	NUM
ejpam-2332	478	6	0.24(1−η	0.24(1−η	PROPN
ejpam-2332	478	7	)	)	PUNCT
ejpam-2332	478	8	17.21y1	17.21y1	NUM
ejpam-2332	479	1	+	+	CCONJ
ejpam-2332	479	2	8.46y2	8.46y2	PROPN
ejpam-2332	479	3	≤	≤	NOUN
ejpam-2332	479	4	u+	u+	NUM
ejpam-2332	479	5	0.14−	0.14−	NOUN
ejpam-2332	479	6	0.24(1−η	0.24(1−η	PROPN
ejpam-2332	479	7	)	)	PUNCT
ejpam-2332	479	8	12.79x1	12.79x1	NUM
ejpam-2332	479	9	+	+	SYM
ejpam-2332	479	10	8.46x2	8.46x2	NUM
ejpam-2332	479	11	≤	≤	NUM
ejpam-2332	479	12	v	v	ADP
ejpam-2332	479	13	+	+	CCONJ
ejpam-2332	479	14	0.18(1−	0.18(1−	NUM
ejpam-2332	479	15	γ	γ	X
ejpam-2332	479	16	)	)	PUNCT
ejpam-2332	479	17	8.46x1	8.46x1	NUM
ejpam-2332	479	18	+	+	CCONJ
ejpam-2332	479	19	17.21x2	17.21x2	NUM
ejpam-2332	479	20	≤	≤	NUM
ejpam-2332	479	21	v	v	ADP
ejpam-2332	479	22	+	+	CCONJ
ejpam-2332	479	23	0.18(1−	0.18(1−	NUM
ejpam-2332	479	24	γ	γ	X
ejpam-2332	479	25	)	)	PUNCT
ejpam-2332	479	26	12.79x1	12.79x1	NUM
ejpam-2332	479	27	+	+	SYM
ejpam-2332	479	28	8.46x2	8.46x2	NUM
ejpam-2332	479	29	≤	≤	NUM
ejpam-2332	479	30	v	v	ADP
ejpam-2332	479	31	+	+	CCONJ
ejpam-2332	479	32	0.18−	0.18−	NOUN
ejpam-2332	479	33	0.22(1−δ	0.22(1−δ	NUM
ejpam-2332	479	34	)	)	PUNCT
ejpam-2332	479	35	(	(	PUNCT
ejpam-2332	479	36	17	17	NUM
ejpam-2332	479	37	)	)	PUNCT
ejpam-2332	479	38	8.46x1	8.46x1	NUM
ejpam-2332	480	1	+	+	CCONJ
ejpam-2332	480	2	17.21x2	17.21x2	NUM
ejpam-2332	480	3	≤	≤	NUM
ejpam-2332	480	4	v	v	ADP
ejpam-2332	480	5	+	+	CCONJ
ejpam-2332	480	6	0.18−	0.18−	NOUN
ejpam-2332	480	7	0.22(1−δ	0.22(1−δ	NUM
ejpam-2332	480	8	)	)	PUNCT
ejpam-2332	480	9	12.79x1	12.79x1	NUM
ejpam-2332	480	10	y1	y1	NOUN
ejpam-2332	480	11	+	+	CCONJ
ejpam-2332	480	12	19.42x1	19.42x1	NUM
ejpam-2332	480	13	y2	y2	NOUN
ejpam-2332	480	14	+	+	CCONJ
ejpam-2332	480	15	17.21x2	17.21x2	NUM
ejpam-2332	480	16	y1	y1	NOUN
ejpam-2332	480	17	+	+	CCONJ
ejpam-2332	480	18	8.46x2	8.46x2	NUM
ejpam-2332	480	19	y2	y2	NOUN
ejpam-2332	480	20	≥	≥	NOUN
ejpam-2332	480	21	u−	u−	PROPN
ejpam-2332	480	22	0.14(1−	0.14(1−	NUM
ejpam-2332	480	23	ξ	ξ	NOUN
ejpam-2332	480	24	)	)	PUNCT
ejpam-2332	480	25	12.79x1	12.79x1	NUM
ejpam-2332	480	26	y1	y1	NOUN
ejpam-2332	480	27	+	+	CCONJ
ejpam-2332	480	28	19.42x1	19.42x1	NUM
ejpam-2332	480	29	y2	y2	NOUN
ejpam-2332	480	30	+	+	CCONJ
ejpam-2332	480	31	17.21x2	17.21x2	NUM
ejpam-2332	480	32	y1	y1	NOUN
ejpam-2332	480	33	+	+	CCONJ
ejpam-2332	480	34	8.46x2	8.46x2	NUM
ejpam-2332	480	35	y2	y2	NOUN
ejpam-2332	480	36	≥	≥	NOUN
ejpam-2332	480	37	u−	u−	PROPN
ejpam-2332	480	38	0.14	0.14	NUM
ejpam-2332	480	39	+	+	NOUN
ejpam-2332	480	40	0.24(1−η	0.24(1−η	X
ejpam-2332	480	41	)	)	PUNCT
ejpam-2332	480	42	12.79x1	12.79x1	NUM
ejpam-2332	480	43	y1	y1	NOUN
ejpam-2332	480	44	+	+	CCONJ
ejpam-2332	480	45	8.46x1	8.46x1	NUM
ejpam-2332	480	46	y2	y2	NOUN
ejpam-2332	480	47	+	+	CCONJ
ejpam-2332	480	48	8.46x2	8.46x2	NUM
ejpam-2332	480	49	y1	y1	NOUN
ejpam-2332	480	50	+	+	CCONJ
ejpam-2332	480	51	17.21x2	17.21x2	NUM
ejpam-2332	480	52	y2	y2	NOUN
ejpam-2332	480	53	≥	≥	NOUN
ejpam-2332	480	54	v	v	ADP
ejpam-2332	480	55	−	−	PROPN
ejpam-2332	480	56	0.18(1−	0.18(1−	PUNCT
ejpam-2332	480	57	γ	γ	X
ejpam-2332	480	58	)	)	PUNCT
ejpam-2332	480	59	12.79x1	12.79x1	NUM
ejpam-2332	480	60	y1	y1	NOUN
ejpam-2332	480	61	+	+	CCONJ
ejpam-2332	480	62	8.46x1	8.46x1	NUM
ejpam-2332	480	63	y2	y2	NOUN
ejpam-2332	480	64	+	+	CCONJ
ejpam-2332	480	65	8.46x2	8.46x2	NUM
ejpam-2332	480	66	y1	y1	NOUN
ejpam-2332	480	67	+	+	CCONJ
ejpam-2332	480	68	17.21x2	17.21x2	NUM
ejpam-2332	480	69	y2	y2	NOUN
ejpam-2332	480	70	≥	≥	NOUN
ejpam-2332	480	71	v	v	ADP
ejpam-2332	480	72	−	−	PROPN
ejpam-2332	480	73	0.18	0.18	NUM
ejpam-2332	480	74	+	+	CCONJ
ejpam-2332	480	75	0.22(1−	0.22(1−	NUM
ejpam-2332	480	76	δ	δ	PROPN
ejpam-2332	480	77	)	)	PUNCT
ejpam-2332	480	78	x1	x1	PROPN
ejpam-2332	481	1	+	+	NUM
ejpam-2332	481	2	x2	x2	NOUN
ejpam-2332	481	3	=	=	SYM
ejpam-2332	481	4	1	1	NUM
ejpam-2332	481	5	y1	y1	NOUN
ejpam-2332	481	6	+	+	CCONJ
ejpam-2332	481	7	y2	y2	NOUN
ejpam-2332	481	8	=	=	SYM
ejpam-2332	482	1	1	1	NUM
ejpam-2332	482	2	0≤	0≤	NOUN
ejpam-2332	482	3	ξ≤	ξ≤	PROPN
ejpam-2332	482	4	1,0≤	1,0≤	NUM
ejpam-2332	482	5	η	η	PROPN
ejpam-2332	482	6	≤	≤	NUM
ejpam-2332	482	7	1	1	NUM
ejpam-2332	482	8	0≤	0≤	NUM
ejpam-2332	482	9	γ≤	γ≤	NUM
ejpam-2332	482	10	1,0≤	1,0≤	NUM
ejpam-2332	482	11	δ	δ	PROPN
ejpam-2332	482	12	≤	≤	NUM
ejpam-2332	482	13	1	1	NUM
ejpam-2332	482	14	x1	x1	PROPN
ejpam-2332	482	15	,	,	PUNCT
ejpam-2332	482	16	x2	x2	PROPN
ejpam-2332	482	17	,	,	PUNCT
ejpam-2332	482	18	y1	y1	NOUN
ejpam-2332	482	19	,	,	PUNCT
ejpam-2332	482	20	y2	y2	PROPN
ejpam-2332	482	21	≥	≥	NOUN
ejpam-2332	482	22	0	0	NUM
ejpam-2332	482	23	.	.	PUNCT
ejpam-2332	483	1	solving	solve	VERB
ejpam-2332	483	2	(	(	PUNCT
ejpam-2332	483	3	17	17	NUM
ejpam-2332	483	4	)	)	PUNCT
ejpam-2332	483	5	with	with	ADP
ejpam-2332	483	6	the	the	DET
ejpam-2332	483	7	help	help	NOUN
ejpam-2332	483	8	of	of	ADP
ejpam-2332	483	9	lingo	lingo	NOUN
ejpam-2332	483	10	software	software	NOUN
ejpam-2332	483	11	we	we	PRON
ejpam-2332	483	12	obtained	obtain	VERB
ejpam-2332	483	13	the	the	DET
ejpam-2332	483	14	optimal	optimal	ADJ
ejpam-2332	483	15	solution	solution	NOUN
ejpam-2332	483	16	as	as	ADP
ejpam-2332	483	17	table	table	NOUN
ejpam-2332	483	18	1	1	NUM
ejpam-2332	483	19	:	:	PUNCT
ejpam-2332	483	20	solution	solution	NOUN
ejpam-2332	483	21	of	of	ADP
ejpam-2332	483	22	the	the	DET
ejpam-2332	483	23	non	non	ADJ
ejpam-2332	483	24	-	-	ADJ
ejpam-2332	483	25	linear	linear	ADJ
ejpam-2332	483	26	programming	programming	NOUN
ejpam-2332	483	27	problem	problem	NOUN
ejpam-2332	483	28	.	.	PUNCT
ejpam-2332	484	1	x∗1	x∗1	PROPN
ejpam-2332	484	2	x∗2	x∗2	PROPN
ejpam-2332	485	1	u∗	u∗	VERB
ejpam-2332	485	2	y∗1	y∗1	PROPN
ejpam-2332	485	3	y∗2	y∗2	PROPN
ejpam-2332	485	4	v∗	v∗	VERB
ejpam-2332	485	5	0.746	0.746	NUM
ejpam-2332	485	6	0.254	0.254	NUM
ejpam-2332	485	7	15.03	15.03	NUM
ejpam-2332	485	8	0.641	0.641	NUM
ejpam-2332	485	9	0.359	0.359	NUM
ejpam-2332	485	10	11.51	11.51	NUM
ejpam-2332	485	11	it	it	PRON
ejpam-2332	485	12	can	can	AUX
ejpam-2332	485	13	be	be	AUX
ejpam-2332	485	14	easily	easily	ADV
ejpam-2332	485	15	seen	see	VERB
ejpam-2332	485	16	that	that	SCONJ
ejpam-2332	485	17	the	the	DET
ejpam-2332	485	18	nash	nash	PROPN
ejpam-2332	485	19	equilibrium	equilibrium	NOUN
ejpam-2332	485	20	values	value	NOUN
ejpam-2332	485	21	of	of	ADP
ejpam-2332	485	22	the	the	DET
ejpam-2332	485	23	bi	bi	ADJ
ejpam-2332	485	24	-	-	NOUN
ejpam-2332	485	25	matrix	matrix	NOUN
ejpam-2332	485	26	gameái	gameái	NOUN
ejpam-2332	485	27	fbg	fbg	PROPN
ejpam-2332	485	28	for	for	ADP
ejpam-2332	485	29	player	player	NOUN
ejpam-2332	485	30	i	i	PRON
ejpam-2332	485	31	and	and	CCONJ
ejpam-2332	485	32	ii	ii	PROPN
ejpam-2332	485	33	are	be	AUX
ejpam-2332	485	34	,	,	PUNCT
ejpam-2332	485	35	respectively	respectively	ADV
ejpam-2332	485	36	ũ∗	ũ∗	ADP
ejpam-2332	485	37	=	=	NUM
ejpam-2332	485	38	ẽ(ã	ẽ(ã	X
ejpam-2332	485	39	)	)	PUNCT
ejpam-2332	485	40	=	=	SYM
ejpam-2332	486	1	〈	〈	PROPN
ejpam-2332	486	2	(	(	PUNCT
ejpam-2332	486	3	8.12,9.22,10.13	8.12,9.22,10.13	NUM
ejpam-2332	486	4	)	)	PUNCT
ejpam-2332	486	5	;	;	PUNCT
ejpam-2332	486	6	(	(	PUNCT
ejpam-2332	486	7	7.62,9.22,10.77	7.62,9.22,10.77	NOUN
ejpam-2332	486	8	)	)	PUNCT
ejpam-2332	486	9	〉	〉	NOUN
ejpam-2332	486	10	ṽ∗	ṽ∗	ADP
ejpam-2332	486	11	=	=	NOUN
ejpam-2332	486	12	ẽ(b̃	ẽ(b̃	X
ejpam-2332	486	13	)	)	PUNCT
ejpam-2332	486	14	=	=	SYM
ejpam-2332	487	1	〈	〈	PROPN
ejpam-2332	487	2	(	(	PUNCT
ejpam-2332	487	3	6.15,7.32,8.27	6.15,7.32,8.27	NOUN
ejpam-2332	487	4	)	)	PUNCT
ejpam-2332	487	5	;	;	PUNCT
ejpam-2332	487	6	(	(	PUNCT
ejpam-2332	487	7	5.65,7.32,8.77	5.65,7.32,8.77	X
ejpam-2332	487	8	)	)	PUNCT
ejpam-2332	487	9	〉	〉	NOUN
ejpam-2332	487	10	which	which	PRON
ejpam-2332	487	11	are	be	AUX
ejpam-2332	487	12	tifns	tifns	NOUN
ejpam-2332	487	13	and	and	CCONJ
ejpam-2332	487	14	indicates	indicate	VERB
ejpam-2332	487	15	that	that	SCONJ
ejpam-2332	487	16	the	the	DET
ejpam-2332	487	17	expected	expect	VERB
ejpam-2332	487	18	number	number	NOUN
ejpam-2332	487	19	of	of	ADP
ejpam-2332	487	20	viewers	viewer	NOUN
ejpam-2332	487	21	for	for	ADP
ejpam-2332	487	22	tv	tv	NOUN
ejpam-2332	487	23	station	station	NOUN
ejpam-2332	487	24	t1	t1	NOUN
ejpam-2332	487	25	and	and	CCONJ
ejpam-2332	487	26	t2	t2	NOUN
ejpam-2332	487	27	are	be	AUX
ejpam-2332	487	28	respectively	respectively	ADV
ejpam-2332	487	29	“	"	PUNCT
ejpam-2332	487	30	about	about	ADV
ejpam-2332	487	31	9.22	9.22	NUM
ejpam-2332	487	32	”	"	PUNCT
ejpam-2332	487	33	millions	million	NOUN
ejpam-2332	487	34	and	and	CCONJ
ejpam-2332	487	35	“	"	PUNCT
ejpam-2332	487	36	about	about	ADV
ejpam-2332	487	37	7.32	7.32	NUM
ejpam-2332	487	38	”	"	PUNCT
ejpam-2332	487	39	millions	million	NOUN
ejpam-2332	487	40	respectively	respectively	ADV
ejpam-2332	487	41	,	,	PUNCT
ejpam-2332	487	42	when	when	SCONJ
ejpam-2332	487	43	tv	tv	NOUN
ejpam-2332	487	44	station	station	NOUN
ejpam-2332	487	45	t1	t1	PROPN
ejpam-2332	487	46	chooses	choose	VERB
ejpam-2332	487	47	mixed	mixed	ADJ
ejpam-2332	487	48	strategies	strategy	NOUN
ejpam-2332	487	49	(	(	PUNCT
ejpam-2332	487	50	0.746,0.254)t	0.746,0.254)t	PROPN
ejpam-2332	487	51	and	and	CCONJ
ejpam-2332	487	52	tv	tv	NOUN
ejpam-2332	487	53	station	station	NOUN
ejpam-2332	487	54	t2	t2	PROPN
ejpam-2332	487	55	chooses	choose	VERB
ejpam-2332	487	56	mixed	mixed	ADJ
ejpam-2332	487	57	strategies	strategy	NOUN
ejpam-2332	487	58	(	(	PUNCT
ejpam-2332	487	59	0.641,0.359)t	0.641,0.359)t	NOUN
ejpam-2332	487	60	.	.	PUNCT
ejpam-2332	488	1	in	in	ADP
ejpam-2332	488	2	other	other	ADJ
ejpam-2332	488	3	words	word	NOUN
ejpam-2332	488	4	,	,	PUNCT
ejpam-2332	488	5	the	the	DET
ejpam-2332	488	6	expected	expect	VERB
ejpam-2332	488	7	number	number	NOUN
ejpam-2332	488	8	of	of	ADP
ejpam-2332	488	9	viewers	viewer	NOUN
ejpam-2332	488	10	for	for	ADP
ejpam-2332	488	11	tv	tv	NOUN
ejpam-2332	488	12	station	station	NOUN
ejpam-2332	488	13	t1	t1	NOUN
ejpam-2332	488	14	is	be	AUX
ejpam-2332	488	15	“	"	PUNCT
ejpam-2332	488	16	about	about	ADV
ejpam-2332	488	17	9.22	9.22	NUM
ejpam-2332	488	18	”	"	PUNCT
ejpam-2332	488	19	millions	million	NOUN
ejpam-2332	488	20	when	when	SCONJ
ejpam-2332	488	21	it	it	PRON
ejpam-2332	488	22	broadcast	broadcast	VERB
ejpam-2332	488	23	“	"	PUNCT
ejpam-2332	488	24	tv	tv	NOUN
ejpam-2332	488	25	serials	serial	NOUN
ejpam-2332	488	26	”	"	PUNCT
ejpam-2332	488	27	with	with	ADP
ejpam-2332	488	28	probability	probability	NOUN
ejpam-2332	488	29	75	75	NUM
ejpam-2332	488	30	%	%	NOUN
ejpam-2332	488	31	and	and	CCONJ
ejpam-2332	488	32	“	"	PUNCT
ejpam-2332	488	33	reality	reality	NOUN
ejpam-2332	488	34	show	show	NOUN
ejpam-2332	488	35	”	"	PUNCT
ejpam-2332	488	36	with	with	ADP
ejpam-2332	488	37	probability	probability	NOUN
ejpam-2332	488	38	25	25	NUM
ejpam-2332	488	39	%	%	NOUN
ejpam-2332	488	40	.	.	PUNCT
ejpam-2332	489	1	similarly	similarly	ADV
ejpam-2332	489	2	,	,	PUNCT
ejpam-2332	489	3	the	the	DET
ejpam-2332	489	4	expected	expect	VERB
ejpam-2332	489	5	number	number	NOUN
ejpam-2332	489	6	of	of	ADP
ejpam-2332	489	7	viewers	viewer	NOUN
ejpam-2332	489	8	for	for	ADP
ejpam-2332	489	9	tv	tv	NOUN
ejpam-2332	489	10	station	station	NOUN
ejpam-2332	489	11	t2	t2	NOUN
ejpam-2332	489	12	is	be	AUX
ejpam-2332	489	13	“	"	PUNCT
ejpam-2332	489	14	about	about	ADV
ejpam-2332	489	15	7.32	7.32	NUM
ejpam-2332	489	16	”	"	PUNCT
ejpam-2332	489	17	millions	million	NOUN
ejpam-2332	489	18	when	when	SCONJ
ejpam-2332	489	19	it	it	PRON
ejpam-2332	489	20	broadcast	broadcast	VERB
ejpam-2332	489	21	“	"	PUNCT
ejpam-2332	489	22	tv	tv	NOUN
ejpam-2332	489	23	serials	serial	NOUN
ejpam-2332	489	24	”	"	PUNCT
ejpam-2332	489	25	with	with	ADP
ejpam-2332	489	26	probability	probability	NOUN
ejpam-2332	489	27	64	64	NUM
ejpam-2332	489	28	%	%	NOUN
ejpam-2332	489	29	and	and	CCONJ
ejpam-2332	489	30	“	"	PUNCT
ejpam-2332	489	31	reality	reality	NOUN
ejpam-2332	489	32	show	show	NOUN
ejpam-2332	489	33	”	"	PUNCT
ejpam-2332	489	34	with	with	ADP
ejpam-2332	489	35	probability	probability	NOUN
ejpam-2332	489	36	36	36	NUM
ejpam-2332	489	37	%	%	NOUN
ejpam-2332	489	38	.	.	PUNCT
ejpam-2332	490	1	references	reference	NOUN
ejpam-2332	490	2	169	169	NUM
ejpam-2332	490	3	6	6	NUM
ejpam-2332	490	4	.	.	PUNCT
ejpam-2332	490	5	conclusion	conclusion	VERB
ejpam-2332	490	6	the	the	DET
ejpam-2332	490	7	solution	solution	NOUN
ejpam-2332	490	8	concept	concept	NOUN
ejpam-2332	490	9	for	for	ADP
ejpam-2332	490	10	the	the	DET
ejpam-2332	490	11	bi	bi	ADJ
ejpam-2332	490	12	-	-	ADJ
ejpam-2332	490	13	matrix	matrix	NOUN
ejpam-2332	490	14	games	game	NOUN
ejpam-2332	490	15	with	with	ADP
ejpam-2332	490	16	pay	pay	NOUN
ejpam-2332	490	17	-	-	PUNCT
ejpam-2332	490	18	offs	off	NOUN
ejpam-2332	490	19	of	of	ADP
ejpam-2332	490	20	tifns	tifns	NOUN
ejpam-2332	490	21	is	be	AUX
ejpam-2332	490	22	discussed	discuss	VERB
ejpam-2332	490	23	here	here	ADV
ejpam-2332	490	24	.	.	PUNCT
ejpam-2332	491	1	it	it	PRON
ejpam-2332	491	2	is	be	AUX
ejpam-2332	491	3	shown	show	VERB
ejpam-2332	491	4	that	that	SCONJ
ejpam-2332	491	5	the	the	DET
ejpam-2332	491	6	equilibrium	equilibrium	NOUN
ejpam-2332	491	7	solution	solution	NOUN
ejpam-2332	491	8	for	for	ADP
ejpam-2332	491	9	each	each	DET
ejpam-2332	491	10	player	player	NOUN
ejpam-2332	491	11	is	be	AUX
ejpam-2332	491	12	obtained	obtain	VERB
ejpam-2332	491	13	by	by	ADP
ejpam-2332	491	14	solving	solve	VERB
ejpam-2332	491	15	a	a	DET
ejpam-2332	491	16	crisp	crisp	ADJ
ejpam-2332	491	17	nonlinear	nonlinear	ADJ
ejpam-2332	491	18	programming	programming	NOUN
ejpam-2332	491	19	problem	problem	NOUN
ejpam-2332	491	20	which	which	PRON
ejpam-2332	491	21	is	be	AUX
ejpam-2332	491	22	derived	derive	VERB
ejpam-2332	491	23	from	from	ADP
ejpam-2332	491	24	a	a	DET
ejpam-2332	491	25	i	i	NOUN
ejpam-2332	491	26	-	-	PUNCT
ejpam-2332	491	27	fuzzy	fuzzy	ADJ
ejpam-2332	491	28	non	non	ADJ
ejpam-2332	491	29	-	-	ADJ
ejpam-2332	491	30	linear	linear	ADJ
ejpam-2332	491	31	programming	programming	NOUN
ejpam-2332	491	32	problem	problem	NOUN
ejpam-2332	491	33	by	by	ADP
ejpam-2332	491	34	employing	employ	VERB
ejpam-2332	491	35	a	a	DET
ejpam-2332	491	36	suitable	suitable	ADJ
ejpam-2332	491	37	ranking	ranking	ADJ
ejpam-2332	491	38	function	function	NOUN
ejpam-2332	491	39	.	.	PUNCT
ejpam-2332	492	1	further	far	ADV
ejpam-2332	492	2	,	,	PUNCT
ejpam-2332	492	3	it	it	PRON
ejpam-2332	492	4	should	should	AUX
ejpam-2332	492	5	be	be	AUX
ejpam-2332	492	6	noted	note	VERB
ejpam-2332	492	7	that	that	SCONJ
ejpam-2332	492	8	the	the	DET
ejpam-2332	492	9	proposed	propose	VERB
ejpam-2332	492	10	ifuzzy	ifuzzy	PROPN
ejpam-2332	492	11	non	non	ADJ
ejpam-2332	492	12	-	-	ADJ
ejpam-2332	492	13	linear	linear	ADJ
ejpam-2332	492	14	programming	programming	NOUN
ejpam-2332	492	15	problem	problem	NOUN
ejpam-2332	492	16	is	be	AUX
ejpam-2332	492	17	a	a	DET
ejpam-2332	492	18	generalization	generalization	NOUN
ejpam-2332	492	19	of	of	ADP
ejpam-2332	492	20	fuzzy	fuzzy	ADJ
ejpam-2332	492	21	non	non	ADJ
ejpam-2332	492	22	-	-	ADJ
ejpam-2332	492	23	linear	linear	ADJ
ejpam-2332	492	24	programming	programming	NOUN
ejpam-2332	492	25	problem	problem	NOUN
ejpam-2332	492	26	studied	study	VERB
ejpam-2332	492	27	by	by	ADP
ejpam-2332	492	28	vidyottama	vidyottama	NOUN
ejpam-2332	492	29	et	et	PROPN
ejpam-2332	492	30	al	al	PROPN
ejpam-2332	492	31	.	.	PUNCT
ejpam-2332	493	1	[	[	X
ejpam-2332	493	2	32	32	NUM
ejpam-2332	493	3	]	]	PUNCT
ejpam-2332	493	4	.	.	PUNCT
ejpam-2332	494	1	the	the	DET
ejpam-2332	494	2	major	major	ADJ
ejpam-2332	494	3	limitation	limitation	NOUN
ejpam-2332	494	4	of	of	ADP
ejpam-2332	494	5	this	this	DET
ejpam-2332	494	6	proposed	propose	VERB
ejpam-2332	494	7	methodology	methodology	NOUN
ejpam-2332	494	8	is	be	AUX
ejpam-2332	494	9	that	that	SCONJ
ejpam-2332	494	10	it	it	PRON
ejpam-2332	494	11	has	have	AUX
ejpam-2332	494	12	not	not	PART
ejpam-2332	494	13	been	be	AUX
ejpam-2332	494	14	possible	possible	ADJ
ejpam-2332	494	15	to	to	PART
ejpam-2332	494	16	establish	establish	VERB
ejpam-2332	494	17	a	a	DET
ejpam-2332	494	18	nash	nash	ADJ
ejpam-2332	494	19	existence	existence	NOUN
ejpam-2332	494	20	theorem	theorem	NOUN
ejpam-2332	494	21	(	(	PUNCT
ejpam-2332	494	22	theorem	theorem	NOUN
ejpam-2332	494	23	1	1	NUM
ejpam-2332	494	24	)	)	PUNCT
ejpam-2332	494	25	,	,	PUNCT
ejpam-2332	494	26	so	so	SCONJ
ejpam-2332	494	27	as	as	SCONJ
ejpam-2332	494	28	to	to	PART
ejpam-2332	494	29	guarantee	guarantee	VERB
ejpam-2332	494	30	that	that	SCONJ
ejpam-2332	494	31	the	the	DET
ejpam-2332	494	32	all	all	DET
ejpam-2332	494	33	i	i	NOUN
ejpam-2332	494	34	-	-	PUNCT
ejpam-2332	494	35	fuzzy	fuzzy	ADJ
ejpam-2332	494	36	bi	bi	ADJ
ejpam-2332	494	37	-	-	ADJ
ejpam-2332	494	38	matrix	matrix	NOUN
ejpam-2332	494	39	games	game	NOUN
ejpam-2332	494	40	will	will	AUX
ejpam-2332	494	41	have	have	VERB
ejpam-2332	494	42	an	an	DET
ejpam-2332	494	43	“	"	PUNCT
ejpam-2332	494	44	equilibrium	equilibrium	NOUN
ejpam-2332	494	45	solution	solution	NOUN
ejpam-2332	494	46	”	"	PUNCT
ejpam-2332	494	47	.	.	PUNCT
ejpam-2332	495	1	however	however	ADV
ejpam-2332	495	2	,	,	PUNCT
ejpam-2332	495	3	it	it	PRON
ejpam-2332	495	4	is	be	AUX
ejpam-2332	495	5	expected	expect	VERB
ejpam-2332	495	6	that	that	SCONJ
ejpam-2332	495	7	a	a	DET
ejpam-2332	495	8	more	more	ADV
ejpam-2332	495	9	effective	effective	ADJ
ejpam-2332	495	10	methodology	methodology	NOUN
ejpam-2332	495	11	will	will	AUX
ejpam-2332	495	12	be	be	AUX
ejpam-2332	495	13	investigated	investigate	VERB
ejpam-2332	495	14	in	in	ADP
ejpam-2332	495	15	near	near	ADJ
ejpam-2332	495	16	future	future	NOUN
ejpam-2332	495	17	.	.	PUNCT
ejpam-2332	496	1	further	far	ADV
ejpam-2332	496	2	,	,	PUNCT
ejpam-2332	496	3	in	in	ADP
ejpam-2332	496	4	this	this	DET
ejpam-2332	496	5	methodology	methodology	NOUN
ejpam-2332	496	6	the	the	DET
ejpam-2332	496	7	bi	bi	ADJ
ejpam-2332	496	8	-	-	ADJ
ejpam-2332	496	9	matrix	matrix	NOUN
ejpam-2332	496	10	games	game	NOUN
ejpam-2332	496	11	with	with	ADP
ejpam-2332	496	12	i	i	NOUN
ejpam-2332	496	13	-	-	PUNCT
ejpam-2332	496	14	fuzzy	fuzzy	ADJ
ejpam-2332	496	15	pay	pay	NOUN
ejpam-2332	496	16	-	-	PUNCT
ejpam-2332	496	17	offs	off	NOUN
ejpam-2332	496	18	are	be	AUX
ejpam-2332	496	19	considered	consider	VERB
ejpam-2332	496	20	only	only	ADV
ejpam-2332	496	21	but	but	CCONJ
ejpam-2332	496	22	the	the	DET
ejpam-2332	496	23	study	study	NOUN
ejpam-2332	496	24	on	on	ADP
ejpam-2332	496	25	bi	bi	ADJ
ejpam-2332	496	26	-	-	ADJ
ejpam-2332	496	27	matrix	matrix	NOUN
ejpam-2332	496	28	games	game	NOUN
ejpam-2332	496	29	with	with	ADP
ejpam-2332	496	30	i	i	NOUN
ejpam-2332	496	31	-	-	PUNCT
ejpam-2332	496	32	fuzzy	fuzzy	ADJ
ejpam-2332	496	33	goals	goal	NOUN
ejpam-2332	496	34	as	as	ADV
ejpam-2332	496	35	well	well	ADV
ejpam-2332	496	36	as	as	ADP
ejpam-2332	496	37	i	i	PRON
ejpam-2332	496	38	-	-	PUNCT
ejpam-2332	496	39	fuzzy	fuzzy	ADJ
ejpam-2332	496	40	pay	pay	NOUN
ejpam-2332	496	41	-	-	PUNCT
ejpam-2332	496	42	offs	off	NOUN
ejpam-2332	496	43	is	be	AUX
ejpam-2332	496	44	our	our	PRON
ejpam-2332	496	45	future	future	ADJ
ejpam-2332	496	46	work	work	NOUN
ejpam-2332	496	47	.	.	PUNCT
ejpam-2332	497	1	although	although	SCONJ
ejpam-2332	497	2	,	,	PUNCT
ejpam-2332	497	3	the	the	DET
ejpam-2332	497	4	proposed	propose	VERB
ejpam-2332	497	5	method	method	NOUN
ejpam-2332	497	6	is	be	AUX
ejpam-2332	497	7	illustrated	illustrate	VERB
ejpam-2332	497	8	with	with	ADP
ejpam-2332	497	9	a	a	DET
ejpam-2332	497	10	media	media	NOUN
ejpam-2332	497	11	industry	industry	NOUN
ejpam-2332	497	12	problem	problem	NOUN
ejpam-2332	497	13	,	,	PUNCT
ejpam-2332	497	14	it	it	PRON
ejpam-2332	497	15	can	can	AUX
ejpam-2332	497	16	be	be	AUX
ejpam-2332	497	17	applied	apply	VERB
ejpam-2332	497	18	in	in	ADP
ejpam-2332	497	19	decision	decision	NOUN
ejpam-2332	497	20	making	make	VERB
ejpam-2332	497	21	theory	theory	NOUN
ejpam-2332	497	22	such	such	ADJ
ejpam-2332	497	23	as	as	ADP
ejpam-2332	497	24	economics	economic	NOUN
ejpam-2332	497	25	,	,	PUNCT
ejpam-2332	497	26	operations	operation	NOUN
ejpam-2332	497	27	research	research	NOUN
ejpam-2332	497	28	,	,	PUNCT
ejpam-2332	497	29	management	management	NOUN
ejpam-2332	497	30	,	,	PUNCT
ejpam-2332	497	31	war	war	NOUN
ejpam-2332	497	32	science	science	NOUN
ejpam-2332	497	33	etc	etc	X
ejpam-2332	497	34	.	.	X
ejpam-2332	497	35	references	reference	NOUN
ejpam-2332	497	36	[	[	X
ejpam-2332	497	37	1	1	NUM
ejpam-2332	497	38	]	]	PUNCT
ejpam-2332	497	39	a.	a.	NOUN
ejpam-2332	497	40	aggarwal	aggarwal	PROPN
ejpam-2332	497	41	,	,	PUNCT
ejpam-2332	497	42	d.	d.	PROPN
ejpam-2332	497	43	dubey	dubey	PROPN
ejpam-2332	497	44	,	,	PUNCT
ejpam-2332	497	45	s.	s.	PROPN
ejpam-2332	497	46	chandra	chandra	PROPN
ejpam-2332	497	47	,	,	PUNCT
ejpam-2332	497	48	and	and	CCONJ
ejpam-2332	497	49	a.	a.	PROPN
ejpam-2332	497	50	mehra	mehra	PROPN
ejpam-2332	497	51	.	.	PUNCT
ejpam-2332	498	1	application	application	NOUN
ejpam-2332	498	2	of	of	ADP
ejpam-2332	498	3	atanassov	atanassov	PROPN
ejpam-2332	498	4	’s	’s	PROPN
ejpam-2332	498	5	i	i	NOUN
ejpam-2332	498	6	-	-	PUNCT
ejpam-2332	498	7	fuzzy	fuzzy	ADJ
ejpam-2332	498	8	set	set	NOUN
ejpam-2332	498	9	theory	theory	NOUN
ejpam-2332	498	10	to	to	PART
ejpam-2332	498	11	matrix	matrix	VERB
ejpam-2332	498	12	games	game	NOUN
ejpam-2332	498	13	with	with	ADP
ejpam-2332	498	14	fuzzy	fuzzy	ADJ
ejpam-2332	498	15	goals	goal	NOUN
ejpam-2332	498	16	and	and	CCONJ
ejpam-2332	498	17	fuzzy	fuzzy	ADJ
ejpam-2332	498	18	payoffs	payoff	NOUN
ejpam-2332	498	19	.	.	PUNCT
ejpam-2332	499	1	fuzzy	fuzzy	ADJ
ejpam-2332	499	2	information	information	NOUN
ejpam-2332	499	3	and	and	CCONJ
ejpam-2332	499	4	engineering	engineering	NOUN
ejpam-2332	499	5	,	,	PUNCT
ejpam-2332	499	6	4:401	4:401	PROPN
ejpam-2332	499	7	-	-	PUNCT
ejpam-2332	499	8	414	414	NUM
ejpam-2332	499	9	,	,	PUNCT
ejpam-2332	499	10	2012	2012	NUM
ejpam-2332	499	11	.	.	PUNCT
ejpam-2332	500	1	[	[	X
ejpam-2332	500	2	2	2	NUM
ejpam-2332	500	3	]	]	PUNCT
ejpam-2332	500	4	k.	k.	PROPN
ejpam-2332	500	5	atanassov	atanassov	PROPN
ejpam-2332	500	6	.	.	PUNCT
ejpam-2332	501	1	intuitionistic	intuitionistic	ADJ
ejpam-2332	501	2	fuzzy	fuzzy	ADJ
ejpam-2332	501	3	sets	set	NOUN
ejpam-2332	501	4	.	.	PUNCT
ejpam-2332	502	1	fuzzy	fuzzy	ADJ
ejpam-2332	502	2	sets	set	NOUN
ejpam-2332	502	3	and	and	CCONJ
ejpam-2332	502	4	systems	system	NOUN
ejpam-2332	502	5	,	,	PUNCT
ejpam-2332	502	6	20(1):87	20(1):87	PROPN
ejpam-2332	502	7	-	-	SYM
ejpam-2332	502	8	96	96	NUM
ejpam-2332	502	9	,	,	PUNCT
ejpam-2332	502	10	1986	1986	NUM
ejpam-2332	502	11	.	.	PUNCT
ejpam-2332	503	1	[	[	X
ejpam-2332	503	2	3	3	X
ejpam-2332	503	3	]	]	PUNCT
ejpam-2332	503	4	k.	k.	PROPN
ejpam-2332	503	5	atanassov	atanassov	PROPN
ejpam-2332	503	6	.	.	PUNCT
ejpam-2332	504	1	intuitionistic	intuitionistic	ADJ
ejpam-2332	504	2	fuzzy	fuzzy	ADJ
ejpam-2332	504	3	sets	set	NOUN
ejpam-2332	504	4	:	:	PUNCT
ejpam-2332	504	5	theory	theory	NOUN
ejpam-2332	504	6	and	and	CCONJ
ejpam-2332	504	7	applications	application	NOUN
ejpam-2332	504	8	.	.	PUNCT
ejpam-2332	505	1	physica	physica	NOUN
ejpam-2332	505	2	-	-	PUNCT
ejpam-2332	505	3	verlag	verlag	PROPN
ejpam-2332	505	4	,	,	PUNCT
ejpam-2332	505	5	1999	1999	NUM
ejpam-2332	505	6	.	.	PUNCT
ejpam-2332	506	1	[	[	X
ejpam-2332	506	2	4	4	NUM
ejpam-2332	506	3	]	]	X
ejpam-2332	506	4	c.	c.	PROPN
ejpam-2332	506	5	r.	r.	PROPN
ejpam-2332	506	6	bector	bector	PROPN
ejpam-2332	506	7	and	and	CCONJ
ejpam-2332	506	8	s.	s.	PROPN
ejpam-2332	506	9	chandra	chandra	PROPN
ejpam-2332	506	10	.	.	PUNCT
ejpam-2332	506	11	fuzzy	fuzzy	ADJ
ejpam-2332	506	12	mathematical	mathematical	ADJ
ejpam-2332	506	13	programming	programming	NOUN
ejpam-2332	506	14	and	and	CCONJ
ejpam-2332	506	15	fuzzy	fuzzy	ADJ
ejpam-2332	506	16	matrix	matrix	NOUN
ejpam-2332	506	17	games	game	NOUN
ejpam-2332	506	18	.	.	PUNCT
ejpam-2332	507	1	springer	springer	PROPN
ejpam-2332	507	2	verlag	verlag	PROPN
ejpam-2332	507	3	,	,	PUNCT
ejpam-2332	507	4	berlin	berlin	PROPN
ejpam-2332	507	5	,	,	PUNCT
ejpam-2332	507	6	germany	germany	PROPN
ejpam-2332	507	7	,	,	PUNCT
ejpam-2332	507	8	2005	2005	NUM
ejpam-2332	507	9	.	.	PUNCT
ejpam-2332	508	1	[	[	X
ejpam-2332	508	2	5	5	NUM
ejpam-2332	508	3	]	]	PUNCT
ejpam-2332	508	4	a.	a.	NOUN
ejpam-2332	508	5	c.	c.	PROPN
ejpam-2332	508	6	cevikel	cevikel	PROPN
ejpam-2332	508	7	and	and	CCONJ
ejpam-2332	508	8	m.	m.	NOUN
ejpam-2332	508	9	ahlatcioglu	ahlatcioglu	PROPN
ejpam-2332	508	10	.	.	PUNCT
ejpam-2332	509	1	a	a	DET
ejpam-2332	509	2	linear	linear	ADJ
ejpam-2332	509	3	interactive	interactive	ADJ
ejpam-2332	509	4	solution	solution	NOUN
ejpam-2332	509	5	concept	concept	NOUN
ejpam-2332	509	6	for	for	ADP
ejpam-2332	509	7	fuzzy	fuzzy	ADJ
ejpam-2332	509	8	multiobjective	multiobjective	ADJ
ejpam-2332	509	9	games	game	NOUN
ejpam-2332	509	10	.	.	PUNCT
ejpam-2332	510	1	european	european	PROPN
ejpam-2332	510	2	journal	journal	PROPN
ejpam-2332	510	3	of	of	ADP
ejpam-2332	510	4	pure	pure	ADJ
ejpam-2332	510	5	and	and	CCONJ
ejpam-2332	510	6	applied	applied	ADJ
ejpam-2332	510	7	mathematics	mathematic	NOUN
ejpam-2332	510	8	,	,	PUNCT
ejpam-2332	510	9	3(1):107	3(1):107	NUM
ejpam-2332	510	10	-	-	SYM
ejpam-2332	510	11	117	117	NUM
ejpam-2332	510	12	,	,	PUNCT
ejpam-2332	510	13	2010	2010	NUM
ejpam-2332	510	14	.	.	PUNCT
ejpam-2332	511	1	[	[	X
ejpam-2332	511	2	6	6	NUM
ejpam-2332	511	3	]	]	X
ejpam-2332	511	4	d.	d.	PROPN
ejpam-2332	511	5	dubois	dubois	PROPN
ejpam-2332	511	6	and	and	CCONJ
ejpam-2332	511	7	h.	h.	PROPN
ejpam-2332	511	8	prade	prade	PROPN
ejpam-2332	511	9	.	.	PUNCT
ejpam-2332	512	1	fuzzy	fuzzy	ADJ
ejpam-2332	512	2	sets	set	NOUN
ejpam-2332	512	3	and	and	CCONJ
ejpam-2332	512	4	systems	system	NOUN
ejpam-2332	512	5	:	:	PUNCT
ejpam-2332	512	6	theory	theory	NOUN
ejpam-2332	512	7	and	and	CCONJ
ejpam-2332	512	8	application	application	NOUN
ejpam-2332	512	9	.	.	PUNCT
ejpam-2332	513	1	academic	academic	ADJ
ejpam-2332	513	2	press	press	NOUN
ejpam-2332	513	3	,	,	PUNCT
ejpam-2332	513	4	new	new	PROPN
ejpam-2332	513	5	york	york	PROPN
ejpam-2332	513	6	,	,	PUNCT
ejpam-2332	513	7	1980	1980	NUM
ejpam-2332	513	8	.	.	PUNCT
ejpam-2332	514	1	[	[	X
ejpam-2332	514	2	7	7	X
ejpam-2332	514	3	]	]	X
ejpam-2332	514	4	h.	h.	PROPN
ejpam-2332	514	5	g.	g.	PROPN
ejpam-2332	514	6	kocken	kocken	PROPN
ejpam-2332	514	7	,	,	PUNCT
ejpam-2332	514	8	b.	b.	PROPN
ejpam-2332	514	9	a.	a.	PROPN
ejpam-2332	514	10	ozkok	ozkok	PROPN
ejpam-2332	514	11	and	and	CCONJ
ejpam-2332	514	12	f.tiryaki	f.tiryaki	ADJ
ejpam-2332	514	13	.	.	PUNCT
ejpam-2332	515	1	a	a	DET
ejpam-2332	515	2	compensatory	compensatory	ADJ
ejpam-2332	515	3	fuzzy	fuzzy	ADJ
ejpam-2332	515	4	approach	approach	NOUN
ejpam-2332	515	5	to	to	ADP
ejpam-2332	515	6	multiobjective	multiobjective	ADJ
ejpam-2332	515	7	linear	linear	PROPN
ejpam-2332	515	8	transportation	transportation	NOUN
ejpam-2332	515	9	problem	problem	NOUN
ejpam-2332	515	10	with	with	ADP
ejpam-2332	515	11	fuzzy	fuzzy	ADJ
ejpam-2332	515	12	parameters	parameter	NOUN
ejpam-2332	515	13	.	.	PUNCT
ejpam-2332	516	1	european	european	ADJ
ejpam-2332	516	2	journal	journal	PROPN
ejpam-2332	516	3	of	of	ADP
ejpam-2332	516	4	pure	pure	ADJ
ejpam-2332	516	5	and	and	CCONJ
ejpam-2332	516	6	applied	applied	ADJ
ejpam-2332	516	7	mathematics	mathematic	NOUN
ejpam-2332	516	8	,	,	PUNCT
ejpam-2332	516	9	7(3):369	7(3):369	NUM
ejpam-2332	516	10	-	-	SYM
ejpam-2332	516	11	386	386	NUM
ejpam-2332	516	12	,	,	PUNCT
ejpam-2332	516	13	2014	2014	NUM
ejpam-2332	516	14	.	.	PUNCT
ejpam-2332	517	1	[	[	X
ejpam-2332	517	2	8	8	NUM
ejpam-2332	517	3	]	]	X
ejpam-2332	517	4	d.	d.	PROPN
ejpam-2332	517	5	f.	f.	PROPN
ejpam-2332	517	6	li	li	PROPN
ejpam-2332	517	7	.	.	PUNCT
ejpam-2332	518	1	a	a	DET
ejpam-2332	518	2	ratio	ratio	NOUN
ejpam-2332	518	3	ranking	ranking	NOUN
ejpam-2332	518	4	method	method	NOUN
ejpam-2332	518	5	of	of	ADP
ejpam-2332	518	6	triangular	triangular	NOUN
ejpam-2332	518	7	intuiutionistic	intuiutionistic	ADJ
ejpam-2332	518	8	fuzzy	fuzzy	ADJ
ejpam-2332	518	9	numbers	number	NOUN
ejpam-2332	518	10	and	and	CCONJ
ejpam-2332	518	11	its	its	PRON
ejpam-2332	518	12	application	application	NOUN
ejpam-2332	518	13	to	to	PART
ejpam-2332	518	14	madm	madm	VERB
ejpam-2332	518	15	problems	problem	NOUN
ejpam-2332	518	16	.	.	PUNCT
ejpam-2332	519	1	computer	computer	NOUN
ejpam-2332	519	2	and	and	CCONJ
ejpam-2332	519	3	mathematics	mathematic	NOUN
ejpam-2332	519	4	with	with	ADP
ejpam-2332	519	5	applications	application	NOUN
ejpam-2332	519	6	,	,	PUNCT
ejpam-2332	519	7	60(6):15571570	60(6):15571570	NUM
ejpam-2332	519	8	,	,	PUNCT
ejpam-2332	519	9	2010	2010	NUM
ejpam-2332	519	10	.	.	PUNCT
ejpam-2332	520	1	references	reference	NOUN
ejpam-2332	520	2	170	170	NUM
ejpam-2332	520	3	[	[	X
ejpam-2332	520	4	9	9	NUM
ejpam-2332	520	5	]	]	PUNCT
ejpam-2332	520	6	d.	d.	PROPN
ejpam-2332	520	7	f.	f.	PROPN
ejpam-2332	520	8	li	li	PROPN
ejpam-2332	520	9	.	.	PUNCT
ejpam-2332	521	1	a	a	DET
ejpam-2332	521	2	fast	fast	ADJ
ejpam-2332	521	3	approach	approach	NOUN
ejpam-2332	521	4	to	to	PART
ejpam-2332	521	5	compute	compute	VERB
ejpam-2332	521	6	fuzzy	fuzzy	ADJ
ejpam-2332	521	7	values	value	NOUN
ejpam-2332	521	8	of	of	ADP
ejpam-2332	521	9	matrix	matrix	NOUN
ejpam-2332	521	10	games	game	NOUN
ejpam-2332	521	11	with	with	ADP
ejpam-2332	521	12	payoffs	payoff	NOUN
ejpam-2332	521	13	of	of	ADP
ejpam-2332	521	14	triangular	triangular	ADJ
ejpam-2332	521	15	fuzzy	fuzzy	ADJ
ejpam-2332	521	16	numbers	number	NOUN
ejpam-2332	521	17	.	.	PUNCT
ejpam-2332	522	1	european	european	ADJ
ejpam-2332	522	2	journal	journal	PROPN
ejpam-2332	522	3	of	of	ADP
ejpam-2332	522	4	operational	operational	ADJ
ejpam-2332	522	5	research	research	NOUN
ejpam-2332	522	6	,	,	PUNCT
ejpam-2332	522	7	223:421	223:421	PROPN
ejpam-2332	522	8	-	-	PUNCT
ejpam-2332	522	9	429	429	NUM
ejpam-2332	522	10	,	,	PUNCT
ejpam-2332	522	11	2012	2012	NUM
ejpam-2332	522	12	.	.	PUNCT
ejpam-2332	523	1	[	[	X
ejpam-2332	523	2	10	10	NUM
ejpam-2332	523	3	]	]	X
ejpam-2332	523	4	d.	d.	PROPN
ejpam-2332	523	5	f.	f.	PROPN
ejpam-2332	523	6	li	li	PROPN
ejpam-2332	523	7	.	.	PUNCT
ejpam-2332	524	1	an	an	DET
ejpam-2332	524	2	effective	effective	ADJ
ejpam-2332	524	3	methodology	methodology	NOUN
ejpam-2332	524	4	for	for	ADP
ejpam-2332	524	5	solving	solve	VERB
ejpam-2332	524	6	matrix	matrix	NOUN
ejpam-2332	524	7	games	game	NOUN
ejpam-2332	524	8	with	with	ADP
ejpam-2332	524	9	fuzzy	fuzzy	ADJ
ejpam-2332	524	10	payoffs	payoff	NOUN
ejpam-2332	524	11	.	.	PUNCT
ejpam-2332	525	1	ieee	ieee	NOUN
ejpam-2332	525	2	transactions	transaction	NOUN
ejpam-2332	525	3	on	on	ADP
ejpam-2332	525	4	cybernatics	cybernatic	NOUN
ejpam-2332	525	5	,	,	PUNCT
ejpam-2332	525	6	43(2):610	43(2):610	NUM
ejpam-2332	525	7	-	-	SYM
ejpam-2332	525	8	621	621	NUM
ejpam-2332	525	9	,	,	PUNCT
ejpam-2332	525	10	2013	2013	NUM
ejpam-2332	525	11	.	.	PUNCT
ejpam-2332	526	1	[	[	X
ejpam-2332	526	2	11	11	NUM
ejpam-2332	526	3	]	]	X
ejpam-2332	526	4	d.	d.	PROPN
ejpam-2332	526	5	f.	f.	PROPN
ejpam-2332	526	6	li	li	PROPN
ejpam-2332	526	7	.	.	PROPN
ejpam-2332	527	1	and	and	CCONJ
ejpam-2332	527	2	j.	j.	PROPN
ejpam-2332	527	3	yang	yang	PROPN
ejpam-2332	527	4	.	.	PUNCT
ejpam-2332	528	1	a	a	DET
ejpam-2332	528	2	difference	difference	NOUN
ejpam-2332	528	3	-	-	PUNCT
ejpam-2332	528	4	index	index	NOUN
ejpam-2332	528	5	based	base	VERB
ejpam-2332	528	6	ranking	rank	VERB
ejpam-2332	528	7	bilinear	bilinear	NOUN
ejpam-2332	528	8	programming	programming	NOUN
ejpam-2332	528	9	approach	approach	NOUN
ejpam-2332	528	10	to	to	ADP
ejpam-2332	528	11	solving	solve	VERB
ejpam-2332	528	12	bi	bi	ADJ
ejpam-2332	528	13	-	-	ADJ
ejpam-2332	528	14	matrix	matrix	NOUN
ejpam-2332	528	15	games	game	NOUN
ejpam-2332	528	16	with	with	ADP
ejpam-2332	528	17	payoffs	payoff	NOUN
ejpam-2332	528	18	of	of	ADP
ejpam-2332	528	19	trapezoidal	trapezoidal	ADJ
ejpam-2332	528	20	intuitionistic	intuitionistic	ADJ
ejpam-2332	528	21	fuzzy	fuzzy	ADJ
ejpam-2332	528	22	numbers	number	NOUN
ejpam-2332	528	23	.	.	PUNCT
ejpam-2332	529	1	journal	journal	NOUN
ejpam-2332	529	2	of	of	ADP
ejpam-2332	529	3	applied	apply	VERB
ejpam-2332	529	4	mathematics	mathematic	NOUN
ejpam-2332	529	5	,	,	PUNCT
ejpam-2332	529	6	13:1	13:1	NUM
ejpam-2332	529	7	-	-	SYM
ejpam-2332	529	8	10	10	NUM
ejpam-2332	529	9	,	,	PUNCT
ejpam-2332	529	10	2013	2013	NUM
ejpam-2332	529	11	.	.	PUNCT
ejpam-2332	530	1	[	[	X
ejpam-2332	530	2	12	12	NUM
ejpam-2332	530	3	]	]	X
ejpam-2332	530	4	d.	d.	PROPN
ejpam-2332	530	5	f.	f.	PROPN
ejpam-2332	530	6	li	li	PROPN
ejpam-2332	530	7	.	.	PUNCT
ejpam-2332	531	1	bi	bi	ADJ
ejpam-2332	531	2	-	-	ADJ
ejpam-2332	531	3	matrix	matrix	NOUN
ejpam-2332	531	4	games	game	NOUN
ejpam-2332	531	5	with	with	ADP
ejpam-2332	531	6	payoffs	payoff	NOUN
ejpam-2332	531	7	of	of	ADP
ejpam-2332	531	8	intuitionistic	intuitionistic	ADJ
ejpam-2332	531	9	fuzzy	fuzzy	ADJ
ejpam-2332	531	10	sets	set	NOUN
ejpam-2332	531	11	and	and	CCONJ
ejpam-2332	531	12	bilinear	bilinear	NOUN
ejpam-2332	531	13	programming	programming	NOUN
ejpam-2332	531	14	method	method	NOUN
ejpam-2332	531	15	.	.	PUNCT
ejpam-2332	532	1	decision	decision	NOUN
ejpam-2332	532	2	and	and	CCONJ
ejpam-2332	532	3	game	game	NOUN
ejpam-2332	532	4	theory	theory	NOUN
ejpam-2332	532	5	in	in	ADP
ejpam-2332	532	6	management	management	NOUN
ejpam-2332	532	7	with	with	ADP
ejpam-2332	532	8	intuitionistic	intuitionistic	ADJ
ejpam-2332	532	9	fuzzy	fuzzy	ADJ
ejpam-2332	532	10	sets	set	NOUN
ejpam-2332	532	11	,	,	PUNCT
ejpam-2332	532	12	springer	springer	NOUN
ejpam-2332	532	13	berlin	berlin	PROPN
ejpam-2332	532	14	heidelberg	heidelberg	PROPN
ejpam-2332	532	15	,	,	PUNCT
ejpam-2332	532	16	421	421	NUM
ejpam-2332	532	17	-	-	SYM
ejpam-2332	532	18	441	441	NUM
ejpam-2332	532	19	,	,	PUNCT
ejpam-2332	532	20	2014	2014	NUM
ejpam-2332	532	21	.	.	PUNCT
ejpam-2332	533	1	[	[	X
ejpam-2332	533	2	13	13	NUM
ejpam-2332	533	3	]	]	PUNCT
ejpam-2332	533	4	t.	t.	PROPN
ejpam-2332	533	5	maeda	maeda	PROPN
ejpam-2332	533	6	.	.	PUNCT
ejpam-2332	533	7	characterization	characterization	NOUN
ejpam-2332	533	8	of	of	ADP
ejpam-2332	533	9	the	the	DET
ejpam-2332	533	10	equilibrium	equilibrium	NOUN
ejpam-2332	533	11	strategy	strategy	NOUN
ejpam-2332	533	12	of	of	ADP
ejpam-2332	533	13	the	the	DET
ejpam-2332	533	14	bi	bi	ADJ
ejpam-2332	533	15	-	-	ADJ
ejpam-2332	533	16	matrix	matrix	NOUN
ejpam-2332	533	17	game	game	NOUN
ejpam-2332	533	18	with	with	ADP
ejpam-2332	533	19	fuzzy	fuzzy	ADJ
ejpam-2332	533	20	payoff	payoff	NOUN
ejpam-2332	533	21	.	.	PUNCT
ejpam-2332	534	1	journal	journal	PROPN
ejpam-2332	534	2	of	of	ADP
ejpam-2332	534	3	mathematical	mathematical	ADJ
ejpam-2332	534	4	analysis	analysis	NOUN
ejpam-2332	534	5	and	and	CCONJ
ejpam-2332	534	6	applications	application	NOUN
ejpam-2332	534	7	,	,	PUNCT
ejpam-2332	534	8	251:885	251:885	NOUN
ejpam-2332	534	9	-	-	SYM
ejpam-2332	534	10	896	896	NUM
ejpam-2332	534	11	,	,	PUNCT
ejpam-2332	534	12	2000	2000	NUM
ejpam-2332	534	13	.	.	PUNCT
ejpam-2332	535	1	[	[	X
ejpam-2332	535	2	14	14	NUM
ejpam-2332	535	3	]	]	X
ejpam-2332	535	4	o.	o.	PROPN
ejpam-2332	535	5	l.	l.	PROPN
ejpam-2332	535	6	mangasarian	mangasarian	PROPN
ejpam-2332	535	7	and	and	CCONJ
ejpam-2332	535	8	h.	h.	PROPN
ejpam-2332	535	9	stone	stone	PROPN
ejpam-2332	535	10	.	.	PUNCT
ejpam-2332	536	1	two	two	NUM
ejpam-2332	536	2	-	-	PUNCT
ejpam-2332	536	3	person	person	NOUN
ejpam-2332	536	4	non	non	ADJ
ejpam-2332	536	5	-	-	ADJ
ejpam-2332	536	6	zero	zero	NUM
ejpam-2332	536	7	sum	sum	NOUN
ejpam-2332	536	8	games	game	NOUN
ejpam-2332	536	9	and	and	CCONJ
ejpam-2332	536	10	quadratic	quadratic	ADJ
ejpam-2332	536	11	programming	programming	NOUN
ejpam-2332	536	12	.	.	PUNCT
ejpam-2332	537	1	journal	journal	PROPN
ejpam-2332	537	2	of	of	ADP
ejpam-2332	537	3	mathematical	mathematical	ADJ
ejpam-2332	537	4	analysis	analysis	NOUN
ejpam-2332	537	5	and	and	CCONJ
ejpam-2332	537	6	applications	application	NOUN
ejpam-2332	537	7	,	,	PUNCT
ejpam-2332	537	8	9:348	9:348	NOUN
ejpam-2332	537	9	-	-	SYM
ejpam-2332	537	10	355	355	NUM
ejpam-2332	537	11	,	,	PUNCT
ejpam-2332	537	12	1964	1964	NUM
ejpam-2332	537	13	.	.	PUNCT
ejpam-2332	538	1	[	[	X
ejpam-2332	538	2	15	15	NUM
ejpam-2332	538	3	]	]	X
ejpam-2332	538	4	j.	j.	PROPN
ejpam-2332	538	5	x.	x.	PROPN
ejpam-2332	538	6	nan	nan	PROPN
ejpam-2332	538	7	,	,	PUNCT
ejpam-2332	538	8	d.	d.	PROPN
ejpam-2332	538	9	f.	f.	PROPN
ejpam-2332	538	10	li	li	PROPN
ejpam-2332	538	11	,	,	PUNCT
ejpam-2332	538	12	and	and	CCONJ
ejpam-2332	538	13	m.	m.	PROPN
ejpam-2332	538	14	j.	j.	PROPN
ejpam-2332	538	15	zhang	zhang	PROPN
ejpam-2332	538	16	.	.	PUNCT
ejpam-2332	539	1	a	a	DET
ejpam-2332	539	2	lexicographic	lexicographic	ADJ
ejpam-2332	539	3	method	method	NOUN
ejpam-2332	539	4	for	for	ADP
ejpam-2332	539	5	matrix	matrix	NOUN
ejpam-2332	539	6	games	game	NOUN
ejpam-2332	539	7	with	with	ADP
ejpam-2332	539	8	payoffs	payoff	NOUN
ejpam-2332	539	9	of	of	ADP
ejpam-2332	539	10	triangular	triangular	NOUN
ejpam-2332	539	11	intuitinistic	intuitinistic	ADJ
ejpam-2332	539	12	fuzzy	fuzzy	ADJ
ejpam-2332	539	13	numbers	number	NOUN
ejpam-2332	539	14	.	.	PUNCT
ejpam-2332	540	1	international	international	ADJ
ejpam-2332	540	2	journal	journal	NOUN
ejpam-2332	540	3	of	of	ADP
ejpam-2332	540	4	computational	computational	ADJ
ejpam-2332	540	5	intelligence	intelligence	NOUN
ejpam-2332	540	6	systems	system	NOUN
ejpam-2332	540	7	,	,	PUNCT
ejpam-2332	540	8	3(3):280	3(3):280	NUM
ejpam-2332	540	9	-	-	SYM
ejpam-2332	540	10	289	289	NUM
ejpam-2332	540	11	.	.	PUNCT
ejpam-2332	541	1	[	[	X
ejpam-2332	541	2	16	16	NUM
ejpam-2332	541	3	]	]	X
ejpam-2332	541	4	j.	j.	PROPN
ejpam-2332	541	5	x.	x.	PROPN
ejpam-2332	541	6	nan	nan	PROPN
ejpam-2332	541	7	and	and	CCONJ
ejpam-2332	541	8	d.	d.	PROPN
ejpam-2332	541	9	f.	f.	PROPN
ejpam-2332	541	10	li	li	PROPN
ejpam-2332	541	11	.	.	PROPN
ejpam-2332	541	12	linear	linear	PROPN
ejpam-2332	541	13	programming	programming	NOUN
ejpam-2332	541	14	approach	approach	NOUN
ejpam-2332	541	15	to	to	ADP
ejpam-2332	541	16	matrix	matrix	NOUN
ejpam-2332	541	17	games	game	NOUN
ejpam-2332	541	18	with	with	ADP
ejpam-2332	541	19	intuitionistic	intuitionistic	ADJ
ejpam-2332	541	20	fuzzy	fuzzy	ADJ
ejpam-2332	541	21	goals	goal	NOUN
ejpam-2332	541	22	.	.	PUNCT
ejpam-2332	542	1	international	international	ADJ
ejpam-2332	542	2	journal	journal	NOUN
ejpam-2332	542	3	of	of	ADP
ejpam-2332	542	4	computational	computational	ADJ
ejpam-2332	542	5	intelligence	intelligence	NOUN
ejpam-2332	542	6	systems	system	NOUN
ejpam-2332	542	7	,	,	PUNCT
ejpam-2332	542	8	6(1):186	6(1):186	NUM
ejpam-2332	542	9	-	-	SYM
ejpam-2332	542	10	197	197	NUM
ejpam-2332	542	11	,	,	PUNCT
ejpam-2332	542	12	2013	2013	NUM
ejpam-2332	542	13	.	.	PUNCT
ejpam-2332	543	1	[	[	X
ejpam-2332	543	2	17	17	NUM
ejpam-2332	543	3	]	]	PUNCT
ejpam-2332	543	4	j.	j.	PROPN
ejpam-2332	543	5	f.	f.	PROPN
ejpam-2332	543	6	nash	nash	PROPN
ejpam-2332	543	7	.	.	PUNCT
ejpam-2332	544	1	non	non	PROPN
ejpam-2332	544	2	cooperative	cooperative	ADJ
ejpam-2332	544	3	games	game	NOUN
ejpam-2332	544	4	.	.	PUNCT
ejpam-2332	545	1	annals	annal	NOUN
ejpam-2332	545	2	of	of	ADP
ejpam-2332	545	3	mathematics	mathematic	NOUN
ejpam-2332	545	4	,	,	PUNCT
ejpam-2332	545	5	54(2):286	54(2):286	PROPN
ejpam-2332	545	6	-	-	PUNCT
ejpam-2332	545	7	295	295	NUM
ejpam-2332	545	8	,	,	PUNCT
ejpam-2332	545	9	1951	1951	NUM
ejpam-2332	545	10	.	.	PUNCT
ejpam-2332	546	1	[	[	X
ejpam-2332	546	2	18	18	NUM
ejpam-2332	546	3	]	]	PUNCT
ejpam-2332	546	4	p.	p.	NOUN
ejpam-2332	546	5	k.	k.	PROPN
ejpam-2332	547	1	nayak	nayak	PROPN
ejpam-2332	547	2	and	and	CCONJ
ejpam-2332	547	3	m.	m.	NOUN
ejpam-2332	547	4	pal	pal	NOUN
ejpam-2332	547	5	.	.	PUNCT
ejpam-2332	548	1	the	the	DET
ejpam-2332	548	2	bi	bi	ADJ
ejpam-2332	548	3	-	-	ADJ
ejpam-2332	548	4	matrix	matrix	NOUN
ejpam-2332	548	5	games	game	NOUN
ejpam-2332	548	6	with	with	ADP
ejpam-2332	548	7	interval	interval	NOUN
ejpam-2332	548	8	payoffs	payoff	NOUN
ejpam-2332	548	9	and	and	CCONJ
ejpam-2332	548	10	its	its	PRON
ejpam-2332	548	11	nash	nash	ADJ
ejpam-2332	548	12	equilibrium	equilibrium	NOUN
ejpam-2332	548	13	strategy	strategy	NOUN
ejpam-2332	548	14	.	.	PUNCT
ejpam-2332	549	1	journal	journal	NOUN
ejpam-2332	549	2	of	of	ADP
ejpam-2332	549	3	fuzzy	fuzzy	ADJ
ejpam-2332	549	4	mathematics	mathematic	NOUN
ejpam-2332	549	5	,	,	PUNCT
ejpam-2332	549	6	17(2):421	17(2):421	PROPN
ejpam-2332	549	7	-	-	SYM
ejpam-2332	549	8	436	436	NUM
ejpam-2332	549	9	,	,	PUNCT
ejpam-2332	549	10	2009	2009	NUM
ejpam-2332	549	11	.	.	PUNCT
ejpam-2332	550	1	[	[	X
ejpam-2332	550	2	19	19	NUM
ejpam-2332	550	3	]	]	PUNCT
ejpam-2332	550	4	p.	p.	NOUN
ejpam-2332	550	5	k.	k.	PROPN
ejpam-2332	551	1	nayak	nayak	PROPN
ejpam-2332	551	2	and	and	CCONJ
ejpam-2332	551	3	m.	m.	PROPN
ejpam-2332	551	4	pal	pal	PROPN
ejpam-2332	551	5	.	.	PUNCT
ejpam-2332	552	1	bi	bi	ADJ
ejpam-2332	552	2	-	-	ADJ
ejpam-2332	552	3	matrix	matrix	NOUN
ejpam-2332	552	4	games	game	NOUN
ejpam-2332	552	5	with	with	ADP
ejpam-2332	552	6	intuitionistic	intuitionistic	ADJ
ejpam-2332	552	7	fuzzy	fuzzy	ADJ
ejpam-2332	552	8	goals	goal	NOUN
ejpam-2332	552	9	.	.	PUNCT
ejpam-2332	553	1	iranian	iranian	ADJ
ejpam-2332	553	2	journal	journal	PROPN
ejpam-2332	553	3	of	of	ADP
ejpam-2332	553	4	fuzzy	fuzzy	ADJ
ejpam-2332	553	5	systems	system	NOUN
ejpam-2332	553	6	,	,	PUNCT
ejpam-2332	553	7	7(1):65	7(1):65	NUM
ejpam-2332	553	8	-	-	SYM
ejpam-2332	553	9	79	79	NUM
ejpam-2332	553	10	,	,	PUNCT
ejpam-2332	553	11	2010	2010	NUM
ejpam-2332	553	12	.	.	PUNCT
ejpam-2332	554	1	[	[	X
ejpam-2332	554	2	20	20	NUM
ejpam-2332	554	3	]	]	PUNCT
ejpam-2332	554	4	p.	p.	NOUN
ejpam-2332	554	5	k.	k.	PROPN
ejpam-2332	555	1	nayak	nayak	PROPN
ejpam-2332	555	2	and	and	CCONJ
ejpam-2332	555	3	m.	m.	NOUN
ejpam-2332	555	4	pal	pal	PROPN
ejpam-2332	555	5	.	.	PUNCT
ejpam-2332	556	1	intuitionistic	intuitionistic	ADJ
ejpam-2332	556	2	fuzzy	fuzzy	ADJ
ejpam-2332	556	3	optimization	optimization	NOUN
ejpam-2332	556	4	technique	technique	NOUN
ejpam-2332	556	5	for	for	ADP
ejpam-2332	556	6	nash	nash	PROPN
ejpam-2332	556	7	equilibrium	equilibrium	NOUN
ejpam-2332	556	8	solution	solution	NOUN
ejpam-2332	556	9	of	of	ADP
ejpam-2332	556	10	multi	multi	ADJ
ejpam-2332	556	11	-	-	ADJ
ejpam-2332	556	12	objective	objective	ADJ
ejpam-2332	556	13	bi	bi	ADJ
ejpam-2332	556	14	-	-	ADJ
ejpam-2332	556	15	marix	marix	ADJ
ejpam-2332	556	16	game	game	NOUN
ejpam-2332	556	17	.	.	PUNCT
ejpam-2332	557	1	journal	journal	PROPN
ejpam-2332	557	2	of	of	ADP
ejpam-2332	557	3	uncertain	uncertain	ADJ
ejpam-2332	557	4	systems	system	NOUN
ejpam-2332	557	5	,	,	PUNCT
ejpam-2332	557	6	5(4):271	5(4):271	NUM
ejpam-2332	557	7	-	-	SYM
ejpam-2332	557	8	285	285	NUM
ejpam-2332	557	9	,	,	PUNCT
ejpam-2332	557	10	2011	2011	NUM
ejpam-2332	557	11	.	.	PUNCT
ejpam-2332	558	1	[	[	X
ejpam-2332	558	2	21	21	NUM
ejpam-2332	558	3	]	]	X
ejpam-2332	558	4	i.	i.	NOUN
ejpam-2332	558	5	nishizaki	nishizaki	PROPN
ejpam-2332	558	6	and	and	CCONJ
ejpam-2332	558	7	m.	m.	NOUN
ejpam-2332	558	8	sakawa	sakawa	PROPN
ejpam-2332	558	9	.	.	PUNCT
ejpam-2332	559	1	equilibrium	equilibrium	NOUN
ejpam-2332	559	2	solution	solution	NOUN
ejpam-2332	559	3	for	for	ADP
ejpam-2332	559	4	multiobjective	multiobjective	ADJ
ejpam-2332	559	5	bi	bi	ADJ
ejpam-2332	559	6	-	-	ADJ
ejpam-2332	559	7	matrix	matrix	NOUN
ejpam-2332	559	8	games	game	NOUN
ejpam-2332	559	9	incorporating	incorporate	VERB
ejpam-2332	559	10	fuzzy	fuzzy	ADJ
ejpam-2332	559	11	goals	goal	NOUN
ejpam-2332	559	12	.	.	PUNCT
ejpam-2332	560	1	journal	journal	NOUN
ejpam-2332	560	2	of	of	ADP
ejpam-2332	560	3	optimization	optimization	NOUN
ejpam-2332	560	4	theory	theory	NOUN
ejpam-2332	560	5	and	and	CCONJ
ejpam-2332	560	6	applications	application	NOUN
ejpam-2332	560	7	,	,	PUNCT
ejpam-2332	560	8	86(2):433	86(2):433	NUM
ejpam-2332	560	9	-	-	SYM
ejpam-2332	560	10	457	457	NUM
ejpam-2332	560	11	,	,	PUNCT
ejpam-2332	560	12	1995	1995	NUM
ejpam-2332	560	13	.	.	PUNCT
ejpam-2332	561	1	[	[	X
ejpam-2332	561	2	22	22	NUM
ejpam-2332	561	3	]	]	PUNCT
ejpam-2332	561	4	i.	i.	NOUN
ejpam-2332	561	5	nishizaki	nishizaki	PROPN
ejpam-2332	561	6	and	and	CCONJ
ejpam-2332	561	7	m.	m.	NOUN
ejpam-2332	561	8	sakawa	sakawa	PROPN
ejpam-2332	561	9	.	.	PUNCT
ejpam-2332	562	1	fuzzy	fuzzy	ADJ
ejpam-2332	562	2	and	and	CCONJ
ejpam-2332	562	3	multiobjective	multiobjective	ADJ
ejpam-2332	562	4	games	game	NOUN
ejpam-2332	562	5	for	for	ADP
ejpam-2332	562	6	conflict	conflict	NOUN
ejpam-2332	562	7	resolution	resolution	NOUN
ejpam-2332	562	8	,	,	PUNCT
ejpam-2332	562	9	physicaverlag	physicaverlag	NOUN
ejpam-2332	562	10	,	,	PUNCT
ejpam-2332	562	11	berlin	berlin	PROPN
ejpam-2332	562	12	,	,	PUNCT
ejpam-2332	562	13	germany	germany	PROPN
ejpam-2332	562	14	,	,	PUNCT
ejpam-2332	562	15	2001	2001	NUM
ejpam-2332	562	16	.	.	PUNCT
ejpam-2332	563	1	[	[	X
ejpam-2332	563	2	23	23	NUM
ejpam-2332	563	3	]	]	X
ejpam-2332	563	4	g.	g.	PROPN
ejpam-2332	563	5	owen	owen	PROPN
ejpam-2332	563	6	.	.	PROPN
ejpam-2332	564	1	game	game	PROPN
ejpam-2332	564	2	theory	theory	NOUN
ejpam-2332	564	3	,	,	PUNCT
ejpam-2332	564	4	academic	academic	ADJ
ejpam-2332	564	5	press	press	NOUN
ejpam-2332	564	6	,	,	PUNCT
ejpam-2332	564	7	san	san	PROPN
ejpam-2332	564	8	diego	diego	PROPN
ejpam-2332	564	9	,	,	PUNCT
ejpam-2332	564	10	1995	1995	NUM
ejpam-2332	564	11	.	.	PUNCT
ejpam-2332	565	1	references	reference	NOUN
ejpam-2332	565	2	171	171	NUM
ejpam-2332	565	3	[	[	X
ejpam-2332	565	4	24	24	NUM
ejpam-2332	565	5	]	]	PUNCT
ejpam-2332	565	6	m.	m.	NOUN
ejpam-2332	565	7	sakawa	sakawa	PROPN
ejpam-2332	565	8	and	and	CCONJ
ejpam-2332	565	9	i.	i.	PROPN
ejpam-2332	565	10	nishizaki	nishizaki	PROPN
ejpam-2332	565	11	.	.	PUNCT
ejpam-2332	566	1	equilibrium	equilibrium	NOUN
ejpam-2332	566	2	solution	solution	NOUN
ejpam-2332	566	3	in	in	ADP
ejpam-2332	566	4	bi	bi	ADJ
ejpam-2332	566	5	-	-	ADJ
ejpam-2332	566	6	matrix	matrix	NOUN
ejpam-2332	566	7	games	game	NOUN
ejpam-2332	566	8	with	with	ADP
ejpam-2332	566	9	fuzzy	fuzzy	ADJ
ejpam-2332	566	10	pay	pay	NOUN
ejpam-2332	566	11	-	-	PUNCT
ejpam-2332	566	12	offs	off	NOUN
ejpam-2332	566	13	.	.	PUNCT
ejpam-2332	567	1	japanese	japanese	ADJ
ejpam-2332	567	2	fuzzy	fuzzy	ADJ
ejpam-2332	567	3	theory	theory	NOUN
ejpam-2332	567	4	and	and	CCONJ
ejpam-2332	567	5	systems	system	NOUN
ejpam-2332	567	6	,	,	PUNCT
ejpam-2332	567	7	9(3):307	9(3):307	NUM
ejpam-2332	567	8	-	-	SYM
ejpam-2332	567	9	324	324	NUM
ejpam-2332	567	10	,	,	PUNCT
ejpam-2332	567	11	1997	1997	NUM
ejpam-2332	567	12	.	.	PUNCT
ejpam-2332	568	1	[	[	X
ejpam-2332	568	2	25	25	NUM
ejpam-2332	568	3	]	]	PUNCT
ejpam-2332	568	4	m.	m.	PROPN
ejpam-2332	568	5	r.	r.	PROPN
ejpam-2332	568	6	seikh	seikh	PROPN
ejpam-2332	568	7	,	,	PUNCT
ejpam-2332	568	8	m.	m.	NOUN
ejpam-2332	568	9	pal	pal	NOUN
ejpam-2332	568	10	,	,	PUNCT
ejpam-2332	568	11	and	and	CCONJ
ejpam-2332	569	1	p.	p.	PROPN
ejpam-2332	569	2	k.	k.	PROPN
ejpam-2332	570	1	nayak	nayak	PROPN
ejpam-2332	570	2	.	.	PUNCT
ejpam-2332	571	1	generalized	generalize	VERB
ejpam-2332	571	2	triangular	triangular	NOUN
ejpam-2332	571	3	fuzzy	fuzzy	ADJ
ejpam-2332	571	4	numbers	number	NOUN
ejpam-2332	571	5	in	in	ADP
ejpam-2332	571	6	intuitionistic	intuitionistic	ADJ
ejpam-2332	571	7	fuzzy	fuzzy	ADJ
ejpam-2332	571	8	environment	environment	NOUN
ejpam-2332	571	9	.	.	PUNCT
ejpam-2332	572	1	international	international	ADJ
ejpam-2332	572	2	journal	journal	PROPN
ejpam-2332	572	3	of	of	ADP
ejpam-2332	572	4	engineering	engineering	NOUN
ejpam-2332	572	5	research	research	NOUN
ejpam-2332	572	6	and	and	CCONJ
ejpam-2332	572	7	development	development	NOUN
ejpam-2332	572	8	,	,	PUNCT
ejpam-2332	572	9	5(1):08	5(1):08	NUM
ejpam-2332	572	10	-	-	SYM
ejpam-2332	572	11	13	13	NUM
ejpam-2332	572	12	,	,	PUNCT
ejpam-2332	572	13	2012	2012	NUM
ejpam-2332	572	14	.	.	PUNCT
ejpam-2332	573	1	[	[	X
ejpam-2332	573	2	26	26	NUM
ejpam-2332	573	3	]	]	PUNCT
ejpam-2332	573	4	m.	m.	PROPN
ejpam-2332	573	5	r.	r.	PROPN
ejpam-2332	573	6	seikh	seikh	PROPN
ejpam-2332	573	7	,	,	PUNCT
ejpam-2332	573	8	m.	m.	NOUN
ejpam-2332	573	9	pal	pal	NOUN
ejpam-2332	573	10	,	,	PUNCT
ejpam-2332	573	11	and	and	CCONJ
ejpam-2332	573	12	p.	p.	PROPN
ejpam-2332	573	13	k.	k.	PROPN
ejpam-2332	574	1	nayak	nayak	PROPN
ejpam-2332	574	2	.	.	PUNCT
ejpam-2332	575	1	application	application	NOUN
ejpam-2332	575	2	of	of	ADP
ejpam-2332	575	3	triangular	triangular	NOUN
ejpam-2332	575	4	intuitionistic	intuitionistic	ADJ
ejpam-2332	575	5	fuzzy	fuzzy	ADJ
ejpam-2332	575	6	numbers	number	NOUN
ejpam-2332	575	7	in	in	ADP
ejpam-2332	575	8	bi	bi	ADJ
ejpam-2332	575	9	-	-	ADJ
ejpam-2332	575	10	matrix	matrix	NOUN
ejpam-2332	575	11	games	game	NOUN
ejpam-2332	575	12	.	.	PUNCT
ejpam-2332	576	1	international	international	ADJ
ejpam-2332	576	2	journal	journal	PROPN
ejpam-2332	576	3	of	of	ADP
ejpam-2332	576	4	pure	pure	ADJ
ejpam-2332	576	5	and	and	CCONJ
ejpam-2332	576	6	applied	applied	ADJ
ejpam-2332	576	7	mathematics	mathematic	NOUN
ejpam-2332	576	8	,	,	PUNCT
ejpam-2332	576	9	79(2):235247	79(2):235247	NUM
ejpam-2332	576	10	,	,	PUNCT
ejpam-2332	576	11	2012	2012	NUM
ejpam-2332	576	12	.	.	PUNCT
ejpam-2332	577	1	[	[	X
ejpam-2332	577	2	27	27	NUM
ejpam-2332	577	3	]	]	PUNCT
ejpam-2332	577	4	m.	m.	PROPN
ejpam-2332	577	5	r.	r.	PROPN
ejpam-2332	577	6	seikh	seikh	PROPN
ejpam-2332	577	7	,	,	PUNCT
ejpam-2332	577	8	p.	p.	PROPN
ejpam-2332	577	9	k.	k.	PROPN
ejpam-2332	577	10	nayak	nayak	PROPN
ejpam-2332	577	11	,	,	PUNCT
ejpam-2332	577	12	and	and	CCONJ
ejpam-2332	577	13	m.	m.	NOUN
ejpam-2332	577	14	pal	pal	PROPN
ejpam-2332	577	15	.	.	PUNCT
ejpam-2332	578	1	notes	note	NOUN
ejpam-2332	578	2	on	on	ADP
ejpam-2332	578	3	triangular	triangular	NOUN
ejpam-2332	578	4	intuitionistic	intuitionistic	ADJ
ejpam-2332	578	5	fuzzy	fuzzy	ADJ
ejpam-2332	578	6	numbers	number	NOUN
ejpam-2332	578	7	.	.	PUNCT
ejpam-2332	579	1	international	international	ADJ
ejpam-2332	579	2	journal	journal	NOUN
ejpam-2332	579	3	of	of	ADP
ejpam-2332	579	4	mathematics	mathematic	NOUN
ejpam-2332	579	5	in	in	ADP
ejpam-2332	579	6	operational	operational	ADJ
ejpam-2332	579	7	research	research	NOUN
ejpam-2332	579	8	,	,	PUNCT
ejpam-2332	579	9	5(4):446	5(4):446	NUM
ejpam-2332	579	10	-	-	SYM
ejpam-2332	579	11	465	465	NUM
ejpam-2332	579	12	,	,	PUNCT
ejpam-2332	579	13	2013	2013	NUM
ejpam-2332	579	14	.	.	PUNCT
ejpam-2332	580	1	[	[	X
ejpam-2332	580	2	28	28	NUM
ejpam-2332	580	3	]	]	X
ejpam-2332	580	4	m.	m.	PROPN
ejpam-2332	580	5	r.	r.	PROPN
ejpam-2332	580	6	seikh	seikh	PROPN
ejpam-2332	580	7	,	,	PUNCT
ejpam-2332	580	8	p.	p.	PROPN
ejpam-2332	580	9	k.	k.	PROPN
ejpam-2332	581	1	nayak	nayak	PROPN
ejpam-2332	581	2	,	,	PUNCT
ejpam-2332	581	3	and	and	CCONJ
ejpam-2332	581	4	m.	m.	NOUN
ejpam-2332	581	5	pal	pal	PROPN
ejpam-2332	581	6	.	.	PROPN
ejpam-2332	581	7	matrix	matrix	NOUN
ejpam-2332	581	8	games	game	NOUN
ejpam-2332	581	9	in	in	ADP
ejpam-2332	581	10	intuitionistic	intuitionistic	ADJ
ejpam-2332	581	11	fuzzy	fuzzy	ADJ
ejpam-2332	581	12	environment	environment	NOUN
ejpam-2332	581	13	.	.	PUNCT
ejpam-2332	582	1	international	international	ADJ
ejpam-2332	582	2	journal	journal	PROPN
ejpam-2332	582	3	of	of	ADP
ejpam-2332	582	4	mathematics	mathematic	NOUN
ejpam-2332	582	5	in	in	ADP
ejpam-2332	582	6	operational	operational	ADJ
ejpam-2332	582	7	research	research	NOUN
ejpam-2332	582	8	,	,	PUNCT
ejpam-2332	582	9	5(6):693	5(6):693	NUM
ejpam-2332	582	10	-	-	SYM
ejpam-2332	582	11	708	708	NUM
ejpam-2332	582	12	,	,	PUNCT
ejpam-2332	582	13	2013	2013	NUM
ejpam-2332	582	14	.	.	PUNCT
ejpam-2332	583	1	[	[	X
ejpam-2332	583	2	29	29	NUM
ejpam-2332	583	3	]	]	PUNCT
ejpam-2332	583	4	m.	m.	PROPN
ejpam-2332	583	5	r.	r.	PROPN
ejpam-2332	583	6	seikh	seikh	PROPN
ejpam-2332	583	7	,	,	PUNCT
ejpam-2332	583	8	p.	p.	PROPN
ejpam-2332	583	9	k.	k.	PROPN
ejpam-2332	584	1	nayak	nayak	PROPN
ejpam-2332	584	2	and	and	CCONJ
ejpam-2332	584	3	m.	m.	NOUN
ejpam-2332	584	4	pal	pal	NOUN
ejpam-2332	584	5	.	.	PUNCT
ejpam-2332	585	1	an	an	DET
ejpam-2332	585	2	alternative	alternative	ADJ
ejpam-2332	585	3	approach	approach	NOUN
ejpam-2332	585	4	for	for	ADP
ejpam-2332	585	5	solving	solve	VERB
ejpam-2332	585	6	fuzzy	fuzzy	ADJ
ejpam-2332	585	7	matrix	matrix	NOUN
ejpam-2332	585	8	games	game	NOUN
ejpam-2332	585	9	.	.	PUNCT
ejpam-2332	586	1	international	international	ADJ
ejpam-2332	586	2	journal	journal	PROPN
ejpam-2332	586	3	of	of	ADP
ejpam-2332	586	4	mathematics	mathematic	NOUN
ejpam-2332	586	5	and	and	CCONJ
ejpam-2332	586	6	soft	soft	ADJ
ejpam-2332	586	7	computing	computing	NOUN
ejpam-2332	586	8	,	,	PUNCT
ejpam-2332	586	9	5(1):79	5(1):79	NUM
ejpam-2332	586	10	-	-	SYM
ejpam-2332	586	11	92	92	NUM
ejpam-2332	586	12	,	,	PUNCT
ejpam-2332	586	13	2015a	2015a	NUM
ejpam-2332	586	14	.	.	PUNCT
ejpam-2332	587	1	[	[	X
ejpam-2332	587	2	30	30	NUM
ejpam-2332	587	3	]	]	X
ejpam-2332	587	4	m.	m.	PROPN
ejpam-2332	587	5	r.	r.	PROPN
ejpam-2332	587	6	seikh	seikh	PROPN
ejpam-2332	587	7	,	,	PUNCT
ejpam-2332	587	8	p.	p.	PROPN
ejpam-2332	587	9	k.	k.	PROPN
ejpam-2332	587	10	nayak	nayak	PROPN
ejpam-2332	587	11	,	,	PUNCT
ejpam-2332	587	12	and	and	CCONJ
ejpam-2332	587	13	m.	m.	NOUN
ejpam-2332	587	14	pal	pal	NOUN
ejpam-2332	587	15	.	.	PUNCT
ejpam-2332	588	1	application	application	NOUN
ejpam-2332	588	2	of	of	ADP
ejpam-2332	588	3	intuitionistic	intuitionistic	ADJ
ejpam-2332	588	4	fuzzy	fuzzy	ADJ
ejpam-2332	588	5	mathematical	mathematical	ADJ
ejpam-2332	588	6	programming	programming	NOUN
ejpam-2332	588	7	with	with	ADP
ejpam-2332	588	8	exponential	exponential	ADJ
ejpam-2332	588	9	membership	membership	NOUN
ejpam-2332	588	10	and	and	CCONJ
ejpam-2332	588	11	quadratic	quadratic	ADJ
ejpam-2332	588	12	non	non	ADJ
ejpam-2332	588	13	-	-	ADJ
ejpam-2332	588	14	membership	membership	ADJ
ejpam-2332	588	15	functions	function	NOUN
ejpam-2332	588	16	in	in	ADP
ejpam-2332	588	17	matrix	matrix	NOUN
ejpam-2332	588	18	games	game	NOUN
ejpam-2332	588	19	.	.	PUNCT
ejpam-2332	589	1	annals	annal	NOUN
ejpam-2332	589	2	of	of	ADP
ejpam-2332	589	3	fuzzy	fuzzy	ADJ
ejpam-2332	589	4	mathematics	mathematic	NOUN
ejpam-2332	589	5	and	and	CCONJ
ejpam-2332	589	6	informatics	informatic	NOUN
ejpam-2332	589	7	,	,	PUNCT
ejpam-2332	589	8	9(2):183	9(2):183	NUM
ejpam-2332	589	9	-	-	SYM
ejpam-2332	589	10	195	195	NUM
ejpam-2332	589	11	,	,	PUNCT
ejpam-2332	589	12	2015	2015	NUM
ejpam-2332	589	13	.	.	PUNCT
ejpam-2332	590	1	[	[	X
ejpam-2332	590	2	31	31	NUM
ejpam-2332	590	3	]	]	PUNCT
ejpam-2332	590	4	m.	m.	PROPN
ejpam-2332	590	5	r.	r.	PROPN
ejpam-2332	590	6	seikh	seikh	PROPN
ejpam-2332	590	7	,	,	PUNCT
ejpam-2332	590	8	p.	p.	PROPN
ejpam-2332	590	9	k.	k.	PROPN
ejpam-2332	591	1	nayak	nayak	PROPN
ejpam-2332	591	2	,	,	PUNCT
ejpam-2332	591	3	and	and	CCONJ
ejpam-2332	591	4	m.	m.	NOUN
ejpam-2332	591	5	pal	pal	PROPN
ejpam-2332	591	6	.	.	PROPN
ejpam-2332	591	7	matrix	matrix	NOUN
ejpam-2332	591	8	games	game	NOUN
ejpam-2332	591	9	with	with	ADP
ejpam-2332	591	10	intuitionistic	intuitionistic	ADJ
ejpam-2332	591	11	fuzzy	fuzzy	ADJ
ejpam-2332	591	12	pay	pay	NOUN
ejpam-2332	591	13	-	-	PUNCT
ejpam-2332	591	14	offs	off	NOUN
ejpam-2332	591	15	.	.	PUNCT
ejpam-2332	592	1	journal	journal	PROPN
ejpam-2332	592	2	of	of	ADP
ejpam-2332	592	3	information	information	NOUN
ejpam-2332	592	4	&	&	CCONJ
ejpam-2332	592	5	optimization	optimization	NOUN
ejpam-2332	592	6	sciences	science	NOUN
ejpam-2332	592	7	,	,	PUNCT
ejpam-2332	592	8	36(1	36(1	NUM
ejpam-2332	592	9	-	-	PUNCT
ejpam-2332	592	10	2):159	2):159	NUM
ejpam-2332	592	11	-	-	PUNCT
ejpam-2332	592	12	181	181	NUM
ejpam-2332	592	13	,	,	PUNCT
ejpam-2332	592	14	2015	2015	NUM
ejpam-2332	592	15	.	.	PUNCT
ejpam-2332	593	1	[	[	X
ejpam-2332	593	2	32	32	NUM
ejpam-2332	593	3	]	]	PUNCT
ejpam-2332	593	4	v.	v.	PROPN
ejpam-2332	593	5	vidyottama	vidyottama	PROPN
ejpam-2332	593	6	,	,	PUNCT
ejpam-2332	593	7	s.	s.	PROPN
ejpam-2332	593	8	chandra	chandra	PROPN
ejpam-2332	593	9	,	,	PUNCT
ejpam-2332	593	10	and	and	CCONJ
ejpam-2332	593	11	c.	c.	PROPN
ejpam-2332	593	12	r.	r.	PROPN
ejpam-2332	593	13	bector	bector	PROPN
ejpam-2332	593	14	.	.	PUNCT
ejpam-2332	594	1	bi	bi	ADJ
ejpam-2332	594	2	-	-	ADJ
ejpam-2332	594	3	matrix	matrix	NOUN
ejpam-2332	594	4	games	game	NOUN
ejpam-2332	594	5	with	with	ADP
ejpam-2332	594	6	fuzzy	fuzzy	ADJ
ejpam-2332	594	7	goals	goal	NOUN
ejpam-2332	594	8	and	and	CCONJ
ejpam-2332	594	9	fuzzy	fuzzy	ADJ
ejpam-2332	594	10	payoffs	payoff	NOUN
ejpam-2332	594	11	.	.	PUNCT
ejpam-2332	595	1	fuzzy	fuzzy	ADJ
ejpam-2332	595	2	opimization	opimization	NOUN
ejpam-2332	595	3	and	and	CCONJ
ejpam-2332	595	4	decision	decision	NOUN
ejpam-2332	595	5	making	making	NOUN
ejpam-2332	595	6	,	,	PUNCT
ejpam-2332	595	7	3:327	3:327	NUM
ejpam-2332	595	8	-	-	SYM
ejpam-2332	595	9	344	344	NUM
ejpam-2332	595	10	,	,	PUNCT
ejpam-2332	595	11	2004	2004	NUM
ejpam-2332	595	12	.	.	PUNCT
ejpam-2332	596	1	[	[	X
ejpam-2332	596	2	33	33	NUM
ejpam-2332	596	3	]	]	X
ejpam-2332	596	4	v.	v.	X
ejpam-2332	596	5	vijay	vijay	PROPN
ejpam-2332	596	6	,	,	PUNCT
ejpam-2332	596	7	s.	s.	PROPN
ejpam-2332	596	8	chandra	chandra	PROPN
ejpam-2332	596	9	,	,	PUNCT
ejpam-2332	596	10	and	and	CCONJ
ejpam-2332	596	11	c.	c.	PROPN
ejpam-2332	596	12	r.	r.	PROPN
ejpam-2332	596	13	bector	bector	PROPN
ejpam-2332	596	14	.	.	PUNCT
ejpam-2332	597	1	matrix	matrix	NOUN
ejpam-2332	597	2	games	game	NOUN
ejpam-2332	597	3	with	with	ADP
ejpam-2332	597	4	fuzzy	fuzzy	ADJ
ejpam-2332	597	5	goals	goal	NOUN
ejpam-2332	597	6	and	and	CCONJ
ejpam-2332	597	7	fuzzy	fuzzy	ADJ
ejpam-2332	597	8	payoffs	payoff	NOUN
ejpam-2332	597	9	.	.	PUNCT
ejpam-2332	598	1	omega	omega	NOUN
ejpam-2332	598	2	,	,	PUNCT
ejpam-2332	598	3	33(5):425	33(5):425	NUM
ejpam-2332	598	4	-	-	SYM
ejpam-2332	598	5	429	429	NUM
ejpam-2332	598	6	,	,	PUNCT
ejpam-2332	598	7	2005	2005	NUM
ejpam-2332	598	8	.	.	PUNCT
ejpam-2332	599	1	[	[	X
ejpam-2332	599	2	34	34	NUM
ejpam-2332	599	3	]	]	X
ejpam-2332	599	4	v.	v.	X
ejpam-2332	599	5	vijay	vijay	PROPN
ejpam-2332	599	6	,	,	PUNCT
ejpam-2332	599	7	a.	a.	PROPN
ejpam-2332	599	8	mehra	mehra	PROPN
ejpam-2332	599	9	,	,	PUNCT
ejpam-2332	599	10	s.	s.	PROPN
ejpam-2332	599	11	chandra	chandra	PROPN
ejpam-2332	599	12	,	,	PUNCT
ejpam-2332	599	13	and	and	CCONJ
ejpam-2332	599	14	c.	c.	PROPN
ejpam-2332	599	15	r.	r.	PROPN
ejpam-2332	599	16	bector	bector	PROPN
ejpam-2332	599	17	.	.	PUNCT
ejpam-2332	600	1	fuzzy	fuzzy	ADJ
ejpam-2332	600	2	matrix	matrix	NOUN
ejpam-2332	600	3	games	game	NOUN
ejpam-2332	600	4	via	via	ADP
ejpam-2332	600	5	a	a	DET
ejpam-2332	600	6	fuzzy	fuzzy	ADJ
ejpam-2332	600	7	ralation	ralation	NOUN
ejpam-2332	600	8	approach	approach	NOUN
ejpam-2332	600	9	.	.	PUNCT
ejpam-2332	601	1	fuzzy	fuzzy	ADJ
ejpam-2332	601	2	optimization	optimization	NOUN
ejpam-2332	601	3	and	and	CCONJ
ejpam-2332	601	4	decision	decision	NOUN
ejpam-2332	601	5	making	making	NOUN
ejpam-2332	601	6	,	,	PUNCT
ejpam-2332	601	7	6(4):299	6(4):299	NUM
ejpam-2332	601	8	-	-	SYM
ejpam-2332	601	9	314	314	NUM
ejpam-2332	601	10	,	,	PUNCT
ejpam-2332	601	11	2007	2007	NUM
ejpam-2332	601	12	.	.	PUNCT
ejpam-2332	602	1	[	[	X
ejpam-2332	602	2	35	35	NUM
ejpam-2332	602	3	]	]	PUNCT
ejpam-2332	602	4	x.	x.	NOUN
ejpam-2332	602	5	wang	wang	PROPN
ejpam-2332	602	6	and	and	CCONJ
ejpam-2332	602	7	e.	e.	PROPN
ejpam-2332	602	8	e.	e.	PROPN
ejpam-2332	602	9	kerre	kerre	PROPN
ejpam-2332	602	10	.	.	PUNCT
ejpam-2332	603	1	reasonable	reasonable	ADJ
ejpam-2332	603	2	properties	property	NOUN
ejpam-2332	603	3	for	for	ADP
ejpam-2332	603	4	the	the	DET
ejpam-2332	603	5	ordering	ordering	NOUN
ejpam-2332	603	6	of	of	ADP
ejpam-2332	603	7	fuzzy	fuzzy	ADJ
ejpam-2332	603	8	quantities(i	quantities(i	NOUN
ejpam-2332	603	9	)	)	PUNCT
ejpam-2332	603	10	.	.	PUNCT
ejpam-2332	604	1	fuzzy	fuzzy	ADJ
ejpam-2332	604	2	sets	set	NOUN
ejpam-2332	604	3	and	and	CCONJ
ejpam-2332	604	4	systems	system	NOUN
ejpam-2332	604	5	,	,	PUNCT
ejpam-2332	604	6	118:375	118:375	PROPN
ejpam-2332	604	7	-	-	SYM
ejpam-2332	604	8	385	385	NUM
ejpam-2332	604	9	,	,	PUNCT
ejpam-2332	604	10	2001	2001	NUM
ejpam-2332	604	11	.	.	PUNCT
ejpam-2332	605	1	[	[	X
ejpam-2332	605	2	36	36	NUM
ejpam-2332	605	3	]	]	X
ejpam-2332	605	4	l.	l.	PROPN
ejpam-2332	605	5	a.	a.	PROPN
ejpam-2332	605	6	zadeh	zadeh	PROPN
ejpam-2332	605	7	.	.	PUNCT
ejpam-2332	605	8	fuzzy	fuzzy	ADJ
ejpam-2332	605	9	sets	set	NOUN
ejpam-2332	605	10	.	.	PUNCT
ejpam-2332	606	1	information	information	NOUN
ejpam-2332	606	2	and	and	CCONJ
ejpam-2332	606	3	control	control	NOUN
ejpam-2332	606	4	,	,	PUNCT
ejpam-2332	606	5	8:338	8:338	NUM
ejpam-2332	606	6	-	-	SYM
ejpam-2332	606	7	352	352	NUM
ejpam-2332	606	8	,	,	PUNCT
ejpam-2332	606	9	1965	1965	NUM
ejpam-2332	606	10	.	.	PUNCT