id	sid	tid	token	lemma	pos
ejpam-522	1	1	9_522_cevikel.dvi	9_522_cevikel.dvi	NUM
ejpam-522	1	2	european	european	PROPN
ejpam-522	1	3	journal	journal	PROPN
ejpam-522	1	4	of	of	ADP
ejpam-522	1	5	pure	pure	ADJ
ejpam-522	1	6	and	and	CCONJ
ejpam-522	1	7	applied	apply	VERB
ejpam-522	1	8	mathematics	mathematic	NOUN
ejpam-522	1	9	vol	vol	NOUN
ejpam-522	1	10	.	.	PUNCT
ejpam-522	2	1	3	3	NUM
ejpam-522	2	2	,	,	PUNCT
ejpam-522	2	3	no	no	INTJ
ejpam-522	2	4	.	.	NOUN
ejpam-522	2	5	1	1	NUM
ejpam-522	2	6	,	,	PUNCT
ejpam-522	2	7	2010	2010	NUM
ejpam-522	2	8	,	,	PUNCT
ejpam-522	2	9	107	107	NUM
ejpam-522	2	10	-	-	SYM
ejpam-522	2	11	117	117	NUM
ejpam-522	2	12	issn	issn	PROPN
ejpam-522	2	13	1307	1307	NUM
ejpam-522	2	14	-	-	SYM
ejpam-522	2	15	5543	5543	NUM
ejpam-522	2	16	–	–	PUNCT
ejpam-522	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-522	2	18	a	a	DET
ejpam-522	2	19	linear	linear	ADJ
ejpam-522	2	20	interactive	interactive	ADJ
ejpam-522	2	21	solution	solution	NOUN
ejpam-522	2	22	concept	concept	NOUN
ejpam-522	2	23	for	for	ADP
ejpam-522	2	24	fuzzy	fuzzy	ADJ
ejpam-522	2	25	multiobjective	multiobjective	ADJ
ejpam-522	2	26	games	game	NOUN
ejpam-522	2	27	adem	adem	PROPN
ejpam-522	2	28	c.	c.	PROPN
ejpam-522	2	29	çevikel∗	çevikel∗	PROPN
ejpam-522	2	30	and	and	CCONJ
ejpam-522	2	31	mehmet	mehmet	PROPN
ejpam-522	2	32	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	2	33	yildiz	yildiz	PROPN
ejpam-522	2	34	technical	technical	PROPN
ejpam-522	2	35	university	university	PROPN
ejpam-522	2	36	,	,	PUNCT
ejpam-522	2	37	art	art	NOUN
ejpam-522	2	38	-	-	PUNCT
ejpam-522	2	39	science	science	NOUN
ejpam-522	2	40	faculty	faculty	NOUN
ejpam-522	2	41	,	,	PUNCT
ejpam-522	2	42	department	department	NOUN
ejpam-522	2	43	of	of	ADP
ejpam-522	2	44	mathematics	mathematics	PROPN
ejpam-522	2	45	,	,	PUNCT
ejpam-522	2	46	istanbul	istanbul	PROPN
ejpam-522	2	47	,	,	PUNCT
ejpam-522	2	48	turkey	turkey	PROPN
ejpam-522	2	49	abstract	abstract	NOUN
ejpam-522	2	50	.	.	PUNCT
ejpam-522	3	1	in	in	ADP
ejpam-522	3	2	this	this	DET
ejpam-522	3	3	paper	paper	NOUN
ejpam-522	3	4	,	,	PUNCT
ejpam-522	3	5	we	we	PRON
ejpam-522	3	6	deal	deal	VERB
ejpam-522	3	7	with	with	ADP
ejpam-522	3	8	multiobjective	multiobjective	ADJ
ejpam-522	3	9	two	two	NUM
ejpam-522	3	10	-	-	PUNCT
ejpam-522	3	11	person	person	NOUN
ejpam-522	3	12	zero	zero	NUM
ejpam-522	3	13	-	-	PUNCT
ejpam-522	3	14	sum	sum	NOUN
ejpam-522	3	15	games	game	NOUN
ejpam-522	3	16	with	with	ADP
ejpam-522	3	17	fuzzy	fuzzy	ADJ
ejpam-522	3	18	payoffs	payoff	NOUN
ejpam-522	3	19	and	and	CCONJ
ejpam-522	3	20	fuzzy	fuzzy	ADJ
ejpam-522	3	21	goals	goal	NOUN
ejpam-522	3	22	.	.	PUNCT
ejpam-522	4	1	the	the	DET
ejpam-522	4	2	aim	aim	NOUN
ejpam-522	4	3	of	of	ADP
ejpam-522	4	4	the	the	DET
ejpam-522	4	5	paper	paper	NOUN
ejpam-522	4	6	is	be	AUX
ejpam-522	4	7	to	to	PART
ejpam-522	4	8	explain	explain	VERB
ejpam-522	4	9	new	new	ADJ
ejpam-522	4	10	concepts	concept	NOUN
ejpam-522	4	11	of	of	ADP
ejpam-522	4	12	solutions	solution	NOUN
ejpam-522	4	13	for	for	ADP
ejpam-522	4	14	multiobjective	multiobjective	ADJ
ejpam-522	4	15	two	two	NUM
ejpam-522	4	16	-	-	PUNCT
ejpam-522	4	17	person	person	NOUN
ejpam-522	4	18	zero	zero	NUM
ejpam-522	4	19	-	-	PUNCT
ejpam-522	4	20	sum	sum	NOUN
ejpam-522	4	21	games	game	NOUN
ejpam-522	4	22	with	with	ADP
ejpam-522	4	23	fuzzy	fuzzy	ADJ
ejpam-522	4	24	payoffs	payoff	NOUN
ejpam-522	4	25	and	and	CCONJ
ejpam-522	4	26	fuzzy	fuzzy	ADJ
ejpam-522	4	27	goals	goal	NOUN
ejpam-522	4	28	.	.	PUNCT
ejpam-522	5	1	we	we	PRON
ejpam-522	5	2	assume	assume	VERB
ejpam-522	5	3	that	that	SCONJ
ejpam-522	5	4	each	each	DET
ejpam-522	5	5	player	player	NOUN
ejpam-522	5	6	has	have	VERB
ejpam-522	5	7	a	a	DET
ejpam-522	5	8	fuzzy	fuzzy	ADJ
ejpam-522	5	9	goal	goal	NOUN
ejpam-522	5	10	for	for	ADP
ejpam-522	5	11	each	each	PRON
ejpam-522	5	12	of	of	ADP
ejpam-522	5	13	the	the	DET
ejpam-522	5	14	payoffs	payoff	NOUN
ejpam-522	5	15	.	.	PUNCT
ejpam-522	6	1	a	a	DET
ejpam-522	6	2	degree	degree	NOUN
ejpam-522	6	3	of	of	ADP
ejpam-522	6	4	attainment	attainment	NOUN
ejpam-522	6	5	of	of	ADP
ejpam-522	6	6	the	the	DET
ejpam-522	6	7	fuzzy	fuzzy	ADJ
ejpam-522	6	8	goal	goal	NOUN
ejpam-522	6	9	is	be	AUX
ejpam-522	6	10	defined	define	VERB
ejpam-522	6	11	and	and	CCONJ
ejpam-522	6	12	the	the	DET
ejpam-522	6	13	max	max	PROPN
ejpam-522	6	14	-	-	PUNCT
ejpam-522	6	15	min	min	NOUN
ejpam-522	6	16	strategy	strategy	NOUN
ejpam-522	6	17	with	with	ADP
ejpam-522	6	18	respect	respect	NOUN
ejpam-522	6	19	to	to	ADP
ejpam-522	6	20	the	the	DET
ejpam-522	6	21	degree	degree	NOUN
ejpam-522	6	22	of	of	ADP
ejpam-522	6	23	attainment	attainment	NOUN
ejpam-522	6	24	of	of	ADP
ejpam-522	6	25	the	the	DET
ejpam-522	6	26	fuzzy	fuzzy	ADJ
ejpam-522	6	27	goal	goal	NOUN
ejpam-522	6	28	is	be	AUX
ejpam-522	6	29	examined	examine	VERB
ejpam-522	6	30	.	.	PUNCT
ejpam-522	7	1	if	if	SCONJ
ejpam-522	7	2	all	all	PRON
ejpam-522	7	3	of	of	ADP
ejpam-522	7	4	the	the	DET
ejpam-522	7	5	membership	membership	NOUN
ejpam-522	7	6	functions	function	NOUN
ejpam-522	7	7	both	both	PRON
ejpam-522	7	8	for	for	ADP
ejpam-522	7	9	the	the	DET
ejpam-522	7	10	fuzzy	fuzzy	ADJ
ejpam-522	7	11	payoffs	payoff	NOUN
ejpam-522	7	12	and	and	CCONJ
ejpam-522	7	13	for	for	ADP
ejpam-522	7	14	the	the	DET
ejpam-522	7	15	fuzzy	fuzzy	ADJ
ejpam-522	7	16	goals	goal	NOUN
ejpam-522	7	17	are	be	AUX
ejpam-522	7	18	linear	linear	ADJ
ejpam-522	7	19	,	,	PUNCT
ejpam-522	7	20	the	the	DET
ejpam-522	7	21	max	max	PROPN
ejpam-522	7	22	-	-	PUNCT
ejpam-522	7	23	min	min	NOUN
ejpam-522	7	24	solution	solution	NOUN
ejpam-522	7	25	is	be	AUX
ejpam-522	7	26	formulated	formulate	VERB
ejpam-522	7	27	as	as	ADP
ejpam-522	7	28	a	a	DET
ejpam-522	7	29	nonlinear	nonlinear	ADJ
ejpam-522	7	30	programming	programming	NOUN
ejpam-522	7	31	problem	problem	NOUN
ejpam-522	7	32	.	.	PUNCT
ejpam-522	8	1	the	the	DET
ejpam-522	8	2	problem	problem	NOUN
ejpam-522	8	3	can	can	AUX
ejpam-522	8	4	be	be	AUX
ejpam-522	8	5	reduced	reduce	VERB
ejpam-522	8	6	to	to	ADP
ejpam-522	8	7	a	a	DET
ejpam-522	8	8	linear	linear	ADJ
ejpam-522	8	9	programming	programming	NOUN
ejpam-522	8	10	problem	problem	NOUN
ejpam-522	8	11	by	by	ADP
ejpam-522	8	12	making	make	VERB
ejpam-522	8	13	use	use	NOUN
ejpam-522	8	14	of	of	ADP
ejpam-522	8	15	sakawa	sakawa	PROPN
ejpam-522	8	16	’s	’s	PART
ejpam-522	8	17	method	method	NOUN
ejpam-522	8	18	,	,	PUNCT
ejpam-522	8	19	the	the	DET
ejpam-522	8	20	variable	variable	ADJ
ejpam-522	8	21	transformation	transformation	NOUN
ejpam-522	8	22	by	by	ADP
ejpam-522	8	23	charnes	charne	NOUN
ejpam-522	8	24	and	and	CCONJ
ejpam-522	8	25	cooper	cooper	NOUN
ejpam-522	8	26	and	and	CCONJ
ejpam-522	8	27	the	the	DET
ejpam-522	8	28	relaxation	relaxation	NOUN
ejpam-522	8	29	procedure	procedure	NOUN
ejpam-522	8	30	.	.	PUNCT
ejpam-522	9	1	2000	2000	NUM
ejpam-522	9	2	mathematics	mathematic	NOUN
ejpam-522	9	3	subject	subject	NOUN
ejpam-522	9	4	classifications	classification	NOUN
ejpam-522	9	5	:	:	PUNCT
ejpam-522	9	6	03e72	03e72	NUM
ejpam-522	9	7	,	,	PUNCT
ejpam-522	9	8	91a05	91a05	NUM
ejpam-522	9	9	,	,	PUNCT
ejpam-522	9	10	91a80	91a80	NUM
ejpam-522	9	11	key	key	ADJ
ejpam-522	9	12	words	word	NOUN
ejpam-522	9	13	and	and	CCONJ
ejpam-522	9	14	phrases	phrase	NOUN
ejpam-522	9	15	:	:	PUNCT
ejpam-522	9	16	agragated	agragate	VERB
ejpam-522	9	17	fuzzy	fuzzy	ADJ
ejpam-522	9	18	goal	goal	NOUN
ejpam-522	9	19	;	;	PUNCT
ejpam-522	9	20	fuzzy	fuzzy	ADJ
ejpam-522	9	21	numbers	number	NOUN
ejpam-522	9	22	;	;	PUNCT
ejpam-522	9	23	fuzzy	fuzzy	ADJ
ejpam-522	9	24	payoff	payoff	NOUN
ejpam-522	9	25	matrix	matrix	NOUN
ejpam-522	9	26	;	;	PUNCT
ejpam-522	9	27	nonlinear	nonlinear	ADJ
ejpam-522	9	28	programming	programming	NOUN
ejpam-522	9	29	problem;max	problem;max	PROPN
ejpam-522	9	30	-	-	PUNCT
ejpam-522	9	31	min	min	NOUN
ejpam-522	9	32	solution	solution	NOUN
ejpam-522	9	33	;	;	PUNCT
ejpam-522	9	34	multiple	multiple	ADJ
ejpam-522	9	35	payoff	payoff	NOUN
ejpam-522	9	36	matrices	matrix	NOUN
ejpam-522	9	37	;	;	PUNCT
ejpam-522	9	38	relaxation	relaxation	NOUN
ejpam-522	9	39	procedure	procedure	NOUN
ejpam-522	9	40	;	;	PUNCT
ejpam-522	9	41	two	two	NUM
ejpam-522	9	42	-	-	PUNCT
ejpam-522	9	43	person	person	NOUN
ejpam-522	9	44	zero	zero	NUM
ejpam-522	9	45	-	-	PUNCT
ejpam-522	9	46	sum	sum	NOUN
ejpam-522	9	47	games	game	NOUN
ejpam-522	9	48	.	.	PUNCT
ejpam-522	10	1	1	1	X
ejpam-522	10	2	.	.	X
ejpam-522	10	3	introduction	introduction	NOUN
ejpam-522	10	4	we	we	PRON
ejpam-522	10	5	consider	consider	VERB
ejpam-522	10	6	multiobjective	multiobjective	ADJ
ejpam-522	10	7	two	two	NUM
ejpam-522	10	8	-	-	PUNCT
ejpam-522	10	9	person	person	NOUN
ejpam-522	10	10	zero	zero	NUM
ejpam-522	10	11	-	-	PUNCT
ejpam-522	10	12	sum	sum	NOUN
ejpam-522	10	13	games	game	NOUN
ejpam-522	10	14	with	with	ADP
ejpam-522	10	15	fuzzy	fuzzy	ADJ
ejpam-522	10	16	payoffs	payoff	NOUN
ejpam-522	10	17	and	and	CCONJ
ejpam-522	10	18	fuzzy	fuzzy	ADJ
ejpam-522	10	19	goals.a	goals.a	NOUN
ejpam-522	10	20	payoff	payoff	NOUN
ejpam-522	10	21	matrix	matrix	NOUN
ejpam-522	10	22	with	with	ADP
ejpam-522	10	23	elements	element	NOUN
ejpam-522	10	24	represented	represent	VERB
ejpam-522	10	25	as	as	ADP
ejpam-522	10	26	fuzzy	fuzzy	ADJ
ejpam-522	10	27	payoff	payoff	NOUN
ejpam-522	10	28	matrix	matrix	NOUN
ejpam-522	10	29	.	.	PUNCT
ejpam-522	11	1	for	for	ADP
ejpam-522	11	2	any	any	DET
ejpam-522	11	3	pair	pair	NOUN
ejpam-522	11	4	of	of	ADP
ejpam-522	11	5	strategies	strategy	NOUN
ejpam-522	11	6	,	,	PUNCT
ejpam-522	11	7	a	a	DET
ejpam-522	11	8	player	player	NOUN
ejpam-522	11	9	receives	receive	VERB
ejpam-522	11	10	a	a	DET
ejpam-522	11	11	payoff	payoff	NOUN
ejpam-522	11	12	represented	represent	VERB
ejpam-522	11	13	as	as	ADP
ejpam-522	11	14	a	a	DET
ejpam-522	11	15	fuzzy	fuzzy	ADJ
ejpam-522	11	16	number	number	NOUN
ejpam-522	11	17	,	,	PUNCT
ejpam-522	11	18	i.e.	i.e.	X
ejpam-522	11	19	,	,	PUNCT
ejpam-522	11	20	the	the	DET
ejpam-522	11	21	strategy	strategy	NOUN
ejpam-522	11	22	itself	itself	PRON
ejpam-522	11	23	is	be	AUX
ejpam-522	11	24	not	not	PART
ejpam-522	11	25	fuzzy	fuzzy	ADJ
ejpam-522	11	26	but	but	CCONJ
ejpam-522	11	27	the	the	DET
ejpam-522	11	28	payoffs	payoff	NOUN
ejpam-522	11	29	are	be	AUX
ejpam-522	11	30	fuzzy	fuzzy	ADJ
ejpam-522	11	31	.	.	PUNCT
ejpam-522	12	1	for	for	ADP
ejpam-522	12	2	example	example	NOUN
ejpam-522	12	3	,	,	PUNCT
ejpam-522	12	4	when	when	SCONJ
ejpam-522	12	5	a	a	DET
ejpam-522	12	6	payoff	payoff	NOUN
ejpam-522	12	7	matrix	matrix	NOUN
ejpam-522	12	8	of	of	ADP
ejpam-522	12	9	a	a	DET
ejpam-522	12	10	game	game	NOUN
ejpam-522	12	11	is	be	AUX
ejpam-522	12	12	constructed	construct	VERB
ejpam-522	12	13	by	by	ADP
ejpam-522	12	14	information	information	NOUN
ejpam-522	12	15	from	from	ADP
ejpam-522	12	16	a	a	DET
ejpam-522	12	17	competitive	competitive	ADJ
ejpam-522	12	18	system	system	NOUN
ejpam-522	12	19	,	,	PUNCT
ejpam-522	12	20	elements	element	NOUN
ejpam-522	12	21	of	of	ADP
ejpam-522	12	22	the	the	DET
ejpam-522	12	23	payoff	payoff	NOUN
ejpam-522	12	24	matrix	matrix	NOUN
ejpam-522	12	25	would	would	AUX
ejpam-522	12	26	be	be	AUX
ejpam-522	12	27	ambiguous	ambiguous	ADJ
ejpam-522	12	28	if	if	SCONJ
ejpam-522	12	29	imprecision	imprecision	NOUN
ejpam-522	12	30	or	or	CCONJ
ejpam-522	12	31	vagueness	vagueness	NOUN
ejpam-522	12	32	exists	exist	VERB
ejpam-522	12	33	in	in	ADP
ejpam-522	12	34	the	the	DET
ejpam-522	12	35	information	information	NOUN
ejpam-522	12	36	.	.	PUNCT
ejpam-522	13	1	this	this	DET
ejpam-522	13	2	paper	paper	NOUN
ejpam-522	13	3	is	be	AUX
ejpam-522	13	4	related	relate	VERB
ejpam-522	13	5	to	to	ADP
ejpam-522	13	6	the	the	DET
ejpam-522	13	7	research	research	NOUN
ejpam-522	13	8	fields	field	NOUN
ejpam-522	13	9	both	both	PRON
ejpam-522	13	10	of	of	ADP
ejpam-522	13	11	multiobjective	multiobjective	ADJ
ejpam-522	13	12	games	game	NOUN
ejpam-522	13	13	and	and	CCONJ
ejpam-522	13	14	fuzzy	fuzzy	ADJ
ejpam-522	13	15	games	game	NOUN
ejpam-522	13	16	.	.	PUNCT
ejpam-522	14	1	most	most	ADJ
ejpam-522	14	2	of	of	ADP
ejpam-522	14	3	the	the	DET
ejpam-522	14	4	studies	study	NOUN
ejpam-522	14	5	on	on	ADP
ejpam-522	14	6	multiobjective	multiobjective	ADJ
ejpam-522	14	7	games	game	NOUN
ejpam-522	14	8	are	be	AUX
ejpam-522	14	9	on	on	ADP
ejpam-522	14	10	two	two	NUM
ejpam-522	14	11	-	-	PUNCT
ejpam-522	14	12	person	person	NOUN
ejpam-522	14	13	games	game	NOUN
ejpam-522	14	14	[	[	X
ejpam-522	14	15	5	5	NUM
ejpam-522	14	16	,	,	PUNCT
ejpam-522	14	17	11	11	NUM
ejpam-522	14	18	,	,	PUNCT
ejpam-522	14	19	13	13	NUM
ejpam-522	14	20	,	,	PUNCT
ejpam-522	14	21	20	20	NUM
ejpam-522	14	22	]	]	PUNCT
ejpam-522	14	23	but	but	CCONJ
ejpam-522	14	24	recently	recently	ADV
ejpam-522	14	25	a	a	DET
ejpam-522	14	26	couple	couple	NOUN
ejpam-522	14	27	of	of	ADP
ejpam-522	14	28	articles	article	NOUN
ejpam-522	14	29	have	have	AUX
ejpam-522	14	30	been	be	AUX
ejpam-522	14	31	devoted	devote	VERB
ejpam-522	14	32	to	to	ADP
ejpam-522	14	33	the	the	DET
ejpam-522	14	34	studies	study	NOUN
ejpam-522	14	35	of	of	ADP
ejpam-522	14	36	n	n	CCONJ
ejpam-522	14	37	-	-	PUNCT
ejpam-522	14	38	person	person	NOUN
ejpam-522	14	39	multiobjective	multiobjective	ADJ
ejpam-522	14	40	games	game	NOUN
ejpam-522	15	1	[	[	X
ejpam-522	15	2	10	10	NUM
ejpam-522	15	3	,	,	PUNCT
ejpam-522	15	4	21	21	NUM
ejpam-522	15	5	]	]	PUNCT
ejpam-522	15	6	.	.	PUNCT
ejpam-522	16	1	the	the	DET
ejpam-522	16	2	research	research	NOUN
ejpam-522	16	3	on	on	ADP
ejpam-522	16	4	fuzzy	fuzzy	ADJ
ejpam-522	16	5	games	game	NOUN
ejpam-522	16	6	has	have	AUX
ejpam-522	16	7	been	be	AUX
ejpam-522	16	8	develop	develop	ADJ
ejpam-522	16	9	by	by	ADP
ejpam-522	16	10	aubin	aubin	PROPN
ejpam-522	17	1	[	[	X
ejpam-522	17	2	1	1	NUM
ejpam-522	17	3	,	,	PUNCT
ejpam-522	17	4	2	2	NUM
ejpam-522	17	5	]	]	PUNCT
ejpam-522	17	6	and	and	CCONJ
ejpam-522	17	7	butnariu	butnariu	X
ejpam-522	17	8	[	[	X
ejpam-522	17	9	6	6	NUM
ejpam-522	17	10	,	,	PUNCT
ejpam-522	17	11	7	7	NUM
ejpam-522	17	12	]	]	PUNCT
ejpam-522	17	13	.	.	PUNCT
ejpam-522	18	1	recently	recently	ADV
ejpam-522	18	2	,	,	PUNCT
ejpam-522	18	3	campos	campos	PROPN
ejpam-522	18	4	[	[	X
ejpam-522	18	5	8	8	NUM
ejpam-522	18	6	]	]	PUNCT
ejpam-522	18	7	has	have	AUX
ejpam-522	18	8	explored	explore	VERB
ejpam-522	18	9	∗corresponding	∗corresponde	VERB
ejpam-522	18	10	author	author	NOUN
ejpam-522	18	11	.	.	PUNCT
ejpam-522	19	1	email	email	NOUN
ejpam-522	19	2	addresses	address	NOUN
ejpam-522	19	3	:	:	PUNCT
ejpam-522	19	4	a	a	DET
ejpam-522	19	5	evikel�yildiz.edu.tr	evikel�yildiz.edu.tr	PROPN
ejpam-522	19	6	(	(	PUNCT
ejpam-522	19	7	a.	a.	NOUN
ejpam-522	19	8	çevikel	çevikel	PROPN
ejpam-522	19	9	)	)	PUNCT
ejpam-522	19	10	,	,	PUNCT
ejpam-522	19	11	mahlat	mahlat	ADJ
ejpam-522	19	12	i�yildiz.edu.tr	i�yildiz.edu.tr	PROPN
ejpam-522	19	13	(	(	PUNCT
ejpam-522	19	14	m.	m.	PROPN
ejpam-522	19	15	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	19	16	)	)	PUNCT
ejpam-522	19	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-522	20	1	107	107	NUM
ejpam-522	20	2	c	c	X
ejpam-522	20	3	©	©	PROPN
ejpam-522	20	4	2009	2009	NUM
ejpam-522	20	5	ejpam	ejpam	NOUN
ejpam-522	20	6	all	all	DET
ejpam-522	20	7	rights	right	NOUN
ejpam-522	20	8	reserved	reserve	VERB
ejpam-522	20	9	.	.	PUNCT
ejpam-522	21	1	a.	a.	NOUN
ejpam-522	21	2	çevikel	çevikel	PROPN
ejpam-522	21	3	,	,	PUNCT
ejpam-522	21	4	m.	m.	PROPN
ejpam-522	21	5	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	21	6	/	/	SYM
ejpam-522	21	7	eur	eur	PROPN
ejpam-522	21	8	.	.	PUNCT
ejpam-522	22	1	j.	j.	PROPN
ejpam-522	22	2	pure	pure	PROPN
ejpam-522	22	3	appl	appl	PROPN
ejpam-522	22	4	.	.	PROPN
ejpam-522	22	5	math	math	PROPN
ejpam-522	22	6	,	,	PUNCT
ejpam-522	22	7	3	3	NUM
ejpam-522	22	8	(	(	PUNCT
ejpam-522	22	9	2010	2010	NUM
ejpam-522	22	10	)	)	PUNCT
ejpam-522	22	11	,	,	PUNCT
ejpam-522	22	12	107	107	NUM
ejpam-522	22	13	-	-	SYM
ejpam-522	22	14	117	117	NUM
ejpam-522	22	15	108	108	NUM
ejpam-522	22	16	zero	zero	NUM
ejpam-522	22	17	-	-	PUNCT
ejpam-522	22	18	sum	sum	NOUN
ejpam-522	22	19	fuzzy	fuzzy	ADJ
ejpam-522	22	20	matrix	matrix	NOUN
ejpam-522	22	21	game	game	NOUN
ejpam-522	22	22	.	.	PUNCT
ejpam-522	23	1	the	the	DET
ejpam-522	23	2	problem	problem	NOUN
ejpam-522	23	3	treated	treat	VERB
ejpam-522	23	4	by	by	ADP
ejpam-522	23	5	campos	campos	PROPN
ejpam-522	23	6	was	be	AUX
ejpam-522	23	7	a	a	DET
ejpam-522	23	8	game	game	NOUN
ejpam-522	23	9	with	with	ADP
ejpam-522	23	10	a	a	DET
ejpam-522	23	11	single	single	ADJ
ejpam-522	23	12	payoff	payoff	NOUN
ejpam-522	23	13	,	,	PUNCT
ejpam-522	23	14	and	and	CCONJ
ejpam-522	23	15	the	the	DET
ejpam-522	23	16	min	min	PROPN
ejpam-522	23	17	-	-	ADJ
ejpam-522	23	18	max	max	PROPN
ejpam-522	23	19	problem	problem	NOUN
ejpam-522	23	20	was	be	AUX
ejpam-522	23	21	formulated	formulate	VERB
ejpam-522	23	22	using	use	VERB
ejpam-522	23	23	the	the	DET
ejpam-522	23	24	fuzzy	fuzzy	ADJ
ejpam-522	23	25	mathematical	mathematical	ADJ
ejpam-522	23	26	programming	programming	NOUN
ejpam-522	23	27	method	method	NOUN
ejpam-522	23	28	.	.	PUNCT
ejpam-522	24	1	moreover	moreover	ADV
ejpam-522	24	2	,	,	PUNCT
ejpam-522	24	3	sakawa	sakawa	NOUN
ejpam-522	24	4	and	and	CCONJ
ejpam-522	24	5	nishizaki	nishizaki	NOUN
ejpam-522	24	6	[	[	X
ejpam-522	24	7	14	14	NUM
ejpam-522	24	8	,	,	PUNCT
ejpam-522	24	9	17	17	NUM
ejpam-522	24	10	]	]	PUNCT
ejpam-522	24	11	have	have	AUX
ejpam-522	24	12	explored	explore	VERB
ejpam-522	24	13	zero	zero	NUM
ejpam-522	24	14	-	-	PUNCT
ejpam-522	24	15	sum	sum	NOUN
ejpam-522	24	16	multiobjective	multiobjective	ADJ
ejpam-522	24	17	fuzzy	fuzzy	ADJ
ejpam-522	24	18	matrix	matrix	NOUN
ejpam-522	24	19	games	game	NOUN
ejpam-522	24	20	.	.	PUNCT
ejpam-522	25	1	in	in	ADP
ejpam-522	25	2	this	this	DET
ejpam-522	25	3	paper	paper	NOUN
ejpam-522	25	4	,	,	PUNCT
ejpam-522	25	5	a	a	DET
ejpam-522	25	6	new	new	ADJ
ejpam-522	25	7	solution	solution	NOUN
ejpam-522	25	8	concept	concept	NOUN
ejpam-522	25	9	in	in	ADP
ejpam-522	25	10	a	a	DET
ejpam-522	25	11	two	two	NUM
ejpam-522	25	12	-	-	PUNCT
ejpam-522	25	13	person	person	NOUN
ejpam-522	25	14	zero	zero	NUM
ejpam-522	25	15	-	-	PUNCT
ejpam-522	25	16	sum	sum	NOUN
ejpam-522	25	17	multiobjective	multiobjective	ADJ
ejpam-522	25	18	fuzzy	fuzzy	ADJ
ejpam-522	25	19	matrix	matrix	NOUN
ejpam-522	25	20	game	game	NOUN
ejpam-522	25	21	is	be	AUX
ejpam-522	25	22	proposed	propose	VERB
ejpam-522	25	23	.	.	PUNCT
ejpam-522	26	1	in	in	ADP
ejpam-522	26	2	section	section	NOUN
ejpam-522	26	3	2	2	NUM
ejpam-522	26	4	,	,	PUNCT
ejpam-522	26	5	a	a	DET
ejpam-522	26	6	fuzzy	fuzzy	ADJ
ejpam-522	26	7	expected	expect	VERB
ejpam-522	26	8	payoff	payoff	NOUN
ejpam-522	26	9	is	be	AUX
ejpam-522	26	10	defined	define	VERB
ejpam-522	26	11	,	,	PUNCT
ejpam-522	26	12	and	and	CCONJ
ejpam-522	26	13	a	a	DET
ejpam-522	26	14	degree	degree	NOUN
ejpam-522	26	15	of	of	ADP
ejpam-522	26	16	attainment	attainment	NOUN
ejpam-522	26	17	of	of	ADP
ejpam-522	26	18	a	a	DET
ejpam-522	26	19	fuzzy	fuzzy	ADJ
ejpam-522	26	20	goal	goal	NOUN
ejpam-522	26	21	is	be	AUX
ejpam-522	26	22	considered	consider	VERB
ejpam-522	26	23	in	in	ADP
ejpam-522	26	24	games	game	NOUN
ejpam-522	26	25	with	with	ADP
ejpam-522	26	26	fuzzy	fuzzy	ADJ
ejpam-522	26	27	payoff	payoff	NOUN
ejpam-522	26	28	matrices	matrix	NOUN
ejpam-522	26	29	.	.	PUNCT
ejpam-522	27	1	the	the	DET
ejpam-522	27	2	max	max	PROPN
ejpam-522	27	3	-	-	PUNCT
ejpam-522	27	4	min	min	NOUN
ejpam-522	27	5	solution	solution	NOUN
ejpam-522	27	6	with	with	ADP
ejpam-522	27	7	respect	respect	NOUN
ejpam-522	27	8	to	to	ADP
ejpam-522	27	9	a	a	DET
ejpam-522	27	10	degree	degree	NOUN
ejpam-522	27	11	of	of	ADP
ejpam-522	27	12	attainment	attainment	NOUN
ejpam-522	27	13	of	of	ADP
ejpam-522	27	14	a	a	DET
ejpam-522	27	15	fuzzy	fuzzy	ADJ
ejpam-522	27	16	goal	goal	NOUN
ejpam-522	27	17	is	be	AUX
ejpam-522	27	18	also	also	ADV
ejpam-522	27	19	defined	define	VERB
ejpam-522	27	20	.	.	PUNCT
ejpam-522	28	1	in	in	ADP
ejpam-522	28	2	section	section	NOUN
ejpam-522	28	3	3	3	NUM
ejpam-522	28	4	,	,	PUNCT
ejpam-522	28	5	the	the	DET
ejpam-522	28	6	method	method	NOUN
ejpam-522	28	7	for	for	ADP
ejpam-522	28	8	computing	compute	VERB
ejpam-522	28	9	the	the	DET
ejpam-522	28	10	solution	solution	NOUN
ejpam-522	28	11	of	of	ADP
ejpam-522	28	12	a	a	DET
ejpam-522	28	13	multiobjective	multiobjective	ADJ
ejpam-522	28	14	game	game	NOUN
ejpam-522	28	15	is	be	AUX
ejpam-522	28	16	proposed	propose	VERB
ejpam-522	28	17	when	when	SCONJ
ejpam-522	28	18	membership	membership	NOUN
ejpam-522	28	19	functions	function	NOUN
ejpam-522	28	20	of	of	ADP
ejpam-522	28	21	fuzzy	fuzzy	ADJ
ejpam-522	28	22	goals	goal	NOUN
ejpam-522	28	23	and	and	CCONJ
ejpam-522	28	24	shape	shape	NOUN
ejpam-522	28	25	functions	function	NOUN
ejpam-522	28	26	of	of	ADP
ejpam-522	28	27	l	l	NOUN
ejpam-522	28	28	-	-	NOUN
ejpam-522	28	29	r	r	NOUN
ejpam-522	28	30	fuzzy	fuzzy	ADJ
ejpam-522	28	31	numbers	number	NOUN
ejpam-522	28	32	for	for	ADP
ejpam-522	28	33	fuzzy	fuzzy	ADJ
ejpam-522	28	34	payoffs	payoff	NOUN
ejpam-522	28	35	are	be	AUX
ejpam-522	28	36	linear	linear	ADJ
ejpam-522	28	37	.	.	PUNCT
ejpam-522	29	1	cook	cook	PROPN
ejpam-522	29	2	’s	’s	PART
ejpam-522	29	3	example	example	NOUN
ejpam-522	30	1	[	[	X
ejpam-522	30	2	12	12	NUM
ejpam-522	30	3	]	]	PUNCT
ejpam-522	30	4	for	for	ADP
ejpam-522	30	5	computing	compute	VERB
ejpam-522	30	6	the	the	DET
ejpam-522	30	7	max	max	PROPN
ejpam-522	30	8	-	-	PUNCT
ejpam-522	30	9	min	min	NOUN
ejpam-522	30	10	solution	solution	NOUN
ejpam-522	30	11	is	be	AUX
ejpam-522	30	12	formulated	formulate	VERB
ejpam-522	30	13	as	as	ADP
ejpam-522	30	14	a	a	DET
ejpam-522	30	15	nonlinear	nonlinear	ADJ
ejpam-522	30	16	programming	programming	NOUN
ejpam-522	30	17	problem	problem	NOUN
ejpam-522	30	18	,	,	PUNCT
ejpam-522	30	19	but	but	CCONJ
ejpam-522	30	20	it	it	PRON
ejpam-522	30	21	can	can	AUX
ejpam-522	30	22	be	be	AUX
ejpam-522	30	23	transformed	transform	VERB
ejpam-522	30	24	to	to	ADP
ejpam-522	30	25	a	a	DET
ejpam-522	30	26	linear	linear	ADJ
ejpam-522	30	27	programming	programming	NOUN
ejpam-522	30	28	problem	problem	NOUN
ejpam-522	30	29	by	by	ADP
ejpam-522	30	30	making	make	VERB
ejpam-522	30	31	use	use	NOUN
ejpam-522	30	32	of	of	ADP
ejpam-522	30	33	the	the	DET
ejpam-522	30	34	sakawa	sakawa	PROPN
ejpam-522	30	35	’s	’s	PART
ejpam-522	30	36	method	method	NOUN
ejpam-522	31	1	[	[	X
ejpam-522	31	2	18	18	NUM
ejpam-522	31	3	]	]	PUNCT
ejpam-522	31	4	,	,	PUNCT
ejpam-522	31	5	by	by	ADP
ejpam-522	31	6	using	use	VERB
ejpam-522	31	7	the	the	DET
ejpam-522	31	8	variable	variable	ADJ
ejpam-522	31	9	transformation	transformation	NOUN
ejpam-522	31	10	by	by	ADP
ejpam-522	31	11	charnes	charne	NOUN
ejpam-522	31	12	and	and	CCONJ
ejpam-522	31	13	cooper	cooper	NOUN
ejpam-522	32	1	[	[	X
ejpam-522	32	2	9	9	NUM
ejpam-522	32	3	]	]	PUNCT
ejpam-522	32	4	and	and	CCONJ
ejpam-522	32	5	the	the	DET
ejpam-522	32	6	relaxtion	relaxtion	NOUN
ejpam-522	32	7	procedure	procedure	NOUN
ejpam-522	32	8	[	[	X
ejpam-522	32	9	19	19	NUM
ejpam-522	32	10	]	]	PUNCT
ejpam-522	32	11	.	.	PUNCT
ejpam-522	33	1	2	2	X
ejpam-522	33	2	.	.	X
ejpam-522	33	3	background	background	NOUN
ejpam-522	33	4	definition	definition	NOUN
ejpam-522	33	5	1	1	NUM
ejpam-522	33	6	(	(	PUNCT
ejpam-522	33	7	zero	zero	NUM
ejpam-522	33	8	-	-	PUNCT
ejpam-522	33	9	sum	sum	NOUN
ejpam-522	33	10	game	game	NOUN
ejpam-522	33	11	with	with	ADP
ejpam-522	33	12	fuzzy	fuzzy	ADJ
ejpam-522	33	13	payoffs	payoff	NOUN
ejpam-522	33	14	)	)	PUNCT
ejpam-522	33	15	.	.	PUNCT
ejpam-522	34	1	when	when	SCONJ
ejpam-522	34	2	player	player	NOUN
ejpam-522	34	3	i	i	PRON
ejpam-522	34	4	chooses	choose	VERB
ejpam-522	34	5	a	a	DET
ejpam-522	34	6	pure	pure	ADJ
ejpam-522	34	7	strategy	strategy	NOUN
ejpam-522	34	8	i	i	PRON
ejpam-522	34	9	∈	∈	VERB
ejpam-522	35	1	i	i	PRON
ejpam-522	35	2	and	and	CCONJ
ejpam-522	35	3	player	player	NOUN
ejpam-522	36	1	i	i	PRON
ejpam-522	36	2	i	i	PRON
ejpam-522	36	3	chooses	choose	VERB
ejpam-522	36	4	a	a	DET
ejpam-522	36	5	pure	pure	ADJ
ejpam-522	36	6	strategy	strategy	NOUN
ejpam-522	36	7	j	j	PROPN
ejpam-522	36	8	∈	∈	PROPN
ejpam-522	36	9	j	j	PROPN
ejpam-522	36	10	,	,	PUNCT
ejpam-522	36	11	let	let	VERB
ejpam-522	36	12	eai	eai	PROPN
ejpam-522	36	13	j	j	PROPN
ejpam-522	36	14	be	be	AUX
ejpam-522	36	15	fuzzy	fuzzy	ADJ
ejpam-522	36	16	payoff	payoff	NOUN
ejpam-522	36	17	for	for	ADP
ejpam-522	36	18	player	player	NOUN
ejpam-522	36	19	i	i	PRON
ejpam-522	36	20	and	and	CCONJ
ejpam-522	36	21	−eai	−eai	PROPN
ejpam-522	36	22	j	j	PROPN
ejpam-522	36	23	be	be	VERB
ejpam-522	36	24	a	a	DET
ejpam-522	36	25	fuzzy	fuzzy	ADJ
ejpam-522	36	26	payoff	payoff	NOUN
ejpam-522	36	27	for	for	ADP
ejpam-522	36	28	player	player	NOUN
ejpam-522	37	1	i	i	PRON
ejpam-522	37	2	i.	i.	VERB
ejpam-522	37	3	the	the	DET
ejpam-522	37	4	fuzzy	fuzzy	ADJ
ejpam-522	37	5	payoff	payoff	NOUN
ejpam-522	37	6	eai	eai	PROPN
ejpam-522	37	7	j	j	PROPN
ejpam-522	37	8	is	be	AUX
ejpam-522	37	9	represented	represent	VERB
ejpam-522	37	10	by	by	ADP
ejpam-522	37	11	the	the	DET
ejpam-522	37	12	l	l	NOUN
ejpam-522	37	13	-	-	PUNCT
ejpam-522	37	14	r	r	NOUN
ejpam-522	37	15	fuzzy	fuzzy	ADJ
ejpam-522	37	16	number	number	NOUN
ejpam-522	37	17	:	:	PUNCT
ejpam-522	37	18	eai	eai	PROPN
ejpam-522	37	19	j	j	PROPN
ejpam-522	37	20	=	=	SYM
ejpam-522	37	21	�	�	PROPN
ejpam-522	37	22	ai	ai	VERB
ejpam-522	37	23	j	j	PROPN
ejpam-522	37	24	,	,	PUNCT
ejpam-522	37	25	a′i	a′i	PROPN
ejpam-522	37	26	j	j	PROPN
ejpam-522	37	27	,	,	PUNCT
ejpam-522	37	28	ài	ài	PROPN
ejpam-522	37	29	j	j	PROPN
ejpam-522	37	30	�	�	PROPN
ejpam-522	37	31	lr	lr	X
ejpam-522	37	32	(	(	PUNCT
ejpam-522	37	33	1	1	NUM
ejpam-522	37	34	)	)	PUNCT
ejpam-522	37	35	where	where	SCONJ
ejpam-522	37	36	ai	ai	VERB
ejpam-522	37	37	j	j	PROPN
ejpam-522	37	38	is	be	AUX
ejpam-522	37	39	a	a	DET
ejpam-522	37	40	mean	mean	ADJ
ejpam-522	37	41	value	value	NOUN
ejpam-522	37	42	,	,	PUNCT
ejpam-522	37	43	a′i	a′i	PROPN
ejpam-522	38	1	j	j	PROPN
ejpam-522	38	2	is	be	AUX
ejpam-522	38	3	a	a	DET
ejpam-522	38	4	left	left	ADJ
ejpam-522	38	5	spread	spread	NOUN
ejpam-522	38	6	and	and	CCONJ
ejpam-522	38	7	ài	ài	PROPN
ejpam-522	38	8	j	j	PROPN
ejpam-522	38	9	is	be	AUX
ejpam-522	38	10	a	a	DET
ejpam-522	38	11	right	right	ADJ
ejpam-522	38	12	spread	spread	NOUN
ejpam-522	38	13	.	.	PUNCT
ejpam-522	39	1	the	the	DET
ejpam-522	39	2	two	two	NUM
ejpam-522	39	3	-	-	PUNCT
ejpam-522	39	4	person	person	NOUN
ejpam-522	39	5	zero	zero	NUM
ejpam-522	39	6	-	-	PUNCT
ejpam-522	39	7	sum	sum	NOUN
ejpam-522	39	8	fuzzy	fuzzy	ADJ
ejpam-522	39	9	game	game	NOUN
ejpam-522	39	10	can	can	AUX
ejpam-522	39	11	be	be	AUX
ejpam-522	39	12	represented	represent	VERB
ejpam-522	39	13	as	as	ADP
ejpam-522	39	14	a	a	DET
ejpam-522	39	15	fuzzy	fuzzy	ADJ
ejpam-522	39	16	payoff	payoff	NOUN
ejpam-522	39	17	matrix	matrix	NOUN
ejpam-522	39	18	:	:	PUNCT
ejpam-522	39	19	ea=	ea=	PROPN
ejpam-522	39	20			PROPN
ejpam-522	39	21			VERB
ejpam-522	39	22	ea11	ea11	PROPN
ejpam-522	39	23	...	...	PUNCT
ejpam-522	39	24	ea1n	ea1n	NOUN
ejpam-522	39	25	...	...	PUNCT
ejpam-522	39	26	...	...	PUNCT
ejpam-522	39	27	...	...	PUNCT
ejpam-522	40	1	eam1	eam1	NOUN
ejpam-522	40	2	...	...	PUNCT
ejpam-522	41	1	eamn	eamn	ADJ
ejpam-522	41	2			NUM
ejpam-522	41	3			SYM
ejpam-522	41	4	(	(	PUNCT
ejpam-522	41	5	2	2	X
ejpam-522	41	6	)	)	PUNCT
ejpam-522	42	1	the	the	DET
ejpam-522	42	2	game	game	NOUN
ejpam-522	42	3	defined	define	VERB
ejpam-522	42	4	by	by	ADP
ejpam-522	42	5	(	(	PUNCT
ejpam-522	42	6	2	2	X
ejpam-522	42	7	)	)	PUNCT
ejpam-522	42	8	is	be	AUX
ejpam-522	42	9	called	call	VERB
ejpam-522	42	10	a	a	DET
ejpam-522	42	11	two	two	NUM
ejpam-522	42	12	-	-	PUNCT
ejpam-522	42	13	person	person	NOUN
ejpam-522	42	14	zero	zero	NUM
ejpam-522	42	15	-	-	PUNCT
ejpam-522	42	16	sum	sum	NOUN
ejpam-522	42	17	game	game	NOUN
ejpam-522	42	18	with	with	ADP
ejpam-522	42	19	fuzzy	fuzzy	ADJ
ejpam-522	42	20	payoffs	payoff	NOUN
ejpam-522	42	21	.	.	PUNCT
ejpam-522	43	1	when	when	SCONJ
ejpam-522	43	2	each	each	PRON
ejpam-522	43	3	of	of	ADP
ejpam-522	43	4	the	the	DET
ejpam-522	43	5	players	player	NOUN
ejpam-522	43	6	chooses	choose	VERB
ejpam-522	43	7	a	a	DET
ejpam-522	43	8	strategy	strategy	NOUN
ejpam-522	43	9	,	,	PUNCT
ejpam-522	43	10	a	a	DET
ejpam-522	43	11	payoff	payoff	NOUN
ejpam-522	43	12	for	for	ADP
ejpam-522	43	13	each	each	PRON
ejpam-522	43	14	of	of	ADP
ejpam-522	43	15	them	they	PRON
ejpam-522	43	16	is	be	AUX
ejpam-522	43	17	represented	represent	VERB
ejpam-522	43	18	as	as	ADP
ejpam-522	43	19	a	a	DET
ejpam-522	43	20	fuzzy	fuzzy	ADJ
ejpam-522	43	21	number	number	NOUN
ejpam-522	43	22	,	,	PUNCT
ejpam-522	43	23	but	but	CCONJ
ejpam-522	43	24	an	an	DET
ejpam-522	43	25	outcome	outcome	NOUN
ejpam-522	43	26	of	of	ADP
ejpam-522	43	27	the	the	DET
ejpam-522	43	28	game	game	NOUN
ejpam-522	43	29	has	have	VERB
ejpam-522	43	30	a	a	DET
ejpam-522	43	31	zero	zero	NUM
ejpam-522	43	32	-	-	PUNCT
ejpam-522	43	33	sum	sum	NOUN
ejpam-522	43	34	structure	structure	NOUN
ejpam-522	43	35	such	such	ADJ
ejpam-522	43	36	that	that	SCONJ
ejpam-522	43	37	,	,	PUNCT
ejpam-522	43	38	when	when	SCONJ
ejpam-522	43	39	one	one	NUM
ejpam-522	43	40	player	player	NOUN
ejpam-522	43	41	receives	receive	VERB
ejpam-522	43	42	a	a	DET
ejpam-522	43	43	gain	gain	NOUN
ejpam-522	43	44	the	the	DET
ejpam-522	43	45	order	order	NOUN
ejpam-522	43	46	player	player	NOUN
ejpam-522	43	47	suffers	suffer	VERB
ejpam-522	43	48	an	an	DET
ejpam-522	43	49	equal	equal	ADJ
ejpam-522	43	50	loss	loss	NOUN
ejpam-522	43	51	.	.	PUNCT
ejpam-522	44	1	assuming	assume	VERB
ejpam-522	44	2	that	that	SCONJ
ejpam-522	44	3	each	each	PRON
ejpam-522	44	4	of	of	ADP
ejpam-522	44	5	the	the	DET
ejpam-522	44	6	two	two	NUM
ejpam-522	44	7	players	player	NOUN
ejpam-522	44	8	has	have	VERB
ejpam-522	44	9	r	r	NOUN
ejpam-522	44	10	objectives	objective	NOUN
ejpam-522	44	11	,	,	PUNCT
ejpam-522	44	12	the	the	DET
ejpam-522	44	13	following	follow	VERB
ejpam-522	44	14	multiple	multiple	ADJ
ejpam-522	44	15	fuzzy	fuzzy	ADJ
ejpam-522	44	16	payoff	payoff	NOUN
ejpam-522	44	17	matrices	matrix	NOUN
ejpam-522	44	18	represent	represent	VERB
ejpam-522	44	19	a	a	DET
ejpam-522	44	20	multiobjective	multiobjective	ADJ
ejpam-522	44	21	two	two	NUM
ejpam-522	44	22	-	-	PUNCT
ejpam-522	44	23	person	person	NOUN
ejpam-522	44	24	zero	zero	NUM
ejpam-522	44	25	-	-	PUNCT
ejpam-522	44	26	sum	sum	NOUN
ejpam-522	44	27	game	game	NOUN
ejpam-522	44	28	with	with	ADP
ejpam-522	44	29	fuzzy	fuzzy	ADJ
ejpam-522	44	30	payoffs	payoff	NOUN
ejpam-522	44	31	:	:	PUNCT
ejpam-522	45	1	ea1	ea1	NOUN
ejpam-522	45	2	=	=	PUNCT
ejpam-522	45	3			PROPN
ejpam-522	45	4			ADJ
ejpam-522	45	5	ea1	ea1	NOUN
ejpam-522	45	6	11	11	NUM
ejpam-522	45	7	...	...	PUNCT
ejpam-522	46	1	ea1	ea1	PROPN
ejpam-522	46	2	1n	1n	NUM
ejpam-522	46	3	...	...	PUNCT
ejpam-522	46	4	...	...	PUNCT
ejpam-522	46	5	...	...	PUNCT
ejpam-522	47	1	ea1	ea1	X
ejpam-522	47	2	m1	m1	PROPN
ejpam-522	47	3	...	...	PUNCT
ejpam-522	48	1	ea1	ea1	PROPN
ejpam-522	48	2	mn	mn	PROPN
ejpam-522	48	3			PROPN
ejpam-522	48	4			PROPN
ejpam-522	48	5	,	,	PUNCT
ejpam-522	48	6	...	...	PUNCT
ejpam-522	48	7	,	,	PUNCT
ejpam-522	48	8	ear	ear	X
ejpam-522	48	9	=	=	SYM
ejpam-522	48	10			NOUN
ejpam-522	48	11			ADJ
ejpam-522	48	12	ear	ear	NOUN
ejpam-522	48	13	11	11	NUM
ejpam-522	48	14	...	...	PUNCT
ejpam-522	48	15	ear	ear	X
ejpam-522	48	16	1n	1n	NUM
ejpam-522	48	17	...	...	PUNCT
ejpam-522	48	18	...	...	PUNCT
ejpam-522	48	19	...	...	PUNCT
ejpam-522	49	1	ear	ear	AUX
ejpam-522	49	2	m1	m1	PROPN
ejpam-522	49	3	...	...	PUNCT
ejpam-522	50	1	ear	ear	AUX
ejpam-522	50	2	mn	mn	PROPN
ejpam-522	50	3			PROPN
ejpam-522	50	4			PROPN
ejpam-522	50	5	(	(	PUNCT
ejpam-522	50	6	3	3	X
ejpam-522	50	7	)	)	PUNCT
ejpam-522	50	8	a	a	DET
ejpam-522	50	9	fuzzy	fuzzy	ADJ
ejpam-522	50	10	payoff	payoff	NOUN
ejpam-522	50	11	can	can	AUX
ejpam-522	50	12	be	be	AUX
ejpam-522	50	13	extended	extend	VERB
ejpam-522	50	14	to	to	ADP
ejpam-522	50	15	a	a	DET
ejpam-522	50	16	fuzzy	fuzzy	ADJ
ejpam-522	50	17	expected	expect	VERB
ejpam-522	50	18	payoff	payoff	NOUN
ejpam-522	50	19	by	by	ADP
ejpam-522	50	20	using	use	VERB
ejpam-522	50	21	mixed	mixed	ADJ
ejpam-522	50	22	strategies	strategy	NOUN
ejpam-522	50	23	in	in	ADP
ejpam-522	50	24	a	a	DET
ejpam-522	50	25	procedure	procedure	NOUN
ejpam-522	50	26	similar	similar	ADJ
ejpam-522	50	27	to	to	ADP
ejpam-522	50	28	the	the	DET
ejpam-522	50	29	extension	extension	NOUN
ejpam-522	50	30	from	from	ADP
ejpam-522	50	31	a	a	DET
ejpam-522	50	32	payoff	payoff	NOUN
ejpam-522	50	33	to	to	ADP
ejpam-522	50	34	an	an	DET
ejpam-522	50	35	expected	expect	VERB
ejpam-522	50	36	payoff	payoff	NOUN
ejpam-522	50	37	in	in	ADP
ejpam-522	50	38	conventional	conventional	ADJ
ejpam-522	50	39	twoperson	twoperson	NOUN
ejpam-522	50	40	zero	zero	NUM
ejpam-522	50	41	-	-	PUNCT
ejpam-522	50	42	sum	sum	NOUN
ejpam-522	50	43	games	game	NOUN
ejpam-522	50	44	.	.	PUNCT
ejpam-522	51	1	a.	a.	NOUN
ejpam-522	51	2	çevikel	çevikel	PROPN
ejpam-522	51	3	,	,	PUNCT
ejpam-522	51	4	m.	m.	PROPN
ejpam-522	51	5	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	51	6	/	/	SYM
ejpam-522	51	7	eur	eur	PROPN
ejpam-522	51	8	.	.	PUNCT
ejpam-522	52	1	j.	j.	PROPN
ejpam-522	52	2	pure	pure	PROPN
ejpam-522	52	3	appl	appl	PROPN
ejpam-522	52	4	.	.	PROPN
ejpam-522	52	5	math	math	PROPN
ejpam-522	52	6	,	,	PUNCT
ejpam-522	52	7	3	3	NUM
ejpam-522	52	8	(	(	PUNCT
ejpam-522	52	9	2010	2010	NUM
ejpam-522	52	10	)	)	PUNCT
ejpam-522	52	11	,	,	PUNCT
ejpam-522	52	12	107	107	NUM
ejpam-522	52	13	-	-	SYM
ejpam-522	52	14	117	117	NUM
ejpam-522	52	15	109	109	NUM
ejpam-522	52	16	definition	definition	NOUN
ejpam-522	52	17	2	2	NUM
ejpam-522	52	18	(	(	PUNCT
ejpam-522	52	19	fuzzy	fuzzy	ADJ
ejpam-522	52	20	expected	expect	VERB
ejpam-522	52	21	payoff	payoff	NOUN
ejpam-522	52	22	)	)	PUNCT
ejpam-522	52	23	.	.	PUNCT
ejpam-522	53	1	for	for	ADP
ejpam-522	53	2	any	any	DET
ejpam-522	53	3	pair	pair	NOUN
ejpam-522	53	4	of	of	ADP
ejpam-522	53	5	mixed	mixed	ADJ
ejpam-522	53	6	strategies	strategy	NOUN
ejpam-522	53	7	x	x	SYM
ejpam-522	53	8	∈	∈	NOUN
ejpam-522	53	9	x	x	X
ejpam-522	53	10	and	and	CCONJ
ejpam-522	53	11	y	y	PROPN
ejpam-522	53	12	∈	∈	PROPN
ejpam-522	53	13	y	y	PROPN
ejpam-522	53	14	,	,	PUNCT
ejpam-522	53	15	the	the	DET
ejpam-522	53	16	kth	kth	PROPN
ejpam-522	53	17	fuzzy	fuzzy	PROPN
ejpam-522	53	18	expected	expect	VERB
ejpam-522	53	19	payoff	payoff	NOUN
ejpam-522	53	20	of	of	ADP
ejpam-522	53	21	player	player	NOUN
ejpam-522	53	22	i	i	PRON
ejpam-522	53	23	is	be	AUX
ejpam-522	53	24	defined	define	VERB
ejpam-522	53	25	as	as	ADP
ejpam-522	53	26	the	the	DET
ejpam-522	53	27	fuzzy	fuzzy	ADJ
ejpam-522	53	28	number	number	NOUN
ejpam-522	53	29	x	x	SYM
ejpam-522	53	30	eak	eak	NOUN
ejpam-522	53	31	y	y	PROPN
ejpam-522	53	32	=	=	PUNCT
ejpam-522	53	33			PROPN
ejpam-522	54	1			ADJ
ejpam-522	54	2	m∑	m∑	NOUN
ejpam-522	54	3	i=1	i=1	PROPN
ejpam-522	54	4	n∑	n∑	PROPN
ejpam-522	55	1	j=1	j=1	PROPN
ejpam-522	55	2	ak	ak	PROPN
ejpam-522	56	1	i	i	PRON
ejpam-522	56	2	j	j	PROPN
ejpam-522	56	3	x	x	VERB
ejpam-522	57	1	i	i	VERB
ejpam-522	57	2	y	y	PROPN
ejpam-522	57	3	j	j	PROPN
ejpam-522	57	4	,	,	PUNCT
ejpam-522	57	5	m∑	m∑	INTJ
ejpam-522	57	6	i=1	i=1	PROPN
ejpam-522	57	7	n∑	n∑	PROPN
ejpam-522	58	1	j=1	j=1	PROPN
ejpam-522	58	2	a′ki	a′ki	VERB
ejpam-522	59	1	j	j	NOUN
ejpam-522	59	2	x	x	VERB
ejpam-522	60	1	i	i	PRON
ejpam-522	60	2	y	y	PROPN
ejpam-522	60	3	j	j	PROPN
ejpam-522	60	4	,	,	PUNCT
ejpam-522	60	5	m∑	m∑	INTJ
ejpam-522	60	6	i=1	i=1	PROPN
ejpam-522	60	7	n∑	n∑	PROPN
ejpam-522	61	1	j=1	j=1	PROPN
ejpam-522	61	2	àk	àk	ADV
ejpam-522	61	3	i	i	PRON
ejpam-522	61	4	j	j	VERB
ejpam-522	62	1	x	x	VERB
ejpam-522	63	1	i	i	PRON
ejpam-522	63	2	y	y	PROPN
ejpam-522	63	3	j	j	PROPN
ejpam-522	64	1			PROPN
ejpam-522	64	2			PROPN
ejpam-522	65	1	lr	lr	X
ejpam-522	65	2	(	(	PUNCT
ejpam-522	65	3	4	4	NUM
ejpam-522	65	4	)	)	PUNCT
ejpam-522	65	5	characterized	characterize	VERB
ejpam-522	65	6	by	by	ADP
ejpam-522	65	7	the	the	DET
ejpam-522	65	8	membership	membership	NOUN
ejpam-522	65	9	function	function	NOUN
ejpam-522	65	10	µx	µx	VERB
ejpam-522	65	11	eak	eak	PROPN
ejpam-522	65	12	y	y	PROPN
ejpam-522	65	13	:	:	PUNCT
ejpam-522	65	14	dk→	dk→	X
ejpam-522	66	1	[	[	X
ejpam-522	66	2	0,1	0,1	NUM
ejpam-522	66	3	]	]	PUNCT
ejpam-522	66	4	(	(	PUNCT
ejpam-522	66	5	5	5	NUM
ejpam-522	66	6	)	)	PUNCT
ejpam-522	66	7	where	where	SCONJ
ejpam-522	66	8	dk	dk	PROPN
ejpam-522	66	9	∈	∈	PROPN
ejpam-522	66	10	r	r	NOUN
ejpam-522	66	11	is	be	AUX
ejpam-522	66	12	the	the	DET
ejpam-522	66	13	domain	domain	NOUN
ejpam-522	66	14	of	of	ADP
ejpam-522	66	15	the	the	DET
ejpam-522	66	16	kth	kth	PROPN
ejpam-522	66	17	payoff	payoff	NOUN
ejpam-522	66	18	for	for	ADP
ejpam-522	66	19	player	player	NOUN
ejpam-522	66	20	i	i	PRON
ejpam-522	66	21	.	.	PUNCT
ejpam-522	67	1	definition	definition	NOUN
ejpam-522	67	2	3	3	NUM
ejpam-522	67	3	(	(	PUNCT
ejpam-522	67	4	fuzzy	fuzzy	ADJ
ejpam-522	67	5	goal	goal	NOUN
ejpam-522	67	6	)	)	PUNCT
ejpam-522	67	7	.	.	PUNCT
ejpam-522	68	1	let	let	VERB
ejpam-522	68	2	the	the	DET
ejpam-522	68	3	domain	domain	NOUN
ejpam-522	68	4	of	of	ADP
ejpam-522	68	5	the	the	DET
ejpam-522	68	6	kth	kth	PROPN
ejpam-522	68	7	payoff	payoff	NOUN
ejpam-522	68	8	for	for	ADP
ejpam-522	68	9	player	player	NOUN
ejpam-522	68	10	i	i	PRON
ejpam-522	68	11	be	be	AUX
ejpam-522	68	12	denoted	denote	VERB
ejpam-522	68	13	dk	dk	PRON
ejpam-522	68	14	∈	∈	PROPN
ejpam-522	68	15	r	r	NOUN
ejpam-522	68	16	.	.	PUNCT
ejpam-522	69	1	then	then	ADV
ejpam-522	69	2	the	the	DET
ejpam-522	69	3	fuzzy	fuzzy	ADJ
ejpam-522	69	4	goal	goal	NOUN
ejpam-522	69	5	s	s	VERB
ejpam-522	69	6	g	g	PROPN
ejpam-522	69	7	k	k	NOUN
ejpam-522	69	8	with	with	ADP
ejpam-522	69	9	respect	respect	NOUN
ejpam-522	69	10	to	to	ADP
ejpam-522	69	11	the	the	DET
ejpam-522	69	12	kth	kth	PROPN
ejpam-522	69	13	payoff	payoff	NOUN
ejpam-522	69	14	for	for	ADP
ejpam-522	69	15	player	player	NOUN
ejpam-522	69	16	i	i	PRON
ejpam-522	69	17	is	be	AUX
ejpam-522	69	18	defined	define	VERB
ejpam-522	69	19	as	as	ADP
ejpam-522	69	20	the	the	DET
ejpam-522	69	21	fuzzy	fuzzy	ADJ
ejpam-522	69	22	set	set	NOUN
ejpam-522	69	23	on	on	ADP
ejpam-522	69	24	the	the	DET
ejpam-522	69	25	set	set	NOUN
ejpam-522	69	26	dk	dk	NOUN
ejpam-522	69	27	characterized	characterize	VERB
ejpam-522	69	28	by	by	ADP
ejpam-522	69	29	the	the	DET
ejpam-522	69	30	membership	membership	NOUN
ejpam-522	69	31	function	function	NOUN
ejpam-522	69	32	µegk	µegk	ADJ
ejpam-522	69	33	:	:	PUNCT
ejpam-522	69	34	dk→	dk→	X
ejpam-522	70	1	[	[	X
ejpam-522	70	2	0,1	0,1	NUM
ejpam-522	70	3	]	]	PUNCT
ejpam-522	70	4	(	(	PUNCT
ejpam-522	70	5	6	6	NUM
ejpam-522	70	6	)	)	PUNCT
ejpam-522	70	7	a	a	DET
ejpam-522	70	8	membership	membership	NOUN
ejpam-522	70	9	function	function	NOUN
ejpam-522	70	10	value	value	NOUN
ejpam-522	70	11	of	of	ADP
ejpam-522	70	12	a	a	DET
ejpam-522	70	13	fuzzy	fuzzy	ADJ
ejpam-522	70	14	goal	goal	NOUN
ejpam-522	70	15	can	can	AUX
ejpam-522	70	16	be	be	AUX
ejpam-522	70	17	interpreted	interpret	VERB
ejpam-522	70	18	as	as	ADP
ejpam-522	70	19	a	a	DET
ejpam-522	70	20	degree	degree	NOUN
ejpam-522	70	21	of	of	ADP
ejpam-522	70	22	attainment	attainment	NOUN
ejpam-522	70	23	of	of	ADP
ejpam-522	70	24	the	the	DET
ejpam-522	70	25	fuzzy	fuzzy	ADJ
ejpam-522	70	26	goal	goal	NOUN
ejpam-522	70	27	.	.	PUNCT
ejpam-522	71	1	then	then	ADV
ejpam-522	71	2	we	we	PRON
ejpam-522	71	3	assume	assume	VERB
ejpam-522	71	4	that	that	SCONJ
ejpam-522	71	5	,	,	PUNCT
ejpam-522	71	6	for	for	ADP
ejpam-522	71	7	any	any	DET
ejpam-522	71	8	pair	pair	NOUN
ejpam-522	71	9	of	of	ADP
ejpam-522	71	10	payoffs	payoff	NOUN
ejpam-522	71	11	,	,	PUNCT
ejpam-522	71	12	a	a	DET
ejpam-522	71	13	player	player	NOUN
ejpam-522	71	14	prefers	prefer	VERB
ejpam-522	71	15	the	the	DET
ejpam-522	71	16	payoff	payoff	NOUN
ejpam-522	71	17	having	have	VERB
ejpam-522	71	18	the	the	DET
ejpam-522	71	19	greater	great	ADJ
ejpam-522	71	20	degree	degree	NOUN
ejpam-522	71	21	of	of	ADP
ejpam-522	71	22	attainment	attainment	NOUN
ejpam-522	71	23	of	of	ADP
ejpam-522	71	24	the	the	DET
ejpam-522	71	25	fuzzy	fuzzy	ADJ
ejpam-522	71	26	goal	goal	NOUN
ejpam-522	71	27	to	to	ADP
ejpam-522	71	28	the	the	DET
ejpam-522	71	29	other	other	ADJ
ejpam-522	71	30	payoff.[15	payoff.[15	PROPN
ejpam-522	71	31	]	]	PUNCT
ejpam-522	71	32	definition	definition	NOUN
ejpam-522	71	33	4	4	NUM
ejpam-522	71	34	(	(	PUNCT
ejpam-522	71	35	a	a	DET
ejpam-522	71	36	degree	degree	NOUN
ejpam-522	71	37	of	of	ADP
ejpam-522	71	38	attainment	attainment	NOUN
ejpam-522	71	39	of	of	ADP
ejpam-522	71	40	a	a	DET
ejpam-522	71	41	fuzzy	fuzzy	ADJ
ejpam-522	71	42	goal	goal	NOUN
ejpam-522	71	43	)	)	PUNCT
ejpam-522	71	44	.	.	PUNCT
ejpam-522	72	1	for	for	ADP
ejpam-522	72	2	any	any	DET
ejpam-522	72	3	pair	pair	NOUN
ejpam-522	72	4	of	of	ADP
ejpam-522	72	5	mixed	mixed	ADJ
ejpam-522	72	6	strategies	strategy	NOUN
ejpam-522	72	7	(	(	PUNCT
ejpam-522	72	8	x	x	X
ejpam-522	72	9	,	,	PUNCT
ejpam-522	72	10	y	y	PROPN
ejpam-522	72	11	)	)	PUNCT
ejpam-522	72	12	,	,	PUNCT
ejpam-522	72	13	let	let	VERB
ejpam-522	72	14	the	the	DET
ejpam-522	72	15	kth	kth	PROPN
ejpam-522	72	16	fuzzy	fuzzy	PROPN
ejpam-522	72	17	expected	expect	VERB
ejpam-522	72	18	payoff	payoff	NOUN
ejpam-522	72	19	for	for	ADP
ejpam-522	72	20	player	player	NOUN
ejpam-522	72	21	i	i	PRON
ejpam-522	72	22	be	be	AUX
ejpam-522	72	23	denoted	denote	VERB
ejpam-522	72	24	by	by	ADP
ejpam-522	72	25	x	x	SYM
ejpam-522	72	26	eak	eak	PROPN
ejpam-522	72	27	y	y	PROPN
ejpam-522	72	28	and	and	CCONJ
ejpam-522	72	29	let	let	VERB
ejpam-522	72	30	the	the	DET
ejpam-522	72	31	kth	kth	PROPN
ejpam-522	72	32	fuzzy	fuzzy	ADJ
ejpam-522	72	33	goal	goal	NOUN
ejpam-522	72	34	for	for	ADP
ejpam-522	72	35	player	player	NOUN
ejpam-522	72	36	i	i	PRON
ejpam-522	72	37	be	be	AUX
ejpam-522	72	38	denoted	denote	VERB
ejpam-522	72	39	by	by	ADP
ejpam-522	72	40	s	s	PROPN
ejpam-522	72	41	g	g	PROPN
ejpam-522	72	42	k	k	PROPN
ejpam-522	72	43	.	.	PUNCT
ejpam-522	73	1	then	then	ADV
ejpam-522	73	2	a	a	DET
ejpam-522	73	3	fuzzy	fuzzy	ADJ
ejpam-522	73	4	set	set	NOUN
ejpam-522	73	5	expressing	express	VERB
ejpam-522	73	6	an	an	DET
ejpam-522	73	7	attainment	attainment	ADJ
ejpam-522	73	8	state	state	NOUN
ejpam-522	73	9	of	of	ADP
ejpam-522	73	10	the	the	DET
ejpam-522	73	11	fuzzy	fuzzy	ADJ
ejpam-522	73	12	goal	goal	NOUN
ejpam-522	73	13	is	be	AUX
ejpam-522	73	14	represented	represent	VERB
ejpam-522	73	15	by	by	ADP
ejpam-522	73	16	the	the	DET
ejpam-522	73	17	intersection	intersection	NOUN
ejpam-522	73	18	of	of	ADP
ejpam-522	73	19	the	the	DET
ejpam-522	73	20	fuzzy	fuzzy	ADJ
ejpam-522	73	21	expected	expect	VERB
ejpam-522	73	22	payoff	payoff	NOUN
ejpam-522	73	23	x	x	PUNCT
ejpam-522	73	24	eak	eak	NOUN
ejpam-522	73	25	y	y	PROPN
ejpam-522	73	26	and	and	CCONJ
ejpam-522	73	27	the	the	DET
ejpam-522	73	28	fuzzy	fuzzy	ADJ
ejpam-522	73	29	goal	goal	NOUN
ejpam-522	73	30	s	s	VERB
ejpam-522	73	31	g	g	PROPN
ejpam-522	73	32	k	k	PROPN
ejpam-522	73	33	.	.	PUNCT
ejpam-522	74	1	the	the	DET
ejpam-522	74	2	membership	membership	NOUN
ejpam-522	74	3	function	function	NOUN
ejpam-522	74	4	of	of	ADP
ejpam-522	74	5	the	the	DET
ejpam-522	74	6	fuzzy	fuzzy	ADJ
ejpam-522	74	7	set	set	NOUN
ejpam-522	74	8	is	be	AUX
ejpam-522	74	9	represented	represent	VERB
ejpam-522	74	10	as	as	ADP
ejpam-522	74	11	µk	µk	DET
ejpam-522	74	12	a(x	a(x	PROPN
ejpam-522	74	13	,	,	PUNCT
ejpam-522	74	14	y	y	PROPN
ejpam-522	74	15	)	)	PUNCT
ejpam-522	74	16	(	(	PUNCT
ejpam-522	74	17	p	p	X
ejpam-522	74	18	)	)	PUNCT
ejpam-522	74	19	=	=	NOUN
ejpam-522	74	20	min(µx	min(µx	INTJ
ejpam-522	74	21	eak	eak	NOUN
ejpam-522	74	22	y(p),µegk	y(p),µegk	PROPN
ejpam-522	74	23	(	(	PUNCT
ejpam-522	74	24	p	p	NOUN
ejpam-522	74	25	)	)	PUNCT
ejpam-522	74	26	)	)	PUNCT
ejpam-522	74	27	(	(	PUNCT
ejpam-522	74	28	7	7	X
ejpam-522	74	29	)	)	PUNCT
ejpam-522	74	30	where	where	SCONJ
ejpam-522	74	31	p	p	NOUN
ejpam-522	74	32	∈	∈	PROPN
ejpam-522	74	33	dk	dk	NOUN
ejpam-522	74	34	is	be	AUX
ejpam-522	74	35	a	a	DET
ejpam-522	74	36	payoff	payoff	NOUN
ejpam-522	74	37	for	for	ADP
ejpam-522	74	38	player	player	NOUN
ejpam-522	74	39	i.	i.	NOUN
ejpam-522	74	40	a	a	DET
ejpam-522	74	41	degree	degree	NOUN
ejpam-522	74	42	of	of	ADP
ejpam-522	74	43	attainment	attainment	NOUN
ejpam-522	74	44	of	of	ADP
ejpam-522	74	45	the	the	DET
ejpam-522	74	46	kth	kth	PROPN
ejpam-522	74	47	fuzzy	fuzzy	ADJ
ejpam-522	74	48	goal	goal	NOUN
ejpam-522	74	49	is	be	AUX
ejpam-522	74	50	defined	define	VERB
ejpam-522	74	51	as	as	ADP
ejpam-522	74	52	the	the	DET
ejpam-522	74	53	maximum	maximum	NOUN
ejpam-522	74	54	of	of	ADP
ejpam-522	74	55	the	the	DET
ejpam-522	74	56	membership	membership	NOUN
ejpam-522	74	57	function	function	NOUN
ejpam-522	74	58	(	(	PUNCT
ejpam-522	74	59	7	7	NUM
ejpam-522	74	60	)	)	PUNCT
ejpam-522	74	61	,	,	PUNCT
ejpam-522	74	62	i.e.	i.e.	X
ejpam-522	74	63	,	,	PUNCT
ejpam-522	74	64	⌢	⌢	NUM
ejpam-522	74	65	µ	µ	X
ejpam-522	74	66	k	k	X
ejpam-522	74	67	a(x	a(x	NOUN
ejpam-522	74	68	,	,	PUNCT
ejpam-522	74	69	y)(p	y)(p	NOUN
ejpam-522	74	70	∗	∗	NOUN
ejpam-522	74	71	)	)	PUNCT
ejpam-522	75	1	=	=	NOUN
ejpam-522	75	2	max	max	NOUN
ejpam-522	75	3	p	p	NOUN
ejpam-522	75	4	µk	µk	PRON
ejpam-522	75	5	a(x	a(x	PROPN
ejpam-522	75	6	,	,	PUNCT
ejpam-522	75	7	y	y	PROPN
ejpam-522	75	8	)	)	PUNCT
ejpam-522	75	9	(	(	PUNCT
ejpam-522	75	10	p	p	X
ejpam-522	75	11	)	)	PUNCT
ejpam-522	76	1	=	=	NOUN
ejpam-522	76	2	max	max	NOUN
ejpam-522	76	3	p	p	NOUN
ejpam-522	76	4	n	n	PRON
ejpam-522	76	5	min(µx	min(µx	VERB
ejpam-522	76	6	eak	eak	NOUN
ejpam-522	76	7	y(p),µegk(p	y(p),µegk(p	NOUN
ejpam-522	76	8	)	)	PUNCT
ejpam-522	76	9	)	)	PUNCT
ejpam-522	77	1	o	o	NOUN
ejpam-522	77	2	(	(	PUNCT
ejpam-522	77	3	8)	8)	NUM
ejpam-522	77	4	a	a	DET
ejpam-522	77	5	degree	degree	NOUN
ejpam-522	77	6	of	of	ADP
ejpam-522	77	7	attainment	attainment	NOUN
ejpam-522	77	8	of	of	ADP
ejpam-522	77	9	the	the	DET
ejpam-522	77	10	fuzzy	fuzzy	ADJ
ejpam-522	77	11	goal	goal	NOUN
ejpam-522	77	12	can	can	AUX
ejpam-522	77	13	be	be	AUX
ejpam-522	77	14	consider	consider	VERB
ejpam-522	77	15	to	to	PART
ejpam-522	77	16	be	be	AUX
ejpam-522	77	17	a	a	DET
ejpam-522	77	18	concept	concept	NOUN
ejpam-522	77	19	similar	similar	ADJ
ejpam-522	77	20	to	to	ADP
ejpam-522	77	21	a	a	DET
ejpam-522	77	22	degree	degree	NOUN
ejpam-522	77	23	of	of	ADP
ejpam-522	77	24	satisfaction	satisfaction	NOUN
ejpam-522	77	25	of	of	ADP
ejpam-522	77	26	the	the	DET
ejpam-522	77	27	fuzzy	fuzzy	ADJ
ejpam-522	77	28	decision	decision	NOUN
ejpam-522	77	29	by	by	ADP
ejpam-522	77	30	bellman	bellman	NOUN
ejpam-522	77	31	and	and	CCONJ
ejpam-522	77	32	zadeh	zadeh	PROPN
ejpam-522	78	1	[	[	X
ejpam-522	78	2	4	4	X
ejpam-522	78	3	]	]	PUNCT
ejpam-522	78	4	when	when	SCONJ
ejpam-522	78	5	the	the	DET
ejpam-522	78	6	fuzzy	fuzzy	ADJ
ejpam-522	78	7	constraint	constraint	NOUN
ejpam-522	78	8	is	be	AUX
ejpam-522	78	9	replaced	replace	VERB
ejpam-522	78	10	by	by	ADP
ejpam-522	78	11	the	the	DET
ejpam-522	78	12	fuzzy	fuzzy	ADJ
ejpam-522	78	13	expected	expect	VERB
ejpam-522	78	14	payoff	payoff	NOUN
ejpam-522	78	15	,	,	PUNCT
ejpam-522	78	16	and	and	CCONJ
ejpam-522	78	17	it	it	PRON
ejpam-522	78	18	can	can	AUX
ejpam-522	78	19	be	be	AUX
ejpam-522	78	20	also	also	ADV
ejpam-522	78	21	interpreted	interpret	VERB
ejpam-522	78	22	as	as	ADP
ejpam-522	78	23	a	a	DET
ejpam-522	78	24	possibility	possibility	NOUN
ejpam-522	78	25	of	of	ADP
ejpam-522	78	26	attainment	attainment	NOUN
ejpam-522	78	27	of	of	ADP
ejpam-522	78	28	the	the	DET
ejpam-522	78	29	fuzzy	fuzzy	ADJ
ejpam-522	78	30	goal	goal	NOUN
ejpam-522	78	31	.	.	PUNCT
ejpam-522	79	1	when	when	SCONJ
ejpam-522	79	2	player	player	NOUN
ejpam-522	79	3	i	i	PRON
ejpam-522	79	4	and	and	CCONJ
ejpam-522	79	5	i	i	PRON
ejpam-522	79	6	i	i	PRON
ejpam-522	79	7	choose	choose	VERB
ejpam-522	79	8	mixed	mixed	ADJ
ejpam-522	79	9	strategies	strategy	NOUN
ejpam-522	79	10	⌢	⌢	NUM
ejpam-522	79	11	x	x	X
ejpam-522	79	12	and	and	CCONJ
ejpam-522	79	13	⌢	⌢	NUM
ejpam-522	79	14	y	y	PROPN
ejpam-522	79	15	,	,	PUNCT
ejpam-522	79	16	respectively	respectively	ADV
ejpam-522	79	17	,	,	PUNCT
ejpam-522	79	18	the	the	DET
ejpam-522	79	19	degree	degree	NOUN
ejpam-522	79	20	of	of	ADP
ejpam-522	79	21	attainment	attainment	NOUN
ejpam-522	79	22	of	of	ADP
ejpam-522	79	23	the	the	DET
ejpam-522	79	24	kth	kth	PROPN
ejpam-522	79	25	fuzzy	fuzzy	ADJ
ejpam-522	79	26	goal	goal	NOUN
ejpam-522	79	27	⌢	⌢	NUM
ejpam-522	79	28	µ	µ	X
ejpam-522	79	29	k	k	X
ejpam-522	79	30	a(x	a(x	NOUN
ejpam-522	79	31	,	,	PUNCT
ejpam-522	79	32	y)(p	y)(p	ADJ
ejpam-522	79	33	∗	∗	NOUN
ejpam-522	79	34	)	)	PUNCT
ejpam-522	79	35	is	be	AUX
ejpam-522	79	36	determined	determine	VERB
ejpam-522	79	37	by	by	ADP
ejpam-522	79	38	(	(	PUNCT
ejpam-522	79	39	8)	8)	NUM
ejpam-522	79	40	.	.	PUNCT
ejpam-522	80	1	we	we	PRON
ejpam-522	80	2	assume	assume	VERB
ejpam-522	80	3	that	that	SCONJ
ejpam-522	80	4	player	player	NOUN
ejpam-522	80	5	i	i	PRON
ejpam-522	80	6	supposes	suppose	VERB
ejpam-522	80	7	that	that	DET
ejpam-522	80	8	player	player	NOUN
ejpam-522	81	1	i	i	PRON
ejpam-522	81	2	i	i	PRON
ejpam-522	81	3	choose	choose	VERB
ejpam-522	81	4	a	a	DET
ejpam-522	81	5	strategy	strategy	NOUN
ejpam-522	81	6	⌢	⌢	NUM
ejpam-522	81	7	y	y	NOUN
ejpam-522	81	8	so	so	SCONJ
ejpam-522	81	9	as	as	SCONJ
ejpam-522	81	10	to	to	PART
ejpam-522	81	11	minimize	minimize	VERB
ejpam-522	81	12	player	player	NOUN
ejpam-522	81	13	i	i	PRON
ejpam-522	81	14	’s	’	VERB
ejpam-522	81	15	degree	degree	NOUN
ejpam-522	81	16	of	of	ADP
ejpam-522	81	17	attainment	attainment	NOUN
ejpam-522	81	18	of	of	ADP
ejpam-522	81	19	the	the	DET
ejpam-522	81	20	aggregated	aggregate	VERB
ejpam-522	81	21	fuzzy	fuzzy	ADJ
ejpam-522	81	22	goal	goal	NOUN
ejpam-522	81	23	⌢	⌢	NUM
ejpam-522	81	24	µ	µ	X
ejpam-522	81	25	a	a	PRON
ejpam-522	81	26	(	(	PUNCT
ejpam-522	81	27	⌢	⌢	NUM
ejpam-522	81	28	x	x	X
ejpam-522	81	29	,	,	PUNCT
ejpam-522	81	30	⌢	⌢	NUM
ejpam-522	81	31	y	y	PROPN
ejpam-522	81	32	)	)	PUNCT
ejpam-522	81	33	(	(	PUNCT
ejpam-522	81	34	p∗	p∗	PROPN
ejpam-522	81	35	)	)	PUNCT
ejpam-522	81	36	,	,	PUNCT
ejpam-522	82	1	i.e.	i.e.	X
ejpam-522	82	2	,	,	PUNCT
ejpam-522	82	3	player	player	NOUN
ejpam-522	82	4	i	i	PRON
ejpam-522	82	5	’s	’	VERB
ejpam-522	82	6	degree	degree	NOUN
ejpam-522	82	7	of	of	ADP
ejpam-522	82	8	attainment	attainment	NOUN
ejpam-522	82	9	of	of	ADP
ejpam-522	82	10	the	the	DET
ejpam-522	82	11	aggregated	aggregate	VERB
ejpam-522	82	12	a.	a.	NOUN
ejpam-522	82	13	çevikel	çevikel	PROPN
ejpam-522	82	14	,	,	PUNCT
ejpam-522	82	15	m.	m.	NOUN
ejpam-522	82	16	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	82	17	/	/	SYM
ejpam-522	82	18	eur	eur	PROPN
ejpam-522	82	19	.	.	PUNCT
ejpam-522	83	1	j.	j.	PROPN
ejpam-522	83	2	pure	pure	PROPN
ejpam-522	83	3	appl	appl	PROPN
ejpam-522	83	4	.	.	PROPN
ejpam-522	83	5	math	math	PROPN
ejpam-522	83	6	,	,	PUNCT
ejpam-522	83	7	3	3	NUM
ejpam-522	83	8	(	(	PUNCT
ejpam-522	83	9	2010	2010	NUM
ejpam-522	83	10	)	)	PUNCT
ejpam-522	83	11	,	,	PUNCT
ejpam-522	83	12	107	107	NUM
ejpam-522	83	13	-	-	SYM
ejpam-522	83	14	117	117	NUM
ejpam-522	83	15	110	110	NUM
ejpam-522	83	16	fuzzy	fuzzy	ADJ
ejpam-522	83	17	goal	goal	NOUN
ejpam-522	83	18	,	,	PUNCT
ejpam-522	83	19	assuming	assume	VERB
ejpam-522	83	20	he	he	PRON
ejpam-522	83	21	choose	choose	VERB
ejpam-522	83	22	⌢	⌢	NUM
ejpam-522	83	23	x	x	X
ejpam-522	83	24	,	,	PUNCT
ejpam-522	83	25	will	will	AUX
ejpam-522	83	26	be	be	AUX
ejpam-522	83	27	v(x	v(x	VERB
ejpam-522	83	28	)	)	PUNCT
ejpam-522	84	1	=	=	SYM
ejpam-522	84	2	miny∈y	miny∈y	PROPN
ejpam-522	84	3	⌢	⌢	NUM
ejpam-522	84	4	µ	µ	NOUN
ejpam-522	84	5	a	a	PRON
ejpam-522	84	6	(	(	PUNCT
ejpam-522	84	7	⌢	⌢	NUM
ejpam-522	84	8	x	x	X
ejpam-522	84	9	,	,	PUNCT
ejpam-522	84	10	⌢	⌢	NUM
ejpam-522	84	11	y	y	PROPN
ejpam-522	84	12	)	)	PUNCT
ejpam-522	84	13	(	(	PUNCT
ejpam-522	84	14	p∗	p∗	PROPN
ejpam-522	84	15	)	)	PUNCT
ejpam-522	84	16	.	.	PUNCT
ejpam-522	85	1	hence	hence	ADV
ejpam-522	85	2	,	,	PUNCT
ejpam-522	85	3	player	player	NOUN
ejpam-522	85	4	i	i	PRON
ejpam-522	85	5	chooses	choose	VERB
ejpam-522	85	6	a	a	DET
ejpam-522	85	7	strategy	strategy	NOUN
ejpam-522	85	8	so	so	SCONJ
ejpam-522	85	9	as	as	SCONJ
ejpam-522	85	10	to	to	PART
ejpam-522	85	11	maximize	maximize	VERB
ejpam-522	85	12	his	his	PRON
ejpam-522	85	13	degree	degree	NOUN
ejpam-522	85	14	of	of	ADP
ejpam-522	85	15	attainment	attainment	NOUN
ejpam-522	85	16	of	of	ADP
ejpam-522	85	17	the	the	DET
ejpam-522	85	18	aggregated	aggregate	VERB
ejpam-522	85	19	fuzzy	fuzzy	ADJ
ejpam-522	85	20	goal	goal	NOUN
ejpam-522	85	21	v(x	v(x	PROPN
ejpam-522	85	22	)	)	PUNCT
ejpam-522	85	23	.	.	PUNCT
ejpam-522	86	1	in	in	ADP
ejpam-522	86	2	short	short	ADJ
ejpam-522	86	3	,	,	PUNCT
ejpam-522	86	4	we	we	PRON
ejpam-522	86	5	assume	assume	VERB
ejpam-522	86	6	that	that	SCONJ
ejpam-522	86	7	player	player	NOUN
ejpam-522	86	8	i	i	PRON
ejpam-522	86	9	behaves	behave	VERB
ejpam-522	86	10	according	accord	VERB
ejpam-522	86	11	to	to	ADP
ejpam-522	86	12	the	the	DET
ejpam-522	86	13	maximin	maximin	NOUN
ejpam-522	86	14	principle	principle	NOUN
ejpam-522	86	15	in	in	ADP
ejpam-522	86	16	terms	term	NOUN
ejpam-522	86	17	of	of	ADP
ejpam-522	86	18	a	a	DET
ejpam-522	86	19	degree	degree	NOUN
ejpam-522	86	20	of	of	ADP
ejpam-522	86	21	attainment	attainment	NOUN
ejpam-522	86	22	of	of	ADP
ejpam-522	86	23	the	the	DET
ejpam-522	86	24	aggregated	aggregate	VERB
ejpam-522	86	25	fuzzy	fuzzy	ADJ
ejpam-522	86	26	goal	goal	NOUN
ejpam-522	87	1	[	[	X
ejpam-522	87	2	16	16	NUM
ejpam-522	87	3	]	]	PUNCT
ejpam-522	87	4	.	.	PUNCT
ejpam-522	88	1	definition	definition	NOUN
ejpam-522	88	2	5	5	NUM
ejpam-522	88	3	(	(	PUNCT
ejpam-522	88	4	maximin	maximin	NOUN
ejpam-522	88	5	solution	solution	NOUN
ejpam-522	88	6	with	with	ADP
ejpam-522	88	7	respect	respect	NOUN
ejpam-522	88	8	to	to	ADP
ejpam-522	88	9	a	a	DET
ejpam-522	88	10	degree	degree	NOUN
ejpam-522	88	11	of	of	ADP
ejpam-522	88	12	attainment	attainment	NOUN
ejpam-522	88	13	of	of	ADP
ejpam-522	88	14	the	the	DET
ejpam-522	88	15	aggregated	aggregate	VERB
ejpam-522	88	16	fuzzy	fuzzy	ADJ
ejpam-522	88	17	goal	goal	NOUN
ejpam-522	88	18	)	)	PUNCT
ejpam-522	88	19	.	.	PUNCT
ejpam-522	89	1	for	for	ADP
ejpam-522	89	2	any	any	DET
ejpam-522	89	3	pair	pair	NOUN
ejpam-522	89	4	of	of	ADP
ejpam-522	89	5	mixed	mixed	ADJ
ejpam-522	89	6	strategies	strategy	NOUN
ejpam-522	89	7	(	(	PUNCT
ejpam-522	89	8	x	x	X
ejpam-522	89	9	,	,	PUNCT
ejpam-522	89	10	y	y	PROPN
ejpam-522	89	11	)	)	PUNCT
ejpam-522	89	12	,	,	PUNCT
ejpam-522	89	13	let	let	VERB
ejpam-522	89	14	a	a	DET
ejpam-522	89	15	degree	degree	NOUN
ejpam-522	89	16	of	of	ADP
ejpam-522	89	17	attainment	attainment	NOUN
ejpam-522	89	18	of	of	ADP
ejpam-522	89	19	the	the	DET
ejpam-522	89	20	aggregated	aggregate	VERB
ejpam-522	89	21	fuzzy	fuzzy	ADJ
ejpam-522	89	22	goal	goal	NOUN
ejpam-522	89	23	for	for	ADP
ejpam-522	89	24	player	player	NOUN
ejpam-522	89	25	i	i	PRON
ejpam-522	89	26	be	be	AUX
ejpam-522	89	27	denoted	denote	VERB
ejpam-522	89	28	⌢	⌢	NUM
ejpam-522	89	29	µa(x	µa(x	NOUN
ejpam-522	89	30	,	,	PUNCT
ejpam-522	89	31	y)(p	y)(p	ADJ
ejpam-522	89	32	∗	∗	NOUN
ejpam-522	89	33	)	)	PUNCT
ejpam-522	89	34	.	.	PUNCT
ejpam-522	90	1	then	then	ADV
ejpam-522	90	2	player	player	NOUN
ejpam-522	90	3	i	i	PRON
ejpam-522	90	4	’s	’	VERB
ejpam-522	90	5	maximin	maximin	NOUN
ejpam-522	90	6	value	value	NOUN
ejpam-522	90	7	with	with	ADP
ejpam-522	90	8	respect	respect	NOUN
ejpam-522	90	9	to	to	ADP
ejpam-522	90	10	a	a	DET
ejpam-522	90	11	degree	degree	NOUN
ejpam-522	90	12	of	of	ADP
ejpam-522	90	13	attainment	attainment	NOUN
ejpam-522	90	14	of	of	ADP
ejpam-522	90	15	the	the	DET
ejpam-522	90	16	aggregated	aggregate	VERB
ejpam-522	90	17	fuzzy	fuzzy	ADJ
ejpam-522	90	18	goal	goal	NOUN
ejpam-522	90	19	is	be	AUX
ejpam-522	90	20	max	max	PROPN
ejpam-522	90	21	x∈x	x∈x	PROPN
ejpam-522	90	22	min	min	PROPN
ejpam-522	90	23	y∈y	y∈y	PROPN
ejpam-522	90	24	⌢	⌢	NUM
ejpam-522	90	25	µa(x	µa(x	X
ejpam-522	90	26	,	,	PUNCT
ejpam-522	90	27	y)(p	y)(p	NOUN
ejpam-522	90	28	∗	∗	NOUN
ejpam-522	90	29	)	)	PUNCT
ejpam-522	90	30	(	(	PUNCT
ejpam-522	90	31	9	9	NUM
ejpam-522	90	32	)	)	PUNCT
ejpam-522	90	33	and	and	CCONJ
ejpam-522	90	34	such	such	DET
ejpam-522	90	35	a	a	DET
ejpam-522	90	36	strategy	strategy	NOUN
ejpam-522	90	37	x	x	PUNCT
ejpam-522	90	38	is	be	AUX
ejpam-522	90	39	called	call	VERB
ejpam-522	90	40	the	the	DET
ejpam-522	90	41	maximin	maximin	NOUN
ejpam-522	90	42	solution	solution	NOUN
ejpam-522	90	43	with	with	ADP
ejpam-522	90	44	respect	respect	NOUN
ejpam-522	90	45	to	to	ADP
ejpam-522	90	46	the	the	DET
ejpam-522	90	47	degree	degree	NOUN
ejpam-522	90	48	of	of	ADP
ejpam-522	90	49	attainment	attainment	NOUN
ejpam-522	90	50	of	of	ADP
ejpam-522	90	51	the	the	DET
ejpam-522	90	52	aggregated	aggregate	VERB
ejpam-522	90	53	fuzzy	fuzzy	ADJ
ejpam-522	90	54	goal	goal	NOUN
ejpam-522	90	55	.	.	PUNCT
ejpam-522	91	1	the	the	DET
ejpam-522	91	2	maximin	maximin	NOUN
ejpam-522	91	3	solution	solution	NOUN
ejpam-522	91	4	can	can	AUX
ejpam-522	91	5	be	be	AUX
ejpam-522	91	6	consider	consider	VERB
ejpam-522	91	7	to	to	PART
ejpam-522	91	8	be	be	AUX
ejpam-522	91	9	the	the	DET
ejpam-522	91	10	solution	solution	NOUN
ejpam-522	91	11	maximizing	maximize	VERB
ejpam-522	91	12	the	the	DET
ejpam-522	91	13	function	function	NOUN
ejpam-522	91	14	,	,	PUNCT
ejpam-522	91	15	which	which	PRON
ejpam-522	91	16	is	be	AUX
ejpam-522	91	17	the	the	DET
ejpam-522	91	18	minimal	minimal	ADJ
ejpam-522	91	19	value	value	NOUN
ejpam-522	91	20	of	of	ADP
ejpam-522	91	21	the	the	DET
ejpam-522	91	22	function	function	NOUN
ejpam-522	91	23	with	with	ADP
ejpam-522	91	24	respect	respect	NOUN
ejpam-522	91	25	to	to	ADP
ejpam-522	91	26	the	the	DET
ejpam-522	91	27	opponent	opponent	NOUN
ejpam-522	91	28	’s	’s	PART
ejpam-522	91	29	decision	decision	NOUN
ejpam-522	91	30	variables	variable	NOUN
ejpam-522	91	31	.	.	PUNCT
ejpam-522	92	1	we	we	PRON
ejpam-522	92	2	assume	assume	VERB
ejpam-522	92	3	that	that	SCONJ
ejpam-522	92	4	a	a	DET
ejpam-522	92	5	player	player	NOUN
ejpam-522	92	6	has	have	AUX
ejpam-522	92	7	no	no	DET
ejpam-522	92	8	information	information	NOUN
ejpam-522	92	9	about	about	ADP
ejpam-522	92	10	his	his	PRON
ejpam-522	92	11	opponent	opponent	NOUN
ejpam-522	92	12	or	or	CCONJ
ejpam-522	92	13	the	the	DET
ejpam-522	92	14	information	information	NOUN
ejpam-522	92	15	is	be	AUX
ejpam-522	92	16	not	not	PART
ejpam-522	92	17	useful	useful	ADJ
ejpam-522	92	18	for	for	ADP
ejpam-522	92	19	the	the	DET
ejpam-522	92	20	decision	decision	NOUN
ejpam-522	92	21	making	make	VERB
ejpam-522	92	22	if	if	SCONJ
ejpam-522	92	23	he	he	PRON
ejpam-522	92	24	has	have	VERB
ejpam-522	92	25	.	.	PUNCT
ejpam-522	93	1	we	we	PRON
ejpam-522	93	2	can	can	AUX
ejpam-522	93	3	also	also	ADV
ejpam-522	93	4	consider	consider	VERB
ejpam-522	93	5	player	player	NOUN
ejpam-522	94	1	i	i	PRON
ejpam-522	94	2	i	i	PRON
ejpam-522	94	3	’s	’	VERB
ejpam-522	94	4	minimax	minimax	NOUN
ejpam-522	94	5	solution	solution	NOUN
ejpam-522	94	6	with	with	ADP
ejpam-522	94	7	respect	respect	NOUN
ejpam-522	94	8	to	to	ADP
ejpam-522	94	9	a	a	DET
ejpam-522	94	10	degree	degree	NOUN
ejpam-522	94	11	of	of	ADP
ejpam-522	94	12	attainment	attainment	NOUN
ejpam-522	94	13	of	of	ADP
ejpam-522	94	14	the	the	DET
ejpam-522	94	15	aggregated	aggregate	VERB
ejpam-522	94	16	fuzzy	fuzzy	ADJ
ejpam-522	94	17	goal	goal	NOUN
ejpam-522	94	18	in	in	ADP
ejpam-522	94	19	a	a	DET
ejpam-522	94	20	similar	similar	ADJ
ejpam-522	94	21	way	way	NOUN
ejpam-522	94	22	.	.	PUNCT
ejpam-522	95	1	3	3	X
ejpam-522	95	2	.	.	X
ejpam-522	95	3	solution	solution	NOUN
ejpam-522	95	4	concept	concept	NOUN
ejpam-522	95	5	we	we	PRON
ejpam-522	95	6	show	show	VERB
ejpam-522	95	7	a	a	DET
ejpam-522	95	8	new	new	ADJ
ejpam-522	95	9	method	method	NOUN
ejpam-522	95	10	for	for	ADP
ejpam-522	95	11	computing	compute	VERB
ejpam-522	95	12	the	the	DET
ejpam-522	95	13	max	max	PROPN
ejpam-522	95	14	-	-	PUNCT
ejpam-522	95	15	min	min	NOUN
ejpam-522	95	16	solution	solution	NOUN
ejpam-522	95	17	of	of	ADP
ejpam-522	95	18	multiobjective	multiobjective	ADJ
ejpam-522	95	19	game	game	NOUN
ejpam-522	95	20	.	.	PUNCT
ejpam-522	96	1	3.1	3.1	NUM
ejpam-522	96	2	.	.	PUNCT
ejpam-522	97	1	multiobjective	multiobjective	ADJ
ejpam-522	97	2	two	two	NUM
ejpam-522	97	3	-	-	PUNCT
ejpam-522	97	4	person	person	NOUN
ejpam-522	97	5	zero	zero	NUM
ejpam-522	97	6	-	-	PUNCT
ejpam-522	97	7	sum	sum	NOUN
ejpam-522	97	8	games	game	NOUN
ejpam-522	97	9	with	with	ADP
ejpam-522	97	10	fuzzy	fuzzy	ADJ
ejpam-522	97	11	payoffs	payoff	NOUN
ejpam-522	97	12	and	and	CCONJ
ejpam-522	97	13	fuzzy	fuzzy	ADJ
ejpam-522	97	14	goals	goal	NOUN
ejpam-522	97	15	.	.	PUNCT
ejpam-522	98	1	consider	consider	VERB
ejpam-522	98	2	multiobjective	multiobjective	ADJ
ejpam-522	98	3	two	two	NUM
ejpam-522	98	4	-	-	PUNCT
ejpam-522	98	5	person	person	NOUN
ejpam-522	98	6	zero	zero	NUM
ejpam-522	98	7	-	-	PUNCT
ejpam-522	98	8	sum	sum	NOUN
ejpam-522	98	9	games	game	NOUN
ejpam-522	98	10	with	with	ADP
ejpam-522	98	11	fuzzy	fuzzy	ADJ
ejpam-522	98	12	payoffs	payoff	NOUN
ejpam-522	98	13	eak	eak	VERB
ejpam-522	98	14	,	,	PUNCT
ejpam-522	98	15	k	k	PROPN
ejpam-522	98	16	=	=	SYM
ejpam-522	98	17	1	1	NUM
ejpam-522	98	18	,	,	PUNCT
ejpam-522	98	19	..	..	PUNCT
ejpam-522	98	20	,	,	PUNCT
ejpam-522	98	21	r.	r.	PROPN
ejpam-522	98	22	we	we	PRON
ejpam-522	98	23	assume	assume	VERB
ejpam-522	98	24	that	that	SCONJ
ejpam-522	98	25	a	a	DET
ejpam-522	98	26	player	player	NOUN
ejpam-522	98	27	has	have	VERB
ejpam-522	98	28	a	a	DET
ejpam-522	98	29	fuzzy	fuzzy	ADJ
ejpam-522	98	30	goal	goal	NOUN
ejpam-522	98	31	for	for	ADP
ejpam-522	98	32	each	each	PRON
ejpam-522	98	33	of	of	ADP
ejpam-522	98	34	the	the	DET
ejpam-522	98	35	objectives	objective	NOUN
ejpam-522	98	36	,	,	PUNCT
ejpam-522	98	37	which	which	PRON
ejpam-522	98	38	expresses	express	VERB
ejpam-522	98	39	the	the	DET
ejpam-522	98	40	player	player	NOUN
ejpam-522	98	41	’s	’s	PART
ejpam-522	98	42	degree	degree	NOUN
ejpam-522	98	43	of	of	ADP
ejpam-522	98	44	satisfaction	satisfaction	NOUN
ejpam-522	98	45	for	for	ADP
ejpam-522	98	46	the	the	DET
ejpam-522	98	47	payoff	payoff	NOUN
ejpam-522	98	48	.	.	PUNCT
ejpam-522	99	1	let	let	VERB
ejpam-522	99	2	player	player	NOUN
ejpam-522	100	1	i	i	PRON
ejpam-522	100	2	’s	’	VERB
ejpam-522	100	3	membership	membership	NOUN
ejpam-522	100	4	function	function	NOUN
ejpam-522	100	5	of	of	ADP
ejpam-522	100	6	the	the	DET
ejpam-522	100	7	fuzzy	fuzzy	ADJ
ejpam-522	100	8	goal	goal	NOUN
ejpam-522	100	9	for	for	ADP
ejpam-522	100	10	the	the	DET
ejpam-522	100	11	kth	kth	PROPN
ejpam-522	100	12	objective	objective	NOUN
ejpam-522	100	13	be	be	AUX
ejpam-522	100	14	denoted	denote	VERB
ejpam-522	100	15	by	by	ADP
ejpam-522	100	16	µegk	µegk	ADJ
ejpam-522	100	17	(	(	PUNCT
ejpam-522	100	18	pk	pk	NOUN
ejpam-522	100	19	)	)	PUNCT
ejpam-522	100	20	for	for	ADP
ejpam-522	100	21	the	the	DET
ejpam-522	100	22	kth	kth	PROPN
ejpam-522	100	23	payoff	payoff	PROPN
ejpam-522	100	24	pk	pk	PROPN
ejpam-522	100	25	.	.	PUNCT
ejpam-522	101	1	when	when	SCONJ
ejpam-522	101	2	the	the	DET
ejpam-522	101	3	membership	membership	NOUN
ejpam-522	101	4	function	function	VERB
ejpam-522	101	5	µegk(pk	µegk(pk	ADV
ejpam-522	101	6	)	)	PUNCT
ejpam-522	101	7	of	of	ADP
ejpam-522	101	8	the	the	DET
ejpam-522	101	9	fuzzy	fuzzy	ADJ
ejpam-522	101	10	goal	goal	NOUN
ejpam-522	101	11	is	be	AUX
ejpam-522	101	12	linear	linear	ADJ
ejpam-522	101	13	,	,	PUNCT
ejpam-522	101	14	it	it	PRON
ejpam-522	101	15	can	can	AUX
ejpam-522	101	16	be	be	AUX
ejpam-522	101	17	represented	represent	VERB
ejpam-522	101	18	as	as	ADP
ejpam-522	101	19	µegk(p	µegk(p	PROPN
ejpam-522	101	20	k	k	PROPN
ejpam-522	101	21	)	)	PUNCT
ejpam-522	101	22	=	=	PUNCT
ejpam-522	102	1			PROPN
ejpam-522	102	2			PRON
ejpam-522	102	3			NOUN
ejpam-522	102	4	0	0	NUM
ejpam-522	102	5	1−	1−	NUM
ejpam-522	103	1	ak−pk	ak−pk	INTJ
ejpam-522	103	2	ak−ak	ak−ak	NOUN
ejpam-522	103	3	1	1	NUM
ejpam-522	103	4	if	if	SCONJ
ejpam-522	103	5	pk	pk	NOUN
ejpam-522	103	6	<	<	X
ejpam-522	103	7	ak	ak	PROPN
ejpam-522	103	8	if	if	SCONJ
ejpam-522	103	9	ak	ak	PROPN
ejpam-522	103	10	≤	≤	X
ejpam-522	103	11	pk	pk	NOUN
ejpam-522	103	12	≤	≤	PROPN
ejpam-522	103	13	ak	ak	PROPN
ejpam-522	103	14	if	if	SCONJ
ejpam-522	103	15	ak	ak	PROPN
ejpam-522	103	16	<	<	X
ejpam-522	103	17	pk	pk	NOUN
ejpam-522	103	18			PROPN
ejpam-522	103	19			PROPN
ejpam-522	103	20			NOUN
ejpam-522	103	21	(	(	PUNCT
ejpam-522	103	22	10	10	NUM
ejpam-522	103	23	)	)	PUNCT
ejpam-522	103	24	where	where	SCONJ
ejpam-522	103	25	,	,	PUNCT
ejpam-522	103	26	for	for	ADP
ejpam-522	103	27	the	the	DET
ejpam-522	103	28	kth	kth	PROPN
ejpam-522	103	29	objective	objective	NOUN
ejpam-522	103	30	,	,	PUNCT
ejpam-522	103	31	ak	ak	PROPN
ejpam-522	103	32	is	be	AUX
ejpam-522	103	33	the	the	DET
ejpam-522	103	34	payoff	payoff	NOUN
ejpam-522	103	35	giving	give	VERB
ejpam-522	103	36	the	the	DET
ejpam-522	103	37	worst	bad	ADJ
ejpam-522	103	38	degree	degree	NOUN
ejpam-522	103	39	of	of	ADP
ejpam-522	103	40	satisfaction	satisfaction	NOUN
ejpam-522	103	41	for	for	ADP
ejpam-522	103	42	player	player	NOUN
ejpam-522	103	43	’s	’s	PART
ejpam-522	103	44	i	i	PRON
ejpam-522	103	45	and	and	CCONJ
ejpam-522	103	46	ak	ak	PROPN
ejpam-522	103	47	is	be	AUX
ejpam-522	103	48	the	the	DET
ejpam-522	103	49	payoff	payoff	NOUN
ejpam-522	103	50	giving	give	VERB
ejpam-522	103	51	the	the	DET
ejpam-522	103	52	best	good	ADJ
ejpam-522	103	53	degree	degree	NOUN
ejpam-522	103	54	of	of	ADP
ejpam-522	103	55	satisfaction	satisfaction	NOUN
ejpam-522	103	56	for	for	ADP
ejpam-522	103	57	player	player	NOUN
ejpam-522	103	58	i	i	PRON
ejpam-522	103	59	’	'	PUNCT
ejpam-522	103	60	s.	s.	PROPN
ejpam-522	103	61	morever	morever	PROPN
ejpam-522	103	62	,	,	PUNCT
ejpam-522	103	63	when	when	SCONJ
ejpam-522	103	64	the	the	DET
ejpam-522	103	65	membership	membership	NOUN
ejpam-522	103	66	function	function	NOUN
ejpam-522	103	67	µeak	µeak	VERB
ejpam-522	103	68	i	i	PRON
ejpam-522	103	69	j	j	PROPN
ejpam-522	103	70	(	(	PUNCT
ejpam-522	103	71	pk	pk	NOUN
ejpam-522	103	72	)	)	PUNCT
ejpam-522	103	73	of	of	ADP
ejpam-522	103	74	the	the	DET
ejpam-522	103	75	element	element	NOUN
ejpam-522	103	76	eak	eak	NOUN
ejpam-522	103	77	i	i	PRON
ejpam-522	103	78	j	j	PROPN
ejpam-522	103	79	,	,	PUNCT
ejpam-522	103	80	which	which	PRON
ejpam-522	103	81	is	be	AUX
ejpam-522	103	82	a	a	DET
ejpam-522	103	83	fuzzy	fuzzy	ADJ
ejpam-522	103	84	a.	a.	NOUN
ejpam-522	103	85	çevikel	çevikel	NOUN
ejpam-522	103	86	,	,	PUNCT
ejpam-522	103	87	m.	m.	PROPN
ejpam-522	103	88	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	103	89	/	/	SYM
ejpam-522	103	90	eur	eur	PROPN
ejpam-522	103	91	.	.	PUNCT
ejpam-522	104	1	j.	j.	PROPN
ejpam-522	104	2	pure	pure	PROPN
ejpam-522	104	3	appl	appl	PROPN
ejpam-522	104	4	.	.	PROPN
ejpam-522	104	5	math	math	PROPN
ejpam-522	104	6	,	,	PUNCT
ejpam-522	104	7	3	3	NUM
ejpam-522	104	8	(	(	PUNCT
ejpam-522	104	9	2010	2010	NUM
ejpam-522	104	10	)	)	PUNCT
ejpam-522	104	11	,	,	PUNCT
ejpam-522	104	12	107	107	NUM
ejpam-522	104	13	-	-	SYM
ejpam-522	104	14	117	117	NUM
ejpam-522	104	15	111	111	NUM
ejpam-522	104	16	number	number	NOUN
ejpam-522	104	17	,	,	PUNCT
ejpam-522	104	18	of	of	ADP
ejpam-522	104	19	the	the	DET
ejpam-522	104	20	fuzzy	fuzzy	ADJ
ejpam-522	104	21	payoff	payoff	NOUN
ejpam-522	104	22	matrix	matrix	NOUN
ejpam-522	104	23	eak	eak	NOUN
ejpam-522	104	24	for	for	ADP
ejpam-522	104	25	the	the	DET
ejpam-522	104	26	kth	kth	PROPN
ejpam-522	104	27	objective	objective	NOUN
ejpam-522	104	28	is	be	AUX
ejpam-522	104	29	linear	linear	ADJ
ejpam-522	104	30	,	,	PUNCT
ejpam-522	104	31	it	it	PRON
ejpam-522	104	32	can	can	AUX
ejpam-522	104	33	be	be	AUX
ejpam-522	104	34	represented	represent	VERB
ejpam-522	104	35	as	as	SCONJ
ejpam-522	104	36	µeak	µeak	VERB
ejpam-522	104	37	i	i	PRON
ejpam-522	104	38	j	j	PROPN
ejpam-522	104	39	(	(	PUNCT
ejpam-522	104	40	pk	pk	NOUN
ejpam-522	104	41	)	)	PUNCT
ejpam-522	104	42	=	=	PUNCT
ejpam-522	104	43			VERB
ejpam-522	104	44			NOUN
ejpam-522	104	45			X
ejpam-522	104	46	0	0	PUNCT
ejpam-522	105	1	(	(	PUNCT
ejpam-522	105	2	pk	pk	NOUN
ejpam-522	105	3	−	−	PROPN
ejpam-522	105	4	ak	ak	PROPN
ejpam-522	105	5	i	i	PROPN
ejpam-522	105	6	j	j	PROPN
ejpam-522	106	1	+	+	PUNCT
ejpam-522	106	2	ák	ák	ADJ
ejpam-522	106	3	i	i	PROPN
ejpam-522	106	4	j	j	PROPN
ejpam-522	106	5	)	)	PUNCT
ejpam-522	106	6	�	�	PROPN
ejpam-522	106	7	ák	ák	ADJ
ejpam-522	106	8	i	i	PRON
ejpam-522	106	9	j	j	PROPN
ejpam-522	106	10	(	(	PUNCT
ejpam-522	106	11	ak	ak	PROPN
ejpam-522	106	12	i	i	PROPN
ejpam-522	106	13	j	j	PROPN
ejpam-522	107	1	+	+	CCONJ
ejpam-522	107	2	àk	àk	SCONJ
ejpam-522	108	1	i	i	PROPN
ejpam-522	108	2	j	j	PROPN
ejpam-522	108	3	−	−	PROPN
ejpam-522	108	4	pk	pk	PROPN
ejpam-522	108	5	)	)	PUNCT
ejpam-522	108	6	�	�	PROPN
ejpam-522	108	7	àk	àk	ADJ
ejpam-522	109	1	i	i	PROPN
ejpam-522	109	2	j	j	PROPN
ejpam-522	109	3	0	0	PUNCT
ejpam-522	110	1	if	if	SCONJ
ejpam-522	110	2	pk	pk	NOUN
ejpam-522	110	3	<	<	X
ejpam-522	110	4	ak	ak	PROPN
ejpam-522	110	5	i	i	PROPN
ejpam-522	110	6	j	j	PROPN
ejpam-522	111	1	−	−	PROPN
ejpam-522	111	2	ák	ák	PROPN
ejpam-522	111	3	i	i	PRON
ejpam-522	111	4	j	j	PROPN
ejpam-522	112	1	if	if	SCONJ
ejpam-522	112	2	ak	ak	PROPN
ejpam-522	112	3	i	i	PROPN
ejpam-522	112	4	j	j	PROPN
ejpam-522	113	1	−	−	PROPN
ejpam-522	113	2	ák	ák	PROPN
ejpam-522	113	3	i	i	PROPN
ejpam-522	113	4	j	j	PROPN
ejpam-522	113	5	≤	≤	X
ejpam-522	113	6	pk	pk	NOUN
ejpam-522	113	7	<	<	X
ejpam-522	113	8	ak	ak	PROPN
ejpam-522	113	9	i	i	PRON
ejpam-522	113	10	j	j	PROPN
ejpam-522	114	1	if	if	SCONJ
ejpam-522	114	2	ak	ak	PROPN
ejpam-522	114	3	i	i	PROPN
ejpam-522	114	4	j	j	PROPN
ejpam-522	114	5	≤	≤	PROPN
ejpam-522	114	6	pk	pk	NOUN
ejpam-522	114	7	≤	≤	PUNCT
ejpam-522	114	8	ak	ak	PROPN
ejpam-522	115	1	i	i	PROPN
ejpam-522	115	2	j	j	PROPN
ejpam-522	116	1	+	+	CCONJ
ejpam-522	116	2	àk	àk	SCONJ
ejpam-522	117	1	i	i	PRON
ejpam-522	117	2	j	j	PROPN
ejpam-522	118	1	if	if	SCONJ
ejpam-522	118	2	ak	ak	PROPN
ejpam-522	118	3	i	i	PROPN
ejpam-522	118	4	j	j	PROPN
ejpam-522	119	1	+	+	CCONJ
ejpam-522	119	2	àk	àk	SCONJ
ejpam-522	120	1	i	i	PRON
ejpam-522	120	2	j	j	X
ejpam-522	120	3	<	<	X
ejpam-522	120	4	pk	pk	X
ejpam-522	120	5			PROPN
ejpam-522	120	6			DET
ejpam-522	120	7			PROPN
ejpam-522	120	8	(	(	PUNCT
ejpam-522	120	9	11	11	NUM
ejpam-522	120	10	)	)	PUNCT
ejpam-522	120	11	in	in	ADP
ejpam-522	120	12	general	general	ADJ
ejpam-522	120	13	,	,	PUNCT
ejpam-522	120	14	the	the	DET
ejpam-522	120	15	degree	degree	NOUN
ejpam-522	120	16	of	of	ADP
ejpam-522	120	17	attainment	attainment	NOUN
ejpam-522	120	18	of	of	ADP
ejpam-522	120	19	the	the	DET
ejpam-522	120	20	fuzzy	fuzzy	ADJ
ejpam-522	120	21	goal	goal	NOUN
ejpam-522	120	22	can	can	AUX
ejpam-522	120	23	be	be	AUX
ejpam-522	120	24	represented	represent	VERB
ejpam-522	120	25	as	as	ADP
ejpam-522	120	26	the	the	DET
ejpam-522	120	27	following	follow	VERB
ejpam-522	120	28	vector	vector	NOUN
ejpam-522	120	29	expression	expression	NOUN
ejpam-522	120	30	:	:	PUNCT
ejpam-522	120	31			PROPN
ejpam-522	120	32			ADJ
ejpam-522	120	33	max	max	PROPN
ejpam-522	120	34	p1	p1	PROPN
ejpam-522	120	35	min(µx	min(µx	NOUN
ejpam-522	120	36	ea1	ea1	NOUN
ejpam-522	120	37	y(p	y(p	PROPN
ejpam-522	120	38	1),µeg1(p1	1),µeg1(p1	NUM
ejpam-522	120	39	)	)	PUNCT
ejpam-522	120	40	)	)	PUNCT
ejpam-522	120	41	...............................	...............................	PUNCT
ejpam-522	121	1	max	max	PROPN
ejpam-522	121	2	pr	pr	INTJ
ejpam-522	121	3	min(µx	min(µx	PROPN
ejpam-522	121	4	ear	ear	VERB
ejpam-522	121	5	y(p	y(p	PROPN
ejpam-522	121	6	r),µegr	r),µegr	PROPN
ejpam-522	121	7	(	(	PUNCT
ejpam-522	121	8	pr	pr	NOUN
ejpam-522	121	9	)	)	PUNCT
ejpam-522	121	10	)	)	PUNCT
ejpam-522	122	1			PROPN
ejpam-522	123	1			PROPN
ejpam-522	123	2	.	.	PUNCT
ejpam-522	124	1	(	(	PUNCT
ejpam-522	124	2	12	12	NUM
ejpam-522	124	3	)	)	PUNCT
ejpam-522	124	4	for	for	ADP
ejpam-522	124	5	such	such	DET
ejpam-522	124	6	a	a	DET
ejpam-522	124	7	problem	problem	NOUN
ejpam-522	124	8	,	,	PUNCT
ejpam-522	124	9	we	we	PRON
ejpam-522	124	10	employ	employ	VERB
ejpam-522	124	11	the	the	DET
ejpam-522	124	12	fuzzy	fuzzy	ADJ
ejpam-522	124	13	decision	decision	NOUN
ejpam-522	124	14	rule	rule	NOUN
ejpam-522	124	15	by	by	ADP
ejpam-522	124	16	bellman	bellman	NOUN
ejpam-522	124	17	and	and	CCONJ
ejpam-522	124	18	zadeh	zadeh	PROPN
ejpam-522	125	1	[	[	X
ejpam-522	125	2	4	4	NUM
ejpam-522	125	3	]	]	PUNCT
ejpam-522	125	4	,	,	PUNCT
ejpam-522	125	5	as	as	ADP
ejpam-522	125	6	an	an	DET
ejpam-522	125	7	aggregation	aggregation	NOUN
ejpam-522	125	8	rule	rule	NOUN
ejpam-522	125	9	of	of	ADP
ejpam-522	125	10	multiple	multiple	ADJ
ejpam-522	125	11	fuzzy	fuzzy	ADJ
ejpam-522	125	12	goals	goal	NOUN
ejpam-522	125	13	in	in	ADP
ejpam-522	125	14	a	a	DET
ejpam-522	125	15	way	way	NOUN
ejpam-522	125	16	similar	similar	ADJ
ejpam-522	125	17	to	to	ADP
ejpam-522	125	18	the	the	DET
ejpam-522	125	19	previous	previous	ADJ
ejpam-522	125	20	subsection	subsection	NOUN
ejpam-522	125	21	.	.	PUNCT
ejpam-522	126	1	then	then	ADV
ejpam-522	126	2	the	the	DET
ejpam-522	126	3	membership	membership	NOUN
ejpam-522	126	4	function	function	NOUN
ejpam-522	126	5	of	of	ADP
ejpam-522	126	6	the	the	DET
ejpam-522	126	7	aggregated	aggregate	VERB
ejpam-522	126	8	fuzzy	fuzzy	ADJ
ejpam-522	126	9	goal	goal	NOUN
ejpam-522	126	10	is	be	AUX
ejpam-522	126	11	expressed	express	VERB
ejpam-522	126	12	as	as	ADP
ejpam-522	126	13	⌢	⌢	NUM
ejpam-522	126	14	µa(x	µa(x	X
ejpam-522	126	15	,	,	PUNCT
ejpam-522	126	16	y)(p	y)(p	NOUN
ejpam-522	126	17	∗	∗	NOUN
ejpam-522	126	18	)	)	PUNCT
ejpam-522	127	1	=	=	NOUN
ejpam-522	127	2	min	min	NOUN
ejpam-522	127	3	k∈k	k∈k	NOUN
ejpam-522	127	4	max	max	PROPN
ejpam-522	127	5	pk	pk	PROPN
ejpam-522	127	6	min(µx	min(µx	PROPN
ejpam-522	127	7	eak	eak	PROPN
ejpam-522	127	8	y(p	y(p	PROPN
ejpam-522	127	9	k),µegk(p	k),µegk(p	PROPN
ejpam-522	127	10	k	k	PROPN
ejpam-522	127	11	)	)	PUNCT
ejpam-522	127	12	)	)	PUNCT
ejpam-522	127	13	,	,	PUNCT
ejpam-522	127	14	(	(	PUNCT
ejpam-522	127	15	13	13	NUM
ejpam-522	127	16	)	)	PUNCT
ejpam-522	127	17	where	where	SCONJ
ejpam-522	127	18	p∗	p∗	NOUN
ejpam-522	127	19	=	=	SYM
ejpam-522	127	20	(	(	PUNCT
ejpam-522	127	21	p1∗	p1∗	PROPN
ejpam-522	127	22	,	,	PUNCT
ejpam-522	127	23	...	...	PUNCT
ejpam-522	127	24	,	,	PUNCT
ejpam-522	127	25	pr∗	pr∗	ADJ
ejpam-522	127	26	)	)	PUNCT
ejpam-522	127	27	.	.	PUNCT
ejpam-522	128	1	then	then	ADV
ejpam-522	128	2	,	,	PUNCT
ejpam-522	128	3	player	player	NOUN
ejpam-522	128	4	i	i	PRON
ejpam-522	128	5	’s	’	VERB
ejpam-522	128	6	maximin	maximin	NOUN
ejpam-522	128	7	value	value	NOUN
ejpam-522	128	8	with	with	ADP
ejpam-522	128	9	respect	respect	NOUN
ejpam-522	128	10	to	to	ADP
ejpam-522	128	11	a	a	DET
ejpam-522	128	12	degree	degree	NOUN
ejpam-522	128	13	of	of	ADP
ejpam-522	128	14	attainment	attainment	NOUN
ejpam-522	128	15	of	of	ADP
ejpam-522	128	16	the	the	DET
ejpam-522	128	17	aggregated	aggregate	VERB
ejpam-522	128	18	fuzzy	fuzzy	ADJ
ejpam-522	128	19	goal	goal	NOUN
ejpam-522	128	20	is	be	AUX
ejpam-522	128	21	represented	represent	VERB
ejpam-522	128	22	as	as	ADP
ejpam-522	128	23	max	max	PROPN
ejpam-522	128	24	x∈x	x∈x	PROPN
ejpam-522	128	25	min	min	PROPN
ejpam-522	128	26	y∈y	y∈y	PROPN
ejpam-522	128	27	⌢	⌢	NUM
ejpam-522	128	28	µa(x	µa(x	X
ejpam-522	128	29	,	,	PUNCT
ejpam-522	128	30	y)(p	y)(p	NOUN
ejpam-522	128	31	∗	∗	NOUN
ejpam-522	128	32	)	)	PUNCT
ejpam-522	129	1	=	=	NOUN
ejpam-522	129	2	max	max	PROPN
ejpam-522	129	3	x∈x	x∈x	PROPN
ejpam-522	129	4	min	min	PROPN
ejpam-522	129	5	y∈y	y∈y	PROPN
ejpam-522	129	6	min	min	PROPN
ejpam-522	129	7	k∈k	k∈k	PROPN
ejpam-522	129	8	max	max	PROPN
ejpam-522	129	9	pk	pk	PROPN
ejpam-522	129	10	min(µx	min(µx	PROPN
ejpam-522	129	11	eak	eak	PROPN
ejpam-522	129	12	y(p	y(p	PROPN
ejpam-522	129	13	k),µegk	k),µegk	PROPN
ejpam-522	129	14	(	(	PUNCT
ejpam-522	129	15	pk	pk	NOUN
ejpam-522	129	16	)	)	PUNCT
ejpam-522	129	17	)	)	PUNCT
ejpam-522	129	18	.	.	PUNCT
ejpam-522	130	1	(	(	PUNCT
ejpam-522	130	2	14	14	NUM
ejpam-522	130	3	)	)	PUNCT
ejpam-522	130	4	when	when	SCONJ
ejpam-522	130	5	membership	membership	NOUN
ejpam-522	130	6	functions	function	NOUN
ejpam-522	130	7	are	be	AUX
ejpam-522	130	8	linear	linear	ADJ
ejpam-522	130	9	,	,	PUNCT
ejpam-522	130	10	the	the	DET
ejpam-522	130	11	maximin	maximin	NOUN
ejpam-522	130	12	strategy	strategy	NOUN
ejpam-522	130	13	with	with	ADP
ejpam-522	130	14	respect	respect	NOUN
ejpam-522	130	15	to	to	ADP
ejpam-522	130	16	a	a	DET
ejpam-522	130	17	degree	degree	NOUN
ejpam-522	130	18	of	of	ADP
ejpam-522	130	19	attainment	attainment	NOUN
ejpam-522	130	20	of	of	ADP
ejpam-522	130	21	the	the	DET
ejpam-522	130	22	aggregated	aggregate	VERB
ejpam-522	130	23	fuzzy	fuzzy	ADJ
ejpam-522	130	24	goal	goal	NOUN
ejpam-522	130	25	can	can	AUX
ejpam-522	130	26	be	be	AUX
ejpam-522	130	27	obtained	obtain	VERB
ejpam-522	130	28	by	by	ADP
ejpam-522	130	29	solving	solve	VERB
ejpam-522	130	30	the	the	DET
ejpam-522	130	31	mathematical	mathematical	ADJ
ejpam-522	130	32	programming	programming	NOUN
ejpam-522	130	33	problem	problem	NOUN
ejpam-522	130	34	in	in	ADP
ejpam-522	130	35	the	the	DET
ejpam-522	130	36	following	follow	VERB
ejpam-522	130	37	theorem	theorem	PROPN
ejpam-522	130	38	.	.	PUNCT
ejpam-522	131	1	theorem	theorem	NOUN
ejpam-522	131	2	1	1	NUM
ejpam-522	131	3	.	.	X
ejpam-522	132	1	for	for	ADP
ejpam-522	132	2	multiobjective	multiobjective	ADJ
ejpam-522	132	3	two	two	NUM
ejpam-522	132	4	-	-	PUNCT
ejpam-522	132	5	person	person	NOUN
ejpam-522	132	6	zero	zero	NUM
ejpam-522	132	7	-	-	PUNCT
ejpam-522	132	8	sum	sum	NOUN
ejpam-522	132	9	games	game	NOUN
ejpam-522	132	10	,	,	PUNCT
ejpam-522	132	11	if	if	SCONJ
ejpam-522	132	12	membership	membership	NOUN
ejpam-522	132	13	functions	function	NOUN
ejpam-522	132	14	of	of	ADP
ejpam-522	132	15	the	the	DET
ejpam-522	132	16	fuzzy	fuzzy	ADJ
ejpam-522	132	17	goal	goal	NOUN
ejpam-522	132	18	and	and	CCONJ
ejpam-522	132	19	shape	shape	NOUN
ejpam-522	132	20	functions	function	NOUN
ejpam-522	132	21	of	of	ADP
ejpam-522	132	22	l	l	NOUN
ejpam-522	132	23	-	-	NOUN
ejpam-522	132	24	r	r	NOUN
ejpam-522	132	25	fuzzy	fuzzy	ADJ
ejpam-522	132	26	numbers	number	NOUN
ejpam-522	132	27	for	for	ADP
ejpam-522	132	28	fuzzy	fuzzy	ADJ
ejpam-522	132	29	payoffs	payoff	NOUN
ejpam-522	132	30	are	be	AUX
ejpam-522	132	31	linear	linear	ADJ
ejpam-522	132	32	such	such	ADJ
ejpam-522	132	33	as	as	ADP
ejpam-522	132	34	(	(	PUNCT
ejpam-522	132	35	10	10	NUM
ejpam-522	132	36	)	)	PUNCT
ejpam-522	132	37	and	and	CCONJ
ejpam-522	132	38	(	(	PUNCT
ejpam-522	132	39	11	11	NUM
ejpam-522	132	40	)	)	PUNCT
ejpam-522	132	41	,	,	PUNCT
ejpam-522	132	42	player	player	NOUN
ejpam-522	132	43	i	i	PRON
ejpam-522	132	44	’s	’	VERB
ejpam-522	132	45	maximin	maximin	NOUN
ejpam-522	132	46	solution	solution	NOUN
ejpam-522	132	47	with	with	ADP
ejpam-522	132	48	respect	respect	NOUN
ejpam-522	132	49	to	to	ADP
ejpam-522	132	50	a	a	DET
ejpam-522	132	51	degree	degree	NOUN
ejpam-522	132	52	of	of	ADP
ejpam-522	132	53	attainment	attainment	NOUN
ejpam-522	132	54	of	of	ADP
ejpam-522	132	55	the	the	DET
ejpam-522	132	56	aggregated	aggregate	VERB
ejpam-522	132	57	fuzzy	fuzzy	ADJ
ejpam-522	132	58	goal	goal	NOUN
ejpam-522	132	59	is	be	AUX
ejpam-522	132	60	equal	equal	ADJ
ejpam-522	132	61	to	to	ADP
ejpam-522	132	62	an	an	DET
ejpam-522	132	63	optimal	optimal	ADJ
ejpam-522	132	64	solution	solution	NOUN
ejpam-522	132	65	to	to	ADP
ejpam-522	132	66	the	the	DET
ejpam-522	132	67	nonlinear	nonlinear	ADJ
ejpam-522	132	68	programming	programming	NOUN
ejpam-522	132	69	problem	problem	NOUN
ejpam-522	132	70	:	:	PUNCT
ejpam-522	132	71	maximize	maximize	VERB
ejpam-522	132	72	x	x	SYM
ejpam-522	132	73	,	,	PUNCT
ejpam-522	132	74	σ	σ	PROPN
ejpam-522	132	75	σ	σ	PROPN
ejpam-522	132	76	sub	sub	NOUN
ejpam-522	132	77	ject	ject	PROPN
ejpam-522	132	78	to	to	ADP
ejpam-522	132	79	m∑	m∑	PUNCT
ejpam-522	132	80	i=1	i=1	PROPN
ejpam-522	132	81	n∑	n∑	PROPN
ejpam-522	133	1	j=1	j=1	PROPN
ejpam-522	133	2	(	(	PUNCT
ejpam-522	133	3	ak	ak	PROPN
ejpam-522	133	4	i	i	PROPN
ejpam-522	133	5	j	j	PROPN
ejpam-522	134	1	+	+	PROPN
ejpam-522	134	2	àk	àk	ADJ
ejpam-522	134	3	i	i	PRON
ejpam-522	134	4	j	j	PROPN
ejpam-522	134	5	)	)	PUNCT
ejpam-522	134	6	xi	xi	PROPN
ejpam-522	134	7	y	y	PROPN
ejpam-522	134	8	j−ak	j−ak	PROPN
ejpam-522	134	9	m∑	m∑	VERB
ejpam-522	134	10	i=1	i=1	PROPN
ejpam-522	134	11	n∑	n∑	PROPN
ejpam-522	135	1	j=1	j=1	PROPN
ejpam-522	135	2	àk	àk	ADV
ejpam-522	135	3	i	i	PRON
ejpam-522	135	4	j	j	PROPN
ejpam-522	135	5	xi	xi	PROPN
ejpam-522	135	6	y	y	PROPN
ejpam-522	135	7	j+ak−ak	j+ak−ak	VERB
ejpam-522	135	8	≥	≥	PROPN
ejpam-522	135	9	σ	σ	PROPN
ejpam-522	135	10	,	,	PUNCT
ejpam-522	135	11	∀y	∀y	PROPN
ejpam-522	135	12	∈	∈	PROPN
ejpam-522	135	13	y	y	PROPN
ejpam-522	135	14	,	,	PUNCT
ejpam-522	135	15	k	k	PROPN
ejpam-522	135	16	=	=	SYM
ejpam-522	135	17	1	1	NUM
ejpam-522	135	18	,	,	PUNCT
ejpam-522	135	19	...	...	PUNCT
ejpam-522	135	20	,	,	PUNCT
ejpam-522	136	1	r	r	NOUN
ejpam-522	136	2	m∑	m∑	NOUN
ejpam-522	136	3	i=1	i=1	NOUN
ejpam-522	136	4	x	x	PUNCT
ejpam-522	137	1	i	i	NOUN
ejpam-522	137	2	=	=	NOUN
ejpam-522	137	3	1	1	NUM
ejpam-522	137	4	x	x	X
ejpam-522	137	5	i	i	PRON
ejpam-522	137	6	≥	≥	NOUN
ejpam-522	137	7	0	0	NUM
ejpam-522	137	8	,	,	PUNCT
ejpam-522	137	9	i	i	PRON
ejpam-522	137	10	=	=	NOUN
ejpam-522	137	11	1	1	NUM
ejpam-522	137	12	,	,	PUNCT
ejpam-522	137	13	...	...	PUNCT
ejpam-522	137	14	,	,	PUNCT
ejpam-522	137	15	m	m	VERB
ejpam-522	137	16	(	(	PUNCT
ejpam-522	137	17	15	15	NUM
ejpam-522	137	18	)	)	PUNCT
ejpam-522	137	19	if	if	SCONJ
ejpam-522	137	20	the	the	DET
ejpam-522	137	21	optimal	optimal	ADJ
ejpam-522	137	22	value	value	NOUN
ejpam-522	137	23	σ∗	σ∗	NOUN
ejpam-522	137	24	satisfies	satisfie	NOUN
ejpam-522	137	25	0≤	0≤	NUM
ejpam-522	137	26	σ∗	σ∗	X
ejpam-522	137	27	≤	≤	NUM
ejpam-522	137	28	1	1	NUM
ejpam-522	137	29	[	[	X
ejpam-522	137	30	14	14	NUM
ejpam-522	137	31	,	,	PUNCT
ejpam-522	137	32	17	17	NUM
ejpam-522	137	33	]	]	PUNCT
ejpam-522	137	34	.	.	PUNCT
ejpam-522	138	1	a.	a.	PROPN
ejpam-522	138	2	çevikel	çevikel	PROPN
ejpam-522	138	3	,	,	PUNCT
ejpam-522	138	4	m.	m.	PROPN
ejpam-522	138	5	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	138	6	/	/	SYM
ejpam-522	138	7	eur	eur	PROPN
ejpam-522	138	8	.	.	PUNCT
ejpam-522	139	1	j.	j.	PROPN
ejpam-522	139	2	pure	pure	PROPN
ejpam-522	139	3	appl	appl	PROPN
ejpam-522	139	4	.	.	PROPN
ejpam-522	139	5	math	math	PROPN
ejpam-522	139	6	,	,	PUNCT
ejpam-522	139	7	3	3	NUM
ejpam-522	139	8	(	(	PUNCT
ejpam-522	139	9	2010	2010	NUM
ejpam-522	139	10	)	)	PUNCT
ejpam-522	139	11	,	,	PUNCT
ejpam-522	139	12	107	107	NUM
ejpam-522	139	13	-	-	SYM
ejpam-522	139	14	117	117	NUM
ejpam-522	139	15	112	112	NUM
ejpam-522	139	16	we	we	PRON
ejpam-522	139	17	can	can	AUX
ejpam-522	139	18	calculate	calculate	VERB
ejpam-522	139	19	the	the	DET
ejpam-522	139	20	maximin	maximin	NOUN
ejpam-522	139	21	solution	solution	NOUN
ejpam-522	139	22	with	with	ADP
ejpam-522	139	23	respect	respect	NOUN
ejpam-522	139	24	to	to	ADP
ejpam-522	139	25	a	a	DET
ejpam-522	139	26	degree	degree	NOUN
ejpam-522	139	27	of	of	ADP
ejpam-522	139	28	attainment	attainment	NOUN
ejpam-522	139	29	of	of	ADP
ejpam-522	139	30	the	the	DET
ejpam-522	139	31	fuzzy	fuzzy	ADJ
ejpam-522	139	32	goal	goal	NOUN
ejpam-522	139	33	by	by	ADP
ejpam-522	139	34	applying	apply	VERB
ejpam-522	139	35	a	a	DET
ejpam-522	139	36	method	method	NOUN
ejpam-522	139	37	using	use	VERB
ejpam-522	139	38	the	the	DET
ejpam-522	139	39	relaxation	relaxation	NOUN
ejpam-522	139	40	procedure	procedure	NOUN
ejpam-522	139	41	by	by	ADP
ejpam-522	139	42	shimizu	shimizu	PROPN
ejpam-522	139	43	and	and	CCONJ
ejpam-522	139	44	aiyoshi	aiyoshi	NOUN
ejpam-522	140	1	[	[	X
ejpam-522	140	2	19	19	NUM
ejpam-522	140	3	]	]	X
ejpam-522	140	4	,	,	PUNCT
ejpam-522	140	5	in	in	ADP
ejpam-522	140	6	a	a	DET
ejpam-522	140	7	process	process	NOUN
ejpam-522	140	8	similar	similar	ADJ
ejpam-522	140	9	to	to	ADP
ejpam-522	140	10	a	a	DET
ejpam-522	140	11	single	single	ADJ
ejpam-522	140	12	-	-	PUNCT
ejpam-522	140	13	objective	objective	NOUN
ejpam-522	140	14	case	case	NOUN
ejpam-522	141	1	and	and	CCONJ
ejpam-522	141	2	then	then	ADV
ejpam-522	141	3	we	we	PRON
ejpam-522	141	4	obtain	obtain	VERB
ejpam-522	141	5	the	the	DET
ejpam-522	141	6	maximin	maximin	NOUN
ejpam-522	141	7	solution	solution	NOUN
ejpam-522	141	8	.	.	PUNCT
ejpam-522	142	1	consider	consider	VERB
ejpam-522	142	2	the	the	DET
ejpam-522	142	3	following	follow	VERB
ejpam-522	142	4	relaxed	relaxed	ADJ
ejpam-522	142	5	problem	problem	NOUN
ejpam-522	142	6	for	for	ADP
ejpam-522	142	7	problem	problem	NOUN
ejpam-522	142	8	(	(	PUNCT
ejpam-522	142	9	15	15	NUM
ejpam-522	142	10	)	)	PUNCT
ejpam-522	142	11	by	by	ADP
ejpam-522	142	12	taking	take	VERB
ejpam-522	142	13	l	l	PROPN
ejpam-522	142	14	points	point	NOUN
ejpam-522	142	15	y	y	PROPN
ejpam-522	142	16	l	l	NOUN
ejpam-522	142	17	,	,	PUNCT
ejpam-522	142	18	l	l	NOUN
ejpam-522	142	19	=	=	SYM
ejpam-522	142	20	1	1	NUM
ejpam-522	142	21	,	,	PUNCT
ejpam-522	142	22	...	...	PUNCT
ejpam-522	142	23	,	,	PUNCT
ejpam-522	143	1	l	l	PROPN
ejpam-522	143	2	satisfying	satisfy	VERB
ejpam-522	143	3	y	y	PROPN
ejpam-522	143	4	l	l	NOUN
ejpam-522	143	5	∈	∈	PROPN
ejpam-522	143	6	y	y	PROPN
ejpam-522	143	7	,	,	PUNCT
ejpam-522	143	8	i.e.	i.e.	X
ejpam-522	143	9	,	,	PUNCT
ejpam-522	143	10	n∑	n∑	NOUN
ejpam-522	143	11	j=1	j=1	NOUN
ejpam-522	143	12	y	y	PROPN
ejpam-522	143	13	l	l	PROPN
ejpam-522	143	14	j	j	PROPN
ejpam-522	143	15	=	=	SYM
ejpam-522	143	16	1	1	NUM
ejpam-522	143	17	,	,	PUNCT
ejpam-522	143	18	y	y	PROPN
ejpam-522	143	19	l	l	PROPN
ejpam-522	143	20	j	j	PROPN
ejpam-522	143	21	≥	≥	PROPN
ejpam-522	143	22	0	0	NUM
ejpam-522	143	23	,	,	PUNCT
ejpam-522	143	24	j	j	PROPN
ejpam-522	143	25	=	=	SYM
ejpam-522	143	26	1	1	NUM
ejpam-522	143	27	,	,	PUNCT
ejpam-522	143	28	...	...	PUNCT
ejpam-522	143	29	,	,	PUNCT
ejpam-522	143	30	n.	n.	NOUN
ejpam-522	143	31	maximize	maximize	NOUN
ejpam-522	143	32	x	x	SYM
ejpam-522	143	33	,	,	PUNCT
ejpam-522	143	34	σ	σ	PROPN
ejpam-522	143	35	σ	σ	PROPN
ejpam-522	143	36	sub	sub	NOUN
ejpam-522	143	37	ject	ject	PROPN
ejpam-522	143	38	to	to	ADP
ejpam-522	143	39	m∑	m∑	PUNCT
ejpam-522	143	40	i=1	i=1	PROPN
ejpam-522	143	41	n∑	n∑	PROPN
ejpam-522	144	1	j=1	j=1	PROPN
ejpam-522	144	2	(	(	PUNCT
ejpam-522	144	3	ak	ak	PROPN
ejpam-522	144	4	i	i	PROPN
ejpam-522	144	5	j	j	PROPN
ejpam-522	145	1	+	+	PROPN
ejpam-522	145	2	àk	àk	ADJ
ejpam-522	145	3	i	i	PRON
ejpam-522	145	4	j	j	PROPN
ejpam-522	145	5	)	)	PUNCT
ejpam-522	145	6	xi	xi	PROPN
ejpam-522	145	7	y	y	PROPN
ejpam-522	145	8	l	l	PROPN
ejpam-522	146	1	j	j	PROPN
ejpam-522	146	2	−ak	−ak	INTJ
ejpam-522	146	3	m∑	m∑	INTJ
ejpam-522	146	4	i=1	i=1	PROPN
ejpam-522	146	5	n∑	n∑	PROPN
ejpam-522	147	1	j=1	j=1	PROPN
ejpam-522	147	2	àk	àk	ADV
ejpam-522	147	3	i	i	PRON
ejpam-522	147	4	j	j	PROPN
ejpam-522	147	5	xi	xi	INTJ
ejpam-522	147	6	y	y	PROPN
ejpam-522	147	7	l	l	PROPN
ejpam-522	147	8	j	j	PROPN
ejpam-522	148	1	+	+	PROPN
ejpam-522	148	2	ak−ak	ak−ak	PROPN
ejpam-522	148	3	≥	≥	PROPN
ejpam-522	148	4	σ	σ	NOUN
ejpam-522	148	5	,	,	PUNCT
ejpam-522	148	6	l	l	NOUN
ejpam-522	148	7	=	=	SYM
ejpam-522	148	8	1	1	NUM
ejpam-522	148	9	,	,	PUNCT
ejpam-522	148	10	...	...	PUNCT
ejpam-522	148	11	,	,	PUNCT
ejpam-522	148	12	l	l	NOUN
ejpam-522	148	13	,	,	PUNCT
ejpam-522	148	14	k	k	PROPN
ejpam-522	148	15	=	=	SYM
ejpam-522	148	16	1	1	NUM
ejpam-522	148	17	,	,	PUNCT
ejpam-522	148	18	...	...	PUNCT
ejpam-522	148	19	,	,	PUNCT
ejpam-522	149	1	r	r	NOUN
ejpam-522	149	2	m∑	m∑	NOUN
ejpam-522	149	3	i=1	i=1	NOUN
ejpam-522	149	4	x	x	PUNCT
ejpam-522	150	1	i	i	NOUN
ejpam-522	150	2	=	=	NOUN
ejpam-522	150	3	1	1	NUM
ejpam-522	150	4	x	x	X
ejpam-522	150	5	i	i	PRON
ejpam-522	150	6	≥	≥	NOUN
ejpam-522	150	7	0	0	NUM
ejpam-522	150	8	,	,	PUNCT
ejpam-522	150	9	i	i	PRON
ejpam-522	150	10	=	=	NOUN
ejpam-522	150	11	1	1	NUM
ejpam-522	150	12	,	,	PUNCT
ejpam-522	150	13	...	...	PUNCT
ejpam-522	150	14	,	,	PUNCT
ejpam-522	150	15	m	m	VERB
ejpam-522	150	16	(	(	PUNCT
ejpam-522	150	17	16	16	NUM
ejpam-522	150	18	)	)	PUNCT
ejpam-522	150	19	let	let	VERB
ejpam-522	150	20	σ	σ	PROPN
ejpam-522	150	21	=	=	SYM
ejpam-522	150	22	⌢	⌢	NUM
ejpam-522	150	23	σ	σ	PROPN
ejpam-522	150	24	,	,	PUNCT
ejpam-522	150	25	where	where	SCONJ
ejpam-522	150	26	⌢	⌢	NUM
ejpam-522	150	27	σ	σ	PROPN
ejpam-522	150	28	is	be	AUX
ejpam-522	150	29	a	a	DET
ejpam-522	150	30	constant	constant	ADJ
ejpam-522	150	31	value	value	NOUN
ejpam-522	150	32	in	in	ADP
ejpam-522	150	33	[	[	X
ejpam-522	150	34	0,1	0,1	NUM
ejpam-522	150	35	]	]	PUNCT
ejpam-522	150	36	.	.	PUNCT
ejpam-522	151	1	then	then	ADV
ejpam-522	151	2	the	the	DET
ejpam-522	151	3	constraints	constraint	NOUN
ejpam-522	151	4	of	of	ADP
ejpam-522	151	5	the	the	DET
ejpam-522	151	6	relaxed	relaxed	ADJ
ejpam-522	151	7	problem	problem	NOUN
ejpam-522	151	8	(	(	PUNCT
ejpam-522	151	9	16	16	NUM
ejpam-522	151	10	)	)	PUNCT
ejpam-522	151	11	become	become	VERB
ejpam-522	151	12	as	as	SCONJ
ejpam-522	151	13	follows	follow	VERB
ejpam-522	151	14	:	:	PUNCT
ejpam-522	151	15	m∑	m∑	INTJ
ejpam-522	151	16	i=1	i=1	PROPN
ejpam-522	151	17	n∑	n∑	PROPN
ejpam-522	152	1	j=1	j=1	PROPN
ejpam-522	152	2	(	(	PUNCT
ejpam-522	152	3	ak	ak	PROPN
ejpam-522	152	4	i	i	PROPN
ejpam-522	152	5	j	j	PROPN
ejpam-522	153	1	+	+	CCONJ
ejpam-522	153	2	àk	àk	SCONJ
ejpam-522	153	3	i	i	PRON
ejpam-522	153	4	j)x	j)x	VERB
ejpam-522	154	1	i	i	VERB
ejpam-522	154	2	y	y	PROPN
ejpam-522	154	3	l	l	PROPN
ejpam-522	154	4	j	j	PROPN
ejpam-522	155	1	−	−	PROPN
ejpam-522	155	2	ak	ak	PROPN
ejpam-522	155	3	≥	≥	PROPN
ejpam-522	155	4	⌢	⌢	NUM
ejpam-522	155	5	σ	σ	PROPN
ejpam-522	155	6	(	(	PUNCT
ejpam-522	155	7	m∑	m∑	ADV
ejpam-522	155	8	i=1	i=1	PROPN
ejpam-522	155	9	n∑	n∑	PROPN
ejpam-522	156	1	j=1	j=1	PROPN
ejpam-522	156	2	àk	àk	ADV
ejpam-522	156	3	i	i	PRON
ejpam-522	156	4	j	j	VERB
ejpam-522	157	1	x	x	VERB
ejpam-522	158	1	i	i	PRON
ejpam-522	158	2	y	y	PROPN
ejpam-522	158	3	l	l	NOUN
ejpam-522	158	4	j	j	PROPN
ejpam-522	159	1	+	+	CCONJ
ejpam-522	159	2	ak	ak	PROPN
ejpam-522	159	3	−	−	PROPN
ejpam-522	159	4	ak	ak	PROPN
ejpam-522	159	5	)	)	PUNCT
ejpam-522	159	6	,	,	PUNCT
ejpam-522	159	7	l	l	NOUN
ejpam-522	160	1	=	=	SYM
ejpam-522	160	2	1	1	NUM
ejpam-522	160	3	,	,	PUNCT
ejpam-522	160	4	...	...	PUNCT
ejpam-522	160	5	,	,	PUNCT
ejpam-522	160	6	l	l	NOUN
ejpam-522	160	7	,	,	PUNCT
ejpam-522	160	8	k	k	PROPN
ejpam-522	160	9	=	=	SYM
ejpam-522	160	10	1	1	NUM
ejpam-522	160	11	,	,	PUNCT
ejpam-522	160	12	...	...	PUNCT
ejpam-522	160	13	,	,	PUNCT
ejpam-522	161	1	r	r	NOUN
ejpam-522	161	2	m∑	m∑	NOUN
ejpam-522	161	3	i=1	i=1	NOUN
ejpam-522	161	4	x	x	PUNCT
ejpam-522	162	1	i	i	NOUN
ejpam-522	162	2	=	=	NOUN
ejpam-522	162	3	1	1	NUM
ejpam-522	162	4	x	x	X
ejpam-522	162	5	i	i	PRON
ejpam-522	162	6	≥	≥	NOUN
ejpam-522	162	7	0	0	NUM
ejpam-522	162	8	,	,	PUNCT
ejpam-522	162	9	i	i	PRON
ejpam-522	162	10	=	=	NOUN
ejpam-522	162	11	1	1	NUM
ejpam-522	162	12	,	,	PUNCT
ejpam-522	162	13	...	...	PUNCT
ejpam-522	162	14	,	,	PUNCT
ejpam-522	162	15	m	m	VERB
ejpam-522	162	16	,	,	PUNCT
ejpam-522	162	17	(	(	PUNCT
ejpam-522	162	18	17	17	NUM
ejpam-522	162	19	)	)	PUNCT
ejpam-522	162	20	we	we	PRON
ejpam-522	162	21	can	can	AUX
ejpam-522	162	22	find	find	VERB
ejpam-522	162	23	maximal	maximal	ADJ
ejpam-522	162	24	constant	constant	ADJ
ejpam-522	162	25	value	value	NOUN
ejpam-522	162	26	⌢	⌢	NUM
ejpam-522	162	27	σ	σ	NOUN
ejpam-522	162	28	satisfying	satisfy	VERB
ejpam-522	162	29	the	the	DET
ejpam-522	162	30	constraints	constraint	NOUN
ejpam-522	162	31	(	(	PUNCT
ejpam-522	162	32	17	17	NUM
ejpam-522	162	33	)	)	PUNCT
ejpam-522	162	34	.	.	PUNCT
ejpam-522	163	1	m∑	m∑	X
ejpam-522	163	2	i=1	i=1	PROPN
ejpam-522	164	1	n∑	n∑	PROPN
ejpam-522	165	1	j=1	j=1	PROPN
ejpam-522	165	2	(	(	PUNCT
ejpam-522	165	3	ak	ak	PROPN
ejpam-522	165	4	i	i	PROPN
ejpam-522	165	5	j	j	PROPN
ejpam-522	166	1	+	+	CCONJ
ejpam-522	166	2	àk	àk	SCONJ
ejpam-522	166	3	i	i	PRON
ejpam-522	166	4	j	j	PROPN
ejpam-522	166	5	)	)	PUNCT
ejpam-522	167	1	x	x	PROPN
ejpam-522	168	1	i	i	PRON
ejpam-522	168	2	y	y	PROPN
ejpam-522	168	3	l	l	PROPN
ejpam-522	168	4	j	j	PROPN
ejpam-522	168	5	−	−	PROPN
ejpam-522	168	6	ak	ak	PROPN
ejpam-522	168	7	=	=	PROPN
ejpam-522	168	8	pk	pk	PROPN
ejpam-522	168	9	l	l	NOUN
ejpam-522	168	10	m∑	m∑	NOUN
ejpam-522	168	11	i=1	i=1	PROPN
ejpam-522	168	12	n∑	n∑	PROPN
ejpam-522	169	1	j=1	j=1	PROPN
ejpam-522	169	2	àk	àk	ADV
ejpam-522	169	3	i	i	PRON
ejpam-522	169	4	j	j	VERB
ejpam-522	170	1	x	x	VERB
ejpam-522	171	1	i	i	PRON
ejpam-522	171	2	y	y	PROPN
ejpam-522	171	3	l	l	NOUN
ejpam-522	171	4	j	j	PROPN
ejpam-522	172	1	+	+	CCONJ
ejpam-522	172	2	ak	ak	PROPN
ejpam-522	172	3	−	−	PROPN
ejpam-522	172	4	ak	ak	PROPN
ejpam-522	172	5	=	=	PROPN
ejpam-522	172	6	qk	qk	PROPN
ejpam-522	172	7	l	l	NOUN
ejpam-522	172	8	,	,	PUNCT
ejpam-522	172	9	(	(	PUNCT
ejpam-522	172	10	18	18	NUM
ejpam-522	172	11	)	)	PUNCT
ejpam-522	172	12	the	the	DET
ejpam-522	172	13	first	first	ADJ
ejpam-522	172	14	constraint	constraint	NOUN
ejpam-522	172	15	of	of	ADP
ejpam-522	172	16	the	the	DET
ejpam-522	172	17	relaxed	relaxed	ADJ
ejpam-522	172	18	problem	problem	NOUN
ejpam-522	172	19	(	(	PUNCT
ejpam-522	172	20	16	16	NUM
ejpam-522	172	21	)	)	PUNCT
ejpam-522	172	22	is	be	AUX
ejpam-522	172	23	equivalent	equivalent	ADJ
ejpam-522	172	24	to	to	ADP
ejpam-522	172	25	following	follow	VERB
ejpam-522	172	26	condition	condition	NOUN
ejpam-522	172	27	pk	pk	NOUN
ejpam-522	172	28	l	l	NOUN
ejpam-522	172	29	qk	qk	NOUN
ejpam-522	172	30	l	l	PROPN
ejpam-522	172	31	≥	≥	PROPN
ejpam-522	173	1	σ	σ	PROPN
ejpam-522	173	2	,	,	PUNCT
ejpam-522	173	3	k	k	PROPN
ejpam-522	173	4	=	=	SYM
ejpam-522	173	5	1	1	NUM
ejpam-522	173	6	,	,	PUNCT
ejpam-522	173	7	...	...	PUNCT
ejpam-522	173	8	,	,	PUNCT
ejpam-522	173	9	r	r	X
ejpam-522	173	10	,	,	PUNCT
ejpam-522	173	11	l	l	NOUN
ejpam-522	173	12	=	=	SYM
ejpam-522	173	13	1,2	1,2	NUM
ejpam-522	173	14	,	,	PUNCT
ejpam-522	173	15	...	...	PUNCT
ejpam-522	173	16	,	,	PUNCT
ejpam-522	173	17	l	l	NOUN
ejpam-522	173	18	(	(	PUNCT
ejpam-522	173	19	19	19	NUM
ejpam-522	173	20	)	)	PUNCT
ejpam-522	173	21	we	we	PRON
ejpam-522	173	22	can	can	AUX
ejpam-522	173	23	find	find	VERB
ejpam-522	173	24	the	the	DET
ejpam-522	173	25	maximal	maximal	ADJ
ejpam-522	173	26	constant	constant	ADJ
ejpam-522	173	27	value	value	NOUN
ejpam-522	173	28	⌢	⌢	NUM
ejpam-522	173	29	σ	σ	NOUN
ejpam-522	173	30	of	of	ADP
ejpam-522	173	31	the	the	DET
ejpam-522	173	32	problem	problem	NOUN
ejpam-522	173	33	(	(	PUNCT
ejpam-522	173	34	17	17	NUM
ejpam-522	173	35	)	)	PUNCT
ejpam-522	173	36	by	by	ADP
ejpam-522	173	37	making	make	VERB
ejpam-522	173	38	use	use	NOUN
ejpam-522	173	39	of	of	ADP
ejpam-522	173	40	the	the	DET
ejpam-522	173	41	dinkela	dinkela	PROPN
ejpam-522	173	42	.	.	PUNCT
ejpam-522	174	1	çevikel	çevikel	PROPN
ejpam-522	174	2	,	,	PUNCT
ejpam-522	174	3	m.	m.	PROPN
ejpam-522	174	4	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	174	5	/	/	SYM
ejpam-522	174	6	eur	eur	PROPN
ejpam-522	174	7	.	.	PUNCT
ejpam-522	175	1	j.	j.	PROPN
ejpam-522	175	2	pure	pure	PROPN
ejpam-522	175	3	appl	appl	PROPN
ejpam-522	175	4	.	.	PROPN
ejpam-522	175	5	math	math	PROPN
ejpam-522	175	6	,	,	PUNCT
ejpam-522	175	7	3	3	NUM
ejpam-522	175	8	(	(	PUNCT
ejpam-522	175	9	2010	2010	NUM
ejpam-522	175	10	)	)	PUNCT
ejpam-522	175	11	,	,	PUNCT
ejpam-522	175	12	107	107	NUM
ejpam-522	175	13	-	-	SYM
ejpam-522	175	14	117	117	NUM
ejpam-522	175	15	113	113	NUM
ejpam-522	175	16	bach	bach	NOUN
ejpam-522	175	17	algorithm	algorithm	NOUN
ejpam-522	176	1	[	[	X
ejpam-522	176	2	3	3	X
ejpam-522	176	3	]	]	PUNCT
ejpam-522	176	4	as	as	SCONJ
ejpam-522	176	5	follows	follow	VERB
ejpam-522	176	6	:	:	PUNCT
ejpam-522	176	7	maximize	maximize	VERB
ejpam-522	176	8	r	r	NOUN
ejpam-522	176	9	sub	sub	NOUN
ejpam-522	176	10	ject	ject	PROPN
ejpam-522	176	11	to	to	ADP
ejpam-522	176	12	pk	pk	PROPN
ejpam-522	176	13	l	l	NOUN
ejpam-522	176	14	−	−	PROPN
ejpam-522	176	15	⌢	⌢	NUM
ejpam-522	176	16	σtq	σtq	NOUN
ejpam-522	176	17	k	k	NOUN
ejpam-522	176	18	l	l	NOUN
ejpam-522	177	1	−	−	NOUN
ejpam-522	177	2	r	r	NOUN
ejpam-522	177	3	≥	≥	NOUN
ejpam-522	177	4	0	0	NUM
ejpam-522	178	1	(	(	PUNCT
ejpam-522	178	2	m∑	m∑	INTJ
ejpam-522	178	3	i=1	i=1	PROPN
ejpam-522	178	4	n∑	n∑	PROPN
ejpam-522	178	5	j=1	j=1	PROPN
ejpam-522	178	6	(	(	PUNCT
ejpam-522	178	7	ak	ak	PROPN
ejpam-522	178	8	i	i	PROPN
ejpam-522	178	9	j	j	PROPN
ejpam-522	179	1	+	+	CCONJ
ejpam-522	179	2	àk	àk	SCONJ
ejpam-522	179	3	i	i	PRON
ejpam-522	179	4	j	j	PROPN
ejpam-522	179	5	)	)	PUNCT
ejpam-522	180	1	x	x	PROPN
ejpam-522	181	1	i	i	PRON
ejpam-522	181	2	y	y	PROPN
ejpam-522	181	3	l	l	NOUN
ejpam-522	181	4	j	j	PROPN
ejpam-522	182	1	−	−	ADP
ejpam-522	182	2	ak)−	ak)−	PROPN
ejpam-522	182	3	pk	pk	NOUN
ejpam-522	182	4	l	l	NOUN
ejpam-522	182	5	=	=	SYM
ejpam-522	182	6	0	0	NUM
ejpam-522	182	7	,	,	PUNCT
ejpam-522	182	8	(	(	PUNCT
ejpam-522	182	9	m∑	m∑	INTJ
ejpam-522	182	10	i=1	i=1	PROPN
ejpam-522	182	11	n∑	n∑	PROPN
ejpam-522	183	1	j=1	j=1	PROPN
ejpam-522	183	2	àk	àk	ADV
ejpam-522	183	3	i	i	PRON
ejpam-522	183	4	j	j	VERB
ejpam-522	184	1	x	x	VERB
ejpam-522	185	1	i	i	PRON
ejpam-522	185	2	y	y	PROPN
ejpam-522	185	3	l	l	NOUN
ejpam-522	185	4	j	j	PROPN
ejpam-522	186	1	+	+	CCONJ
ejpam-522	186	2	ak	ak	PROPN
ejpam-522	186	3	−	−	PROPN
ejpam-522	186	4	ak)−qk	ak)−qk	ADJ
ejpam-522	186	5	l	l	NOUN
ejpam-522	187	1	=	=	SYM
ejpam-522	187	2	0	0	NUM
ejpam-522	187	3	m∑	m∑	INTJ
ejpam-522	187	4	i=1	i=1	NOUN
ejpam-522	187	5	x	x	PUNCT
ejpam-522	188	1	i	i	NOUN
ejpam-522	188	2	=	=	NOUN
ejpam-522	188	3	1	1	NUM
ejpam-522	188	4	x	x	X
ejpam-522	188	5	i	i	PRON
ejpam-522	188	6	≥	≥	NOUN
ejpam-522	188	7	0	0	NUM
ejpam-522	188	8	,	,	PUNCT
ejpam-522	188	9	k	k	NOUN
ejpam-522	188	10	=	=	SYM
ejpam-522	188	11	1	1	NUM
ejpam-522	188	12	,	,	PUNCT
ejpam-522	188	13	...	...	PUNCT
ejpam-522	188	14	,	,	PUNCT
ejpam-522	188	15	r	r	X
ejpam-522	188	16	,	,	PUNCT
ejpam-522	188	17	l	l	NOUN
ejpam-522	188	18	=	=	SYM
ejpam-522	188	19	1,2	1,2	NUM
ejpam-522	188	20	,	,	PUNCT
ejpam-522	188	21	...	...	PUNCT
ejpam-522	189	1	l	l	NOUN
ejpam-522	189	2	,	,	PUNCT
ejpam-522	189	3	t	t	NOUN
ejpam-522	189	4	=	=	SYM
ejpam-522	189	5	1,2	1,2	NUM
ejpam-522	189	6	,	,	PUNCT
ejpam-522	189	7	...	...	PUNCT
ejpam-522	189	8	,	,	PUNCT
ejpam-522	189	9	t	t	PROPN
ejpam-522	189	10	(	(	PUNCT
ejpam-522	189	11	20	20	NUM
ejpam-522	189	12	)	)	PUNCT
ejpam-522	189	13	where	where	SCONJ
ejpam-522	189	14	we	we	PRON
ejpam-522	189	15	have	have	AUX
ejpam-522	189	16	denoted	denote	VERB
ejpam-522	189	17	⌢	⌢	NUM
ejpam-522	189	18	σt	σt	ADP
ejpam-522	189	19	=	=	SYM
ejpam-522	189	20	min	min	PROPN
ejpam-522	189	21	§	§	PROPN
ejpam-522	189	22	pk	pk	NOUN
ejpam-522	189	23	l	l	NOUN
ejpam-522	189	24	qk	qk	NOUN
ejpam-522	189	25	l	l	NOUN
ejpam-522	189	26	ª	ª	X
ejpam-522	189	27	and	and	CCONJ
ejpam-522	189	28	⌢	⌢	NUM
ejpam-522	189	29	σ1	σ1	NOUN
ejpam-522	189	30	=	=	SYM
ejpam-522	189	31	0	0	PUNCT
ejpam-522	189	32	.	.	PUNCT
ejpam-522	190	1	if	if	SCONJ
ejpam-522	190	2	maximize	maximize	VERB
ejpam-522	190	3	r	r	NOUN
ejpam-522	190	4	=	=	SYM
ejpam-522	190	5	0	0	NUM
ejpam-522	190	6	,	,	PUNCT
ejpam-522	190	7	terminate	terminate	NOUN
ejpam-522	190	8	,	,	PUNCT
ejpam-522	190	9	then	then	ADV
ejpam-522	190	10	the	the	DET
ejpam-522	190	11	feasible	feasible	ADJ
ejpam-522	190	12	solution	solution	NOUN
ejpam-522	190	13	x∗	x∗	PROPN
ejpam-522	190	14	and	and	CCONJ
ejpam-522	190	15	the	the	DET
ejpam-522	190	16	maximal	maximal	ADJ
ejpam-522	190	17	constant	constant	ADJ
ejpam-522	190	18	value	value	NOUN
ejpam-522	190	19	⌢	⌢	NUM
ejpam-522	190	20	σ	σ	NOUN
ejpam-522	190	21	must	must	AUX
ejpam-522	190	22	be	be	AUX
ejpam-522	190	23	the	the	DET
ejpam-522	190	24	optimal	optimal	ADJ
ejpam-522	190	25	solution	solution	NOUN
ejpam-522	190	26	�	�	PROPN
ejpam-522	190	27	x∗,σ∗	x∗,σ∗	PROPN
ejpam-522	190	28	=	=	SYM
ejpam-522	190	29	⌢	⌢	NUM
ejpam-522	190	30	σ	σ	X
ejpam-522	190	31	�	�	PROPN
ejpam-522	190	32	of	of	ADP
ejpam-522	190	33	the	the	DET
ejpam-522	190	34	relaxed	relaxed	ADJ
ejpam-522	190	35	problem	problem	NOUN
ejpam-522	190	36	(	(	PUNCT
ejpam-522	190	37	16	16	NUM
ejpam-522	190	38	)	)	PUNCT
ejpam-522	190	39	.	.	PUNCT
ejpam-522	191	1	otherwise	otherwise	ADV
ejpam-522	191	2	,	,	PUNCT
ejpam-522	191	3	i.e.	i.e.	X
ejpam-522	191	4	,	,	PUNCT
ejpam-522	191	5	if	if	SCONJ
ejpam-522	191	6	maximize	maximize	VERB
ejpam-522	191	7	r	r	NOUN
ejpam-522	191	8	6=	6=	ADP
ejpam-522	191	9	0	0	NUM
ejpam-522	191	10	,	,	PUNCT
ejpam-522	191	11	set	set	VERB
ejpam-522	191	12	t	t	PROPN
ejpam-522	191	13	=	=	SYM
ejpam-522	191	14	t	t	PROPN
ejpam-522	192	1	+	+	CCONJ
ejpam-522	192	2	1	1	NUM
ejpam-522	192	3	,	,	PUNCT
ejpam-522	192	4	and	and	CCONJ
ejpam-522	192	5	solve	solve	VERB
ejpam-522	192	6	it	it	PRON
ejpam-522	192	7	again	again	ADV
ejpam-522	192	8	.	.	PUNCT
ejpam-522	193	1	we	we	PRON
ejpam-522	193	2	can	can	AUX
ejpam-522	193	3	find	find	VERB
ejpam-522	193	4	the	the	DET
ejpam-522	193	5	maximal	maximal	ADJ
ejpam-522	193	6	constant	constant	ADJ
ejpam-522	193	7	value	value	NOUN
ejpam-522	193	8	⌢	⌢	NUM
ejpam-522	193	9	σ	σ	NOUN
ejpam-522	193	10	by	by	ADP
ejpam-522	193	11	repeating	repeat	VERB
ejpam-522	193	12	this	this	DET
ejpam-522	193	13	procedure	procedure	NOUN
ejpam-522	193	14	in	in	ADP
ejpam-522	193	15	a	a	DET
ejpam-522	193	16	finite	finite	ADJ
ejpam-522	193	17	number	number	NOUN
ejpam-522	193	18	of	of	ADP
ejpam-522	193	19	iterations	iteration	NOUN
ejpam-522	193	20	.	.	PUNCT
ejpam-522	194	1	the	the	DET
ejpam-522	194	2	minimization	minimization	NOUN
ejpam-522	194	3	problems	problem	NOUN
ejpam-522	194	4	for	for	ADP
ejpam-522	194	5	the	the	DET
ejpam-522	194	6	test	test	NOUN
ejpam-522	194	7	of	of	ADP
ejpam-522	194	8	feasibility	feasibility	NOUN
ejpam-522	194	9	and	and	CCONJ
ejpam-522	194	10	the	the	DET
ejpam-522	194	11	generation	generation	NOUN
ejpam-522	194	12	of	of	ADP
ejpam-522	194	13	the	the	DET
ejpam-522	194	14	most	most	ADV
ejpam-522	194	15	violated	violate	VERB
ejpam-522	194	16	constraint	constraint	NOUN
ejpam-522	194	17	are	be	AUX
ejpam-522	194	18	represented	represent	VERB
ejpam-522	194	19	as	as	SCONJ
ejpam-522	194	20	follows	follow	VERB
ejpam-522	194	21	:	:	PUNCT
ejpam-522	194	22	minimize	minimize	VERB
ejpam-522	194	23	m∑	m∑	ADP
ejpam-522	194	24	i=1	i=1	PROPN
ejpam-522	194	25	n∑	n∑	PROPN
ejpam-522	195	1	j=1	j=1	PROPN
ejpam-522	195	2	(	(	PUNCT
ejpam-522	195	3	ak	ak	PROPN
ejpam-522	195	4	i	i	PROPN
ejpam-522	195	5	j	j	PROPN
ejpam-522	196	1	+	+	PROPN
ejpam-522	196	2	àk	àk	ADJ
ejpam-522	196	3	i	i	PRON
ejpam-522	196	4	j	j	NOUN
ejpam-522	196	5	)	)	PUNCT
ejpam-522	196	6	x	x	X
ejpam-522	197	1	l	l	NOUN
ejpam-522	197	2	i	i	PRON
ejpam-522	197	3	y	y	PROPN
ejpam-522	197	4	j−ak	j−ak	PROPN
ejpam-522	197	5	m∑	m∑	VERB
ejpam-522	197	6	i=1	i=1	PROPN
ejpam-522	197	7	n∑	n∑	PROPN
ejpam-522	198	1	j=1	j=1	PROPN
ejpam-522	198	2	àk	àk	ADV
ejpam-522	198	3	i	i	PRON
ejpam-522	198	4	j	j	X
ejpam-522	199	1	x	x	VERB
ejpam-522	199	2	l	l	NOUN
ejpam-522	199	3	i	i	PRON
ejpam-522	199	4	y	y	PROPN
ejpam-522	199	5	j+ak−ak	j+ak−ak	VERB
ejpam-522	199	6	sub	sub	NOUN
ejpam-522	199	7	ject	ject	PROPN
ejpam-522	199	8	to	to	ADP
ejpam-522	199	9	n∑	n∑	PROPN
ejpam-522	199	10	j=1	j=1	PROPN
ejpam-522	200	1	y	y	PROPN
ejpam-522	200	2	j	j	PROPN
ejpam-522	200	3	=	=	SYM
ejpam-522	200	4	1	1	NUM
ejpam-522	200	5	y	y	PROPN
ejpam-522	200	6	j	j	PROPN
ejpam-522	200	7	≥	≥	PROPN
ejpam-522	200	8	0	0	NUM
ejpam-522	200	9	,	,	PUNCT
ejpam-522	200	10	j	j	PROPN
ejpam-522	200	11	=	=	SYM
ejpam-522	200	12	1	1	NUM
ejpam-522	200	13	,	,	PUNCT
ejpam-522	200	14	...	...	PUNCT
ejpam-522	200	15	,	,	PUNCT
ejpam-522	200	16	n	n	CCONJ
ejpam-522	200	17	,	,	PUNCT
ejpam-522	200	18	k	k	PROPN
ejpam-522	200	19	=	=	SYM
ejpam-522	200	20	1	1	NUM
ejpam-522	200	21	,	,	PUNCT
ejpam-522	200	22	...	...	PUNCT
ejpam-522	200	23	,	,	PUNCT
ejpam-522	200	24	r.	r.	PROPN
ejpam-522	200	25	(	(	PUNCT
ejpam-522	200	26	21	21	NUM
ejpam-522	200	27	)	)	PUNCT
ejpam-522	200	28	the	the	DET
ejpam-522	200	29	minimization	minimization	NOUN
ejpam-522	200	30	problems	problem	NOUN
ejpam-522	200	31	(	(	PUNCT
ejpam-522	200	32	21	21	NUM
ejpam-522	200	33	)	)	PUNCT
ejpam-522	200	34	,	,	PUNCT
ejpam-522	200	35	which	which	PRON
ejpam-522	200	36	generates	generate	VERB
ejpam-522	200	37	the	the	DET
ejpam-522	200	38	most	most	ADV
ejpam-522	200	39	violated	violate	VERB
ejpam-522	200	40	constraint	constraint	NOUN
ejpam-522	200	41	,	,	PUNCT
ejpam-522	200	42	can	can	AUX
ejpam-522	200	43	be	be	AUX
ejpam-522	200	44	reduced	reduce	VERB
ejpam-522	200	45	to	to	PART
ejpam-522	200	46	lineear	lineear	VERB
ejpam-522	200	47	programming	programming	NOUN
ejpam-522	200	48	problems	problem	NOUN
ejpam-522	200	49	by	by	ADP
ejpam-522	200	50	using	use	VERB
ejpam-522	200	51	the	the	DET
ejpam-522	200	52	variable	variable	ADJ
ejpam-522	200	53	transformations	transformation	NOUN
ejpam-522	200	54	by	by	ADP
ejpam-522	200	55	charnes	charne	NOUN
ejpam-522	200	56	and	and	CCONJ
ejpam-522	200	57	cooper	cooper	NOUN
ejpam-522	201	1	[	[	X
ejpam-522	201	2	9].set	9].set	NOUN
ejpam-522	201	3	1	1	NUM
ejpam-522	201	4			NOUN
ejpam-522	201	5			ADJ
ejpam-522	201	6	m∑	m∑	NOUN
ejpam-522	201	7	i=1	i=1	PROPN
ejpam-522	201	8	n∑	n∑	PROPN
ejpam-522	202	1	j=1	j=1	PROPN
ejpam-522	202	2	àk	àk	ADV
ejpam-522	202	3	i	i	PRON
ejpam-522	202	4	j	j	X
ejpam-522	203	1	x	x	VERB
ejpam-522	203	2	l	l	NOUN
ejpam-522	204	1	i	i	VERB
ejpam-522	204	2	y	y	PROPN
ejpam-522	204	3	j	j	PROPN
ejpam-522	204	4	+	+	CCONJ
ejpam-522	204	5	ak	ak	PROPN
ejpam-522	204	6	−	−	PROPN
ejpam-522	204	7	ak	ak	PROPN
ejpam-522	204	8			PROPN
ejpam-522	204	9			PROPN
ejpam-522	205	1	=	=	SYM
ejpam-522	205	2	tk	tk	PROPN
ejpam-522	205	3	,	,	PUNCT
ejpam-522	205	4	k	k	PROPN
ejpam-522	205	5	=	=	SYM
ejpam-522	205	6	1	1	NUM
ejpam-522	205	7	,	,	PUNCT
ejpam-522	205	8	...	...	PUNCT
ejpam-522	205	9	,	,	PUNCT
ejpam-522	206	1	r	r	NOUN
ejpam-522	206	2	(	(	PUNCT
ejpam-522	206	3	22	22	NUM
ejpam-522	206	4	)	)	PUNCT
ejpam-522	206	5	and	and	CCONJ
ejpam-522	206	6	y	y	PROPN
ejpam-522	206	7	j	j	PROPN
ejpam-522	207	1	t	t	PROPN
ejpam-522	207	2	k	k	PROPN
ejpam-522	207	3	=	=	PUNCT
ejpam-522	207	4	zk	zk	PROPN
ejpam-522	207	5	j	j	PROPN
ejpam-522	207	6	,	,	PUNCT
ejpam-522	207	7	k	k	PROPN
ejpam-522	207	8	=	=	SYM
ejpam-522	207	9	1	1	NUM
ejpam-522	207	10	,	,	PUNCT
ejpam-522	207	11	...	...	PUNCT
ejpam-522	207	12	,	,	PUNCT
ejpam-522	207	13	r	r	NOUN
ejpam-522	207	14	(	(	PUNCT
ejpam-522	207	15	23	23	NUM
ejpam-522	207	16	)	)	PUNCT
ejpam-522	207	17	a.	a.	NOUN
ejpam-522	207	18	çevikel	çevikel	NOUN
ejpam-522	207	19	,	,	PUNCT
ejpam-522	207	20	m.	m.	PROPN
ejpam-522	207	21	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	207	22	/	/	SYM
ejpam-522	207	23	eur	eur	PROPN
ejpam-522	207	24	.	.	PUNCT
ejpam-522	208	1	j.	j.	PROPN
ejpam-522	208	2	pure	pure	PROPN
ejpam-522	208	3	appl	appl	PROPN
ejpam-522	208	4	.	.	PROPN
ejpam-522	208	5	math	math	PROPN
ejpam-522	208	6	,	,	PUNCT
ejpam-522	208	7	3	3	NUM
ejpam-522	208	8	(	(	PUNCT
ejpam-522	208	9	2010	2010	NUM
ejpam-522	208	10	)	)	PUNCT
ejpam-522	208	11	,	,	PUNCT
ejpam-522	208	12	107	107	NUM
ejpam-522	208	13	-	-	SYM
ejpam-522	208	14	117	117	NUM
ejpam-522	208	15	114	114	NUM
ejpam-522	208	16	the	the	DET
ejpam-522	208	17	minimization	minimization	NOUN
ejpam-522	208	18	problem	problem	NOUN
ejpam-522	208	19	(	(	PUNCT
ejpam-522	208	20	21	21	NUM
ejpam-522	208	21	)	)	PUNCT
ejpam-522	208	22	can	can	AUX
ejpam-522	208	23	be	be	AUX
ejpam-522	208	24	rewritten	rewrite	VERB
ejpam-522	208	25	as	as	SCONJ
ejpam-522	208	26	follows	follow	VERB
ejpam-522	208	27	r	r	NOUN
ejpam-522	208	28	linear	linear	ADJ
ejpam-522	208	29	programming	programming	NOUN
ejpam-522	208	30	problems	problem	NOUN
ejpam-522	208	31	:	:	PUNCT
ejpam-522	208	32	minimize	minimize	VERB
ejpam-522	208	33	zk	zk	PROPN
ejpam-522	208	34	,	,	PUNCT
ejpam-522	208	35	tk	tk	PROPN
ejpam-522	208	36	m∑	m∑	NOUN
ejpam-522	208	37	i=1	i=1	PROPN
ejpam-522	208	38	n∑	n∑	PROPN
ejpam-522	209	1	j=1	j=1	PROPN
ejpam-522	209	2	(	(	PUNCT
ejpam-522	209	3	ak	ak	PROPN
ejpam-522	209	4	i	i	PROPN
ejpam-522	209	5	j	j	PROPN
ejpam-522	210	1	+	+	CCONJ
ejpam-522	210	2	àk	àk	SCONJ
ejpam-522	210	3	i	i	PRON
ejpam-522	210	4	j)x	j)x	NOUN
ejpam-522	211	1	l	l	VERB
ejpam-522	212	1	i	i	PRON
ejpam-522	212	2	zk	zk	PROPN
ejpam-522	213	1	j	j	PROPN
ejpam-522	213	2	−	−	PROPN
ejpam-522	213	3	ak	ak	PROPN
ejpam-522	213	4	tk	tk	PROPN
ejpam-522	213	5	sub	sub	PROPN
ejpam-522	213	6	ject	ject	PROPN
ejpam-522	213	7	to	to	ADP
ejpam-522	213	8	n∑	n∑	PROPN
ejpam-522	213	9	j=1	j=1	PROPN
ejpam-522	214	1	zk	zk	PROPN
ejpam-522	214	2	j	j	PROPN
ejpam-522	215	1	=	=	PROPN
ejpam-522	215	2	tk	tk	PROPN
ejpam-522	215	3	m∑	m∑	NOUN
ejpam-522	215	4	i=1	i=1	PROPN
ejpam-522	215	5	n∑	n∑	PROPN
ejpam-522	216	1	j=1	j=1	PROPN
ejpam-522	216	2	àk	àk	ADV
ejpam-522	216	3	i	i	PRON
ejpam-522	216	4	j	j	X
ejpam-522	217	1	x	x	VERB
ejpam-522	217	2	l	l	NOUN
ejpam-522	218	1	i	i	PRON
ejpam-522	218	2	zk	zk	PROPN
ejpam-522	218	3	j	j	PROPN
ejpam-522	219	1	+	+	CCONJ
ejpam-522	219	2	(	(	PUNCT
ejpam-522	219	3	a−	a−	PROPN
ejpam-522	219	4	a)tk	a)tk	PROPN
ejpam-522	219	5	=	=	SYM
ejpam-522	219	6	1	1	NUM
ejpam-522	219	7	zk	zk	PROPN
ejpam-522	219	8	j	j	PROPN
ejpam-522	219	9	≥	≥	PROPN
ejpam-522	219	10	0	0	NUM
ejpam-522	219	11	,	,	PUNCT
ejpam-522	219	12	j	j	PROPN
ejpam-522	219	13	=	=	SYM
ejpam-522	219	14	1	1	NUM
ejpam-522	219	15	,	,	PUNCT
ejpam-522	219	16	...	...	PUNCT
ejpam-522	219	17	,	,	PUNCT
ejpam-522	219	18	n	n	X
ejpam-522	219	19	,	,	PUNCT
ejpam-522	219	20	k	k	PROPN
ejpam-522	219	21	=	=	SYM
ejpam-522	219	22	1	1	NUM
ejpam-522	219	23	...	...	PUNCT
ejpam-522	219	24	,	,	PUNCT
ejpam-522	219	25	r.	r.	PROPN
ejpam-522	219	26	(	(	PUNCT
ejpam-522	219	27	24	24	NUM
ejpam-522	219	28	)	)	PUNCT
ejpam-522	219	29	the	the	DET
ejpam-522	219	30	kth	kth	PROPN
ejpam-522	219	31	problem	problem	NOUN
ejpam-522	219	32	in	in	ADP
ejpam-522	219	33	(	(	PUNCT
ejpam-522	219	34	24	24	NUM
ejpam-522	219	35	)	)	PUNCT
ejpam-522	219	36	is	be	AUX
ejpam-522	219	37	a	a	DET
ejpam-522	219	38	linear	linear	ADJ
ejpam-522	219	39	programming	programming	NOUN
ejpam-522	219	40	problem	problem	NOUN
ejpam-522	219	41	which	which	PRON
ejpam-522	219	42	has	have	VERB
ejpam-522	219	43	decision	decision	NOUN
ejpam-522	219	44	variables	variable	NOUN
ejpam-522	219	45	zk	zk	PROPN
ejpam-522	220	1	=	=	SYM
ejpam-522	220	2	(	(	PUNCT
ejpam-522	220	3	zk	zk	PROPN
ejpam-522	220	4	1	1	NUM
ejpam-522	220	5	,	,	PUNCT
ejpam-522	220	6	...	...	PUNCT
ejpam-522	220	7	,	,	PUNCT
ejpam-522	220	8	zk	zk	PROPN
ejpam-522	220	9	n	n	CCONJ
ejpam-522	220	10	)	)	PUNCT
ejpam-522	220	11	and	and	CCONJ
ejpam-522	220	12	tk	tk	PROPN
ejpam-522	220	13	,	,	PUNCT
ejpam-522	220	14	and	and	CCONJ
ejpam-522	220	15	has	have	VERB
ejpam-522	220	16	the	the	DET
ejpam-522	220	17	two	two	NUM
ejpam-522	220	18	equality	equality	NOUN
ejpam-522	220	19	constraints	constraint	NOUN
ejpam-522	220	20	and	and	CCONJ
ejpam-522	220	21	the	the	DET
ejpam-522	220	22	nonnegative	nonnegative	ADJ
ejpam-522	220	23	conditions	condition	NOUN
ejpam-522	220	24	of	of	ADP
ejpam-522	220	25	the	the	DET
ejpam-522	220	26	decision	decision	NOUN
ejpam-522	220	27	variables	variable	NOUN
ejpam-522	220	28	.	.	PUNCT
ejpam-522	221	1	since	since	SCONJ
ejpam-522	221	2	there	there	PRON
ejpam-522	221	3	are	be	VERB
ejpam-522	221	4	r	r	NOUN
ejpam-522	221	5	problems	problem	NOUN
ejpam-522	221	6	,	,	PUNCT
ejpam-522	221	7	the	the	DET
ejpam-522	221	8	test	test	NOUN
ejpam-522	221	9	for	for	ADP
ejpam-522	221	10	feasibility	feasibility	NOUN
ejpam-522	221	11	for	for	ADP
ejpam-522	221	12	the	the	DET
ejpam-522	221	13	original	original	ADJ
ejpam-522	221	14	problem	problem	NOUN
ejpam-522	221	15	and	and	CCONJ
ejpam-522	221	16	the	the	DET
ejpam-522	221	17	generation	generation	NOUN
ejpam-522	221	18	of	of	ADP
ejpam-522	221	19	the	the	DET
ejpam-522	221	20	most	most	ADV
ejpam-522	221	21	violated	violate	VERB
ejpam-522	221	22	constraint	constraint	NOUN
ejpam-522	221	23	can	can	AUX
ejpam-522	221	24	be	be	AUX
ejpam-522	221	25	accomplished	accomplish	VERB
ejpam-522	221	26	by	by	ADP
ejpam-522	221	27	solving	solve	VERB
ejpam-522	221	28	the	the	DET
ejpam-522	221	29	r	r	NOUN
ejpam-522	221	30	linear	linear	NOUN
ejpam-522	221	31	programming	programming	NOUN
ejpam-522	221	32	problems	problem	NOUN
ejpam-522	221	33	and	and	CCONJ
ejpam-522	221	34	finding	find	VERB
ejpam-522	221	35	the	the	DET
ejpam-522	221	36	problem	problem	NOUN
ejpam-522	221	37	having	have	VERB
ejpam-522	221	38	the	the	DET
ejpam-522	221	39	smallest	small	ADJ
ejpam-522	221	40	optimal	optimal	ADJ
ejpam-522	221	41	value	value	NOUN
ejpam-522	221	42	.	.	PUNCT
ejpam-522	222	1	the	the	DET
ejpam-522	222	2	algorithm	algorithm	NOUN
ejpam-522	222	3	for	for	ADP
ejpam-522	222	4	computing	compute	VERB
ejpam-522	222	5	the	the	DET
ejpam-522	222	6	maximin	maximin	NOUN
ejpam-522	222	7	solution	solution	NOUN
ejpam-522	222	8	to	to	ADP
ejpam-522	222	9	a	a	DET
ejpam-522	222	10	multiobjective	multiobjective	ADJ
ejpam-522	222	11	two	two	NUM
ejpam-522	222	12	-	-	PUNCT
ejpam-522	222	13	person	person	NOUN
ejpam-522	222	14	zerosum	zerosum	NOUN
ejpam-522	222	15	games	game	NOUN
ejpam-522	222	16	with	with	ADP
ejpam-522	222	17	fuzzy	fuzzy	ADJ
ejpam-522	222	18	payoffs	payoff	NOUN
ejpam-522	222	19	and	and	CCONJ
ejpam-522	222	20	fuzzy	fuzzy	ADJ
ejpam-522	222	21	goals	goal	NOUN
ejpam-522	222	22	can	can	AUX
ejpam-522	222	23	be	be	AUX
ejpam-522	222	24	summarized	summarize	VERB
ejpam-522	222	25	in	in	ADP
ejpam-522	222	26	the	the	DET
ejpam-522	222	27	following	follow	VERB
ejpam-522	222	28	steps	step	NOUN
ejpam-522	222	29	.	.	PUNCT
ejpam-522	223	1	algorithm	algorithm	NOUN
ejpam-522	223	2	step	step	NOUN
ejpam-522	223	3	1	1	NUM
ejpam-522	223	4	:	:	PUNCT
ejpam-522	223	5	identify	identify	VERB
ejpam-522	223	6	r	r	NOUN
ejpam-522	223	7	fuzzy	fuzzy	ADJ
ejpam-522	223	8	goals	goal	NOUN
ejpam-522	223	9	for	for	ADP
ejpam-522	223	10	the	the	DET
ejpam-522	223	11	payoffs	payoff	NOUN
ejpam-522	223	12	.	.	PUNCT
ejpam-522	224	1	choose	choose	VERB
ejpam-522	224	2	an	an	DET
ejpam-522	224	3	initial	initial	ADJ
ejpam-522	224	4	point	point	NOUN
ejpam-522	224	5	y1	y1	NOUN
ejpam-522	224	6	∈	∈	PROPN
ejpam-522	224	7	y	y	PROPN
ejpam-522	224	8	and	and	CCONJ
ejpam-522	224	9	set	set	VERB
ejpam-522	224	10	l	l	NOUN
ejpam-522	224	11	=	=	SYM
ejpam-522	224	12	1	1	X
ejpam-522	224	13	.	.	PUNCT
ejpam-522	224	14	then	then	ADV
ejpam-522	224	15	formulate	formulate	VERB
ejpam-522	224	16	a	a	DET
ejpam-522	224	17	relaxed	relaxed	ADJ
ejpam-522	224	18	problem	problem	NOUN
ejpam-522	224	19	(	(	PUNCT
ejpam-522	224	20	16	16	NUM
ejpam-522	224	21	)	)	PUNCT
ejpam-522	224	22	,	,	PUNCT
ejpam-522	224	23	which	which	PRON
ejpam-522	224	24	is	be	AUX
ejpam-522	224	25	a	a	DET
ejpam-522	224	26	linear	linear	ADJ
ejpam-522	224	27	fractional	fractional	ADJ
ejpam-522	224	28	programming	programming	NOUN
ejpam-522	224	29	problem	problem	NOUN
ejpam-522	224	30	.	.	PUNCT
ejpam-522	225	1	step	step	NOUN
ejpam-522	225	2	2	2	NUM
ejpam-522	225	3	:	:	PUNCT
ejpam-522	225	4	formulate	formulate	VERB
ejpam-522	225	5	the	the	DET
ejpam-522	225	6	constraints	constraint	NOUN
ejpam-522	225	7	(	(	PUNCT
ejpam-522	225	8	17	17	NUM
ejpam-522	225	9	)	)	PUNCT
ejpam-522	225	10	by	by	ADP
ejpam-522	225	11	setting	set	VERB
ejpam-522	225	12	σ	σ	X
ejpam-522	225	13	=	=	SYM
ejpam-522	225	14	⌢	⌢	NUM
ejpam-522	225	15	σ	σ	NOUN
ejpam-522	225	16	in	in	ADP
ejpam-522	225	17	the	the	DET
ejpam-522	225	18	constraints	constraint	NOUN
ejpam-522	225	19	of	of	ADP
ejpam-522	225	20	the	the	DET
ejpam-522	225	21	relaxed	relaxed	ADJ
ejpam-522	225	22	problem	problem	NOUN
ejpam-522	225	23	(	(	PUNCT
ejpam-522	225	24	16	16	NUM
ejpam-522	225	25	)	)	PUNCT
ejpam-522	225	26	and	and	CCONJ
ejpam-522	225	27	set	set	VERB
ejpam-522	225	28	t	t	PROPN
ejpam-522	225	29	=	=	SYM
ejpam-522	225	30	1	1	X
ejpam-522	225	31	.	.	X
ejpam-522	225	32	compute	compute	VERB
ejpam-522	225	33	an	an	DET
ejpam-522	225	34	optimal	optimal	ADJ
ejpam-522	225	35	solution	solution	NOUN
ejpam-522	225	36	(	(	PUNCT
ejpam-522	225	37	x∗,σ∗	x∗,σ∗	PROPN
ejpam-522	225	38	)	)	PUNCT
ejpam-522	225	39	by	by	ADP
ejpam-522	225	40	making	make	VERB
ejpam-522	225	41	use	use	NOUN
ejpam-522	225	42	of	of	ADP
ejpam-522	225	43	the	the	DET
ejpam-522	225	44	problem	problem	NOUN
ejpam-522	225	45	(	(	PUNCT
ejpam-522	225	46	20	20	NUM
ejpam-522	225	47	)	)	PUNCT
ejpam-522	225	48	and	and	CCONJ
ejpam-522	225	49	if	if	SCONJ
ejpam-522	225	50	maximize	maximize	VERB
ejpam-522	225	51	r	r	NOUN
ejpam-522	225	52	=	=	SYM
ejpam-522	225	53	0	0	NUM
ejpam-522	225	54	,	,	PUNCT
ejpam-522	225	55	then	then	ADV
ejpam-522	225	56	the	the	DET
ejpam-522	225	57	feasible	feasible	ADJ
ejpam-522	225	58	solution	solution	NOUN
ejpam-522	225	59	x∗	x∗	PROPN
ejpam-522	225	60	and	and	CCONJ
ejpam-522	225	61	the	the	DET
ejpam-522	225	62	maximal	maximal	ADJ
ejpam-522	225	63	constant	constant	ADJ
ejpam-522	225	64	value	value	NOUN
ejpam-522	225	65	⌢	⌢	NUM
ejpam-522	225	66	σ	σ	NOUN
ejpam-522	225	67	must	must	AUX
ejpam-522	225	68	be	be	AUX
ejpam-522	225	69	the	the	DET
ejpam-522	225	70	optimal	optimal	ADJ
ejpam-522	225	71	solution	solution	NOUN
ejpam-522	225	72	�	�	PROPN
ejpam-522	225	73	x∗,σ∗	x∗,σ∗	PROPN
ejpam-522	225	74	=	=	SYM
ejpam-522	225	75	⌢	⌢	NUM
ejpam-522	225	76	σ	σ	X
ejpam-522	225	77	�	�	PROPN
ejpam-522	225	78	of	of	ADP
ejpam-522	225	79	the	the	DET
ejpam-522	225	80	relaxed	relaxed	ADJ
ejpam-522	225	81	problem	problem	NOUN
ejpam-522	225	82	(	(	PUNCT
ejpam-522	225	83	16	16	NUM
ejpam-522	225	84	)	)	PUNCT
ejpam-522	225	85	.	.	PUNCT
ejpam-522	226	1	then	then	ADV
ejpam-522	226	2	set	set	VERB
ejpam-522	226	3	x	x	PUNCT
ejpam-522	226	4	l	l	NOUN
ejpam-522	226	5	=	=	PUNCT
ejpam-522	226	6	x∗	x∗	PROPN
ejpam-522	226	7	go	go	VERB
ejpam-522	226	8	to	to	PART
ejpam-522	226	9	step	step	VERB
ejpam-522	226	10	3	3	NUM
ejpam-522	226	11	.	.	PUNCT
ejpam-522	227	1	otherwise	otherwise	ADV
ejpam-522	227	2	,	,	PUNCT
ejpam-522	227	3	i.e.	i.e.	X
ejpam-522	227	4	,	,	PUNCT
ejpam-522	227	5	if	if	SCONJ
ejpam-522	227	6	maximize	maximize	VERB
ejpam-522	227	7	r	r	NOUN
ejpam-522	227	8	6=	6=	ADP
ejpam-522	227	9	0	0	NUM
ejpam-522	227	10	,	,	PUNCT
ejpam-522	227	11	set	set	VERB
ejpam-522	227	12	t	t	PROPN
ejpam-522	227	13	=	=	SYM
ejpam-522	227	14	t	t	PROPN
ejpam-522	228	1	+	+	CCONJ
ejpam-522	228	2	1	1	NUM
ejpam-522	228	3	,	,	PUNCT
ejpam-522	228	4	and	and	CCONJ
ejpam-522	228	5	solve	solve	VERB
ejpam-522	228	6	it	it	PRON
ejpam-522	228	7	again	again	ADV
ejpam-522	228	8	.	.	PUNCT
ejpam-522	229	1	step	step	NOUN
ejpam-522	229	2	3	3	NUM
ejpam-522	229	3	:	:	PUNCT
ejpam-522	229	4	formulate	formulate	VERB
ejpam-522	229	5	r	r	NOUN
ejpam-522	229	6	minimization	minimization	NOUN
ejpam-522	229	7	linear	linear	NOUN
ejpam-522	229	8	programming	programming	NOUN
ejpam-522	229	9	problems	problem	NOUN
ejpam-522	229	10	(	(	PUNCT
ejpam-522	229	11	24	24	NUM
ejpam-522	229	12	)	)	PUNCT
ejpam-522	229	13	with	with	ADP
ejpam-522	229	14	x	x	PUNCT
ejpam-522	229	15	l.	l.	PROPN
ejpam-522	229	16	step	step	NOUN
ejpam-522	229	17	4	4	NUM
ejpam-522	229	18	:	:	PUNCT
ejpam-522	229	19	solve	solve	VERB
ejpam-522	229	20	r	r	NOUN
ejpam-522	229	21	problems	problem	NOUN
ejpam-522	229	22	(	(	PUNCT
ejpam-522	229	23	24	24	NUM
ejpam-522	229	24	)	)	PUNCT
ejpam-522	229	25	and	and	CCONJ
ejpam-522	229	26	obtain	obtain	VERB
ejpam-522	229	27	r	r	NOUN
ejpam-522	229	28	optimal	optimal	ADJ
ejpam-522	229	29	solutions	solution	NOUN
ejpam-522	229	30	(	(	PUNCT
ejpam-522	229	31	zk∗	zk∗	NOUN
ejpam-522	229	32	,	,	PUNCT
ejpam-522	229	33	tk∗	tk∗	ADJ
ejpam-522	229	34	)	)	PUNCT
ejpam-522	229	35	,	,	PUNCT
ejpam-522	229	36	k	k	PROPN
ejpam-522	229	37	=	=	SYM
ejpam-522	229	38	1	1	NUM
ejpam-522	229	39	,	,	PUNCT
ejpam-522	229	40	...	...	PUNCT
ejpam-522	229	41	,	,	PUNCT
ejpam-522	229	42	r.	r.	PROPN
ejpam-522	229	43	let	let	VERB
ejpam-522	229	44	each	each	PRON
ejpam-522	229	45	of	of	ADP
ejpam-522	229	46	the	the	DET
ejpam-522	229	47	minimal	minimal	ADJ
ejpam-522	229	48	objective	objective	ADJ
ejpam-522	229	49	function	function	NOUN
ejpam-522	229	50	values	value	NOUN
ejpam-522	229	51	be	be	AUX
ejpam-522	229	52	denoted	denote	VERB
ejpam-522	229	53	by	by	ADP
ejpam-522	229	54	φk(zk∗	φk(zk∗	PROPN
ejpam-522	229	55	,	,	PUNCT
ejpam-522	229	56	tk∗	tk∗	ADJ
ejpam-522	229	57	)	)	PUNCT
ejpam-522	229	58	,	,	PUNCT
ejpam-522	229	59	k	k	PROPN
ejpam-522	230	1	=	=	SYM
ejpam-522	230	2	1	1	NUM
ejpam-522	230	3	,	,	PUNCT
ejpam-522	230	4	...	...	PUNCT
ejpam-522	230	5	,	,	PUNCT
ejpam-522	230	6	r	r	NOUN
ejpam-522	230	7	and	and	CCONJ
ejpam-522	230	8	then	then	ADV
ejpam-522	230	9	let	let	VERB
ejpam-522	230	10	φ	φ	PROPN
ejpam-522	230	11	⌢	⌢	NUM
ejpam-522	230	12	k	k	X
ejpam-522	230	13	(	(	PUNCT
ejpam-522	230	14	z	z	PROPN
ejpam-522	230	15	⌢	⌢	NUM
ejpam-522	230	16	k	k	PROPN
ejpam-522	230	17	∗	∗	NOUN
ejpam-522	230	18	,	,	PUNCT
ejpam-522	230	19	t	t	PROPN
ejpam-522	230	20	⌢	⌢	NUM
ejpam-522	230	21	k	k	PROPN
ejpam-522	230	22	∗	∗	NOUN
ejpam-522	230	23	)	)	PUNCT
ejpam-522	231	1	=	=	NOUN
ejpam-522	231	2	min	min	NOUN
ejpam-522	231	3	k∈k	k∈k	NOUN
ejpam-522	231	4	φk(zk∗	φk(zk∗	PROPN
ejpam-522	231	5	,	,	PUNCT
ejpam-522	231	6	tk∗	tk∗	ADJ
ejpam-522	231	7	)	)	PUNCT
ejpam-522	231	8	.	.	PUNCT
ejpam-522	232	1	step	step	NOUN
ejpam-522	232	2	5	5	NUM
ejpam-522	232	3	:	:	PUNCT
ejpam-522	232	4	if	if	SCONJ
ejpam-522	232	5	φ	φ	PROPN
ejpam-522	232	6	⌢	⌢	NUM
ejpam-522	232	7	k	k	X
ejpam-522	232	8	(	(	PUNCT
ejpam-522	232	9	z	z	PROPN
ejpam-522	232	10	⌢	⌢	NUM
ejpam-522	232	11	k	k	PROPN
ejpam-522	232	12	∗	∗	NOUN
ejpam-522	232	13	,	,	PUNCT
ejpam-522	232	14	t	t	PROPN
ejpam-522	232	15	⌢	⌢	NUM
ejpam-522	232	16	k	k	PROPN
ejpam-522	232	17	∗	∗	X
ejpam-522	232	18	)	)	PUNCT
ejpam-522	232	19	≥	≥	NOUN
ejpam-522	232	20	σ∗	σ∗	VERB
ejpam-522	232	21	+	+	CCONJ
ejpam-522	232	22	ε	ε	PROPN
ejpam-522	232	23	,	,	PUNCT
ejpam-522	232	24	terminate	terminate	NOUN
ejpam-522	232	25	,	,	PUNCT
ejpam-522	232	26	where	where	SCONJ
ejpam-522	232	27	ε	ε	PROPN
ejpam-522	232	28	is	be	AUX
ejpam-522	232	29	a	a	DET
ejpam-522	232	30	predetermined	predetermined	ADJ
ejpam-522	232	31	constant	constant	ADJ
ejpam-522	232	32	.	.	PUNCT
ejpam-522	233	1	then	then	ADV
ejpam-522	233	2	x	x	X
ejpam-522	233	3	l	l	NOUN
ejpam-522	233	4	is	be	AUX
ejpam-522	233	5	a	a	DET
ejpam-522	233	6	maximin	maximin	NOUN
ejpam-522	233	7	solution	solution	NOUN
ejpam-522	233	8	with	with	ADP
ejpam-522	233	9	respect	respect	NOUN
ejpam-522	233	10	to	to	ADP
ejpam-522	233	11	a	a	DET
ejpam-522	233	12	degree	degree	NOUN
ejpam-522	233	13	of	of	ADP
ejpam-522	233	14	attainment	attainment	NOUN
ejpam-522	233	15	of	of	ADP
ejpam-522	233	16	the	the	DET
ejpam-522	233	17	fuzzy	fuzzy	ADJ
ejpam-522	233	18	goal	goal	NOUN
ejpam-522	233	19	.	.	PUNCT
ejpam-522	234	1	otherwise	otherwise	ADV
ejpam-522	234	2	,	,	PUNCT
ejpam-522	234	3	i.e.	i.e.	X
ejpam-522	234	4	,	,	PUNCT
ejpam-522	234	5	if	if	SCONJ
ejpam-522	234	6	φ	φ	PROPN
ejpam-522	234	7	⌢	⌢	NUM
ejpam-522	234	8	k	k	X
ejpam-522	234	9	(	(	PUNCT
ejpam-522	234	10	z	z	PROPN
ejpam-522	234	11	⌢	⌢	NUM
ejpam-522	234	12	k	k	PROPN
ejpam-522	234	13	∗	∗	NOUN
ejpam-522	234	14	,	,	PUNCT
ejpam-522	234	15	t	t	PROPN
ejpam-522	234	16	⌢	⌢	NUM
ejpam-522	234	17	k	k	PROPN
ejpam-522	234	18	∗	∗	NOUN
ejpam-522	234	19	)	)	PUNCT
ejpam-522	234	20	<	<	X
ejpam-522	234	21	σ∗	σ∗	PROPN
ejpam-522	234	22	+	+	CCONJ
ejpam-522	234	23	ε	ε	PROPN
ejpam-522	234	24	,	,	PUNCT
ejpam-522	234	25	set	set	VERB
ejpam-522	234	26	l	l	NOUN
ejpam-522	234	27	=	=	PUNCT
ejpam-522	234	28	l	l	NOUN
ejpam-522	235	1	+	+	NUM
ejpam-522	235	2	1	1	NUM
ejpam-522	235	3	,	,	PUNCT
ejpam-522	235	4	return	return	VERB
ejpam-522	235	5	to	to	PART
ejpam-522	235	6	step	step	NOUN
ejpam-522	235	7	2	2	NUM
ejpam-522	235	8	.	.	PUNCT
ejpam-522	236	1	we	we	PRON
ejpam-522	236	2	can	can	AUX
ejpam-522	236	3	also	also	ADV
ejpam-522	236	4	obtain	obtain	VERB
ejpam-522	236	5	player	player	NOUN
ejpam-522	237	1	i	i	PRON
ejpam-522	237	2	i	i	PRON
ejpam-522	237	3	’s	’	VERB
ejpam-522	237	4	minimax	minimax	NOUN
ejpam-522	237	5	solution	solution	NOUN
ejpam-522	237	6	with	with	ADP
ejpam-522	237	7	respect	respect	NOUN
ejpam-522	237	8	to	to	ADP
ejpam-522	237	9	a	a	DET
ejpam-522	237	10	degree	degree	NOUN
ejpam-522	237	11	of	of	ADP
ejpam-522	237	12	attainment	attainment	NOUN
ejpam-522	237	13	of	of	ADP
ejpam-522	237	14	a	a	DET
ejpam-522	237	15	fuzzy	fuzzy	ADJ
ejpam-522	237	16	goal	goal	NOUN
ejpam-522	237	17	in	in	ADP
ejpam-522	237	18	similar	similar	ADJ
ejpam-522	237	19	way	way	NOUN
ejpam-522	237	20	.	.	PUNCT
ejpam-522	238	1	a.	a.	NOUN
ejpam-522	238	2	çevikel	çevikel	PROPN
ejpam-522	238	3	,	,	PUNCT
ejpam-522	238	4	m.	m.	PROPN
ejpam-522	238	5	ahlatçıoğlu	ahlatçıoğlu	PROPN
ejpam-522	238	6	/	/	SYM
ejpam-522	238	7	eur	eur	PROPN
ejpam-522	238	8	.	.	PUNCT
ejpam-522	239	1	j.	j.	PROPN
ejpam-522	239	2	pure	pure	PROPN
ejpam-522	239	3	appl	appl	PROPN
ejpam-522	239	4	.	.	PROPN
ejpam-522	239	5	math	math	PROPN
ejpam-522	239	6	,	,	PUNCT
ejpam-522	239	7	3	3	NUM
ejpam-522	239	8	(	(	PUNCT
ejpam-522	239	9	2010	2010	NUM
ejpam-522	239	10	)	)	PUNCT
ejpam-522	239	11	,	,	PUNCT
ejpam-522	239	12	107	107	NUM
ejpam-522	239	13	-	-	SYM
ejpam-522	239	14	117	117	NUM
ejpam-522	239	15	115	115	NUM
ejpam-522	239	16	example	example	NOUN
ejpam-522	239	17	1	1	NUM
ejpam-522	239	18	.	.	PUNCT
ejpam-522	240	1	assuming	assume	VERB
ejpam-522	240	2	that	that	SCONJ
ejpam-522	240	3	each	each	DET
ejpam-522	240	4	player	player	NOUN
ejpam-522	240	5	has	have	VERB
ejpam-522	240	6	three	three	NUM
ejpam-522	240	7	pure	pure	ADJ
ejpam-522	240	8	strategies	strategy	NOUN
ejpam-522	240	9	and	and	CCONJ
ejpam-522	240	10	three	three	NUM
ejpam-522	240	11	objectives	objective	NOUN
ejpam-522	240	12	,	,	PUNCT
ejpam-522	240	13	we	we	PRON
ejpam-522	240	14	consider	consider	VERB
ejpam-522	240	15	a	a	DET
ejpam-522	240	16	multiobjective	multiobjective	ADJ
ejpam-522	240	17	two	two	NUM
ejpam-522	240	18	-	-	PUNCT
ejpam-522	240	19	person	person	NOUN
ejpam-522	240	20	zero	zero	NUM
ejpam-522	240	21	-	-	PUNCT
ejpam-522	240	22	sum	sum	NOUN
ejpam-522	240	23	game	game	NOUN
ejpam-522	240	24	with	with	ADP
ejpam-522	240	25	fuzzy	fuzzy	ADJ
ejpam-522	240	26	payoffs	payoff	NOUN
ejpam-522	240	27	be	be	AUX
ejpam-522	240	28	represented	represent	VERB
ejpam-522	240	29	by	by	ADP
ejpam-522	240	30	[	[	X
ejpam-522	240	31	12	12	NUM
ejpam-522	240	32	,	,	PUNCT
ejpam-522	240	33	17	17	NUM
ejpam-522	240	34	]	]	PUNCT
ejpam-522	240	35	.	.	PUNCT
ejpam-522	241	1	ea1	ea1	NOUN
ejpam-522	242	1	=	=	PUNCT
ejpam-522	242	2			PROPN
ejpam-522	242	3			ADJ
ejpam-522	242	4	(	(	PUNCT
ejpam-522	242	5	2,0.2,0.2	2,0.2,0.2	NUM
ejpam-522	242	6	)	)	PUNCT
ejpam-522	242	7	(	(	PUNCT
ejpam-522	242	8	5,0.5,0.5	5,0.5,0.5	NUM
ejpam-522	242	9	)	)	PUNCT
ejpam-522	242	10	(	(	PUNCT
ejpam-522	242	11	1,0.8,0.8	1,0.8,0.8	NUM
ejpam-522	242	12	)	)	PUNCT
ejpam-522	242	13	(	(	PUNCT
ejpam-522	242	14	−1,0.8,0.8	−1,0.8,0.8	PROPN
ejpam-522	242	15	)	)	PUNCT
ejpam-522	242	16	(	(	PUNCT
ejpam-522	242	17	−2,0.4,0.4	−2,0.4,0.4	NUM
ejpam-522	242	18	)	)	PUNCT
ejpam-522	242	19	(	(	PUNCT
ejpam-522	242	20	6,0.1,0.1	6,0.1,0.1	NOUN
ejpam-522	242	21	)	)	PUNCT
ejpam-522	242	22	(	(	PUNCT
ejpam-522	242	23	0,0.1,0.1	0,0.1,0.1	NOUN
ejpam-522	242	24	)	)	PUNCT
ejpam-522	242	25	(	(	PUNCT
ejpam-522	242	26	3,0.5,0.5	3,0.5,0.5	NUM
ejpam-522	242	27	)	)	PUNCT
ejpam-522	242	28	(	(	PUNCT
ejpam-522	242	29	−1,0.8,0.8	−1,0.8,0.8	ADJ
ejpam-522	242	30	)	)	PUNCT
ejpam-522	242	31			PROPN
ejpam-522	242	32			X
ejpam-522	242	33	,	,	PUNCT
ejpam-522	242	34	ea2	ea2	VERB
ejpam-522	242	35	=	=	PUNCT
ejpam-522	242	36			NOUN
ejpam-522	242	37			ADJ
ejpam-522	242	38	(	(	PUNCT
ejpam-522	242	39	−3,0.8,0.8	−3,0.8,0.8	PROPN
ejpam-522	242	40	)	)	PUNCT
ejpam-522	242	41	(	(	PUNCT
ejpam-522	242	42	7,0.3,0.3	7,0.3,0.3	NOUN
ejpam-522	242	43	)	)	PUNCT
ejpam-522	242	44	(	(	PUNCT
ejpam-522	242	45	2,0.4,0.4	2,0.4,0.4	NUM
ejpam-522	242	46	)	)	PUNCT
ejpam-522	242	47	(	(	PUNCT
ejpam-522	242	48	0,0.5,0.5	0,0.5,0.5	PROPN
ejpam-522	242	49	)	)	PUNCT
ejpam-522	242	50	(	(	PUNCT
ejpam-522	242	51	−2,0.2,0.2	−2,0.2,0.2	PROPN
ejpam-522	242	52	)	)	PUNCT
ejpam-522	242	53	(	(	PUNCT
ejpam-522	242	54	0,0.7,0.7	0,0.7,0.7	PROPN
ejpam-522	242	55	)	)	PUNCT
ejpam-522	242	56	(	(	PUNCT
ejpam-522	242	57	3,0.4,0.4	3,0.4,0.4	NUM
ejpam-522	242	58	)	)	PUNCT
ejpam-522	242	59	(	(	PUNCT
ejpam-522	242	60	−1,0.8,0.8	−1,0.8,0.8	PROPN
ejpam-522	242	61	)	)	PUNCT
ejpam-522	242	62	(	(	PUNCT
ejpam-522	242	63	−6,0.5,0.5	−6,0.5,0.5	NUM
ejpam-522	242	64	)	)	PUNCT
ejpam-522	242	65			PROPN
ejpam-522	242	66			PUNCT
ejpam-522	242	67	,	,	PUNCT
ejpam-522	242	68	and	and	CCONJ
ejpam-522	242	69	ea3	ea3	NOUN
ejpam-522	242	70	=	=	SYM
ejpam-522	242	71			PROPN
ejpam-522	242	72			ADJ
ejpam-522	242	73	(	(	PUNCT
ejpam-522	242	74	8,0.1,0.1	8,0.1,0.1	NUM
ejpam-522	242	75	)	)	PUNCT
ejpam-522	242	76	(	(	PUNCT
ejpam-522	242	77	−2,0.5,0.5	−2,0.5,0.5	NOUN
ejpam-522	242	78	)	)	PUNCT
ejpam-522	242	79	(	(	PUNCT
ejpam-522	242	80	3,0.7,0.7	3,0.7,0.7	NUM
ejpam-522	242	81	)	)	PUNCT
ejpam-522	242	82	(	(	PUNCT
ejpam-522	242	83	−5,0.5,0.5	−5,0.5,0.5	PROPN
ejpam-522	242	84	)	)	PUNCT
ejpam-522	242	85	(	(	PUNCT
ejpam-522	242	86	6,0.4,0.4	6,0.4,0.4	NUM
ejpam-522	242	87	)	)	PUNCT
ejpam-522	242	88	(	(	PUNCT
ejpam-522	242	89	0,0.6,0.6	0,0.6,0.6	PROPN
ejpam-522	242	90	)	)	PUNCT
ejpam-522	242	91	(	(	PUNCT
ejpam-522	242	92	−3,0.8,0.8	−3,0.8,0.8	PROPN
ejpam-522	242	93	)	)	PUNCT
ejpam-522	242	94	(	(	PUNCT
ejpam-522	242	95	1,0.6,0.6	1,0.6,0.6	NUM
ejpam-522	242	96	)	)	PUNCT
ejpam-522	242	97	(	(	PUNCT
ejpam-522	242	98	6,0.1,0.1	6,0.1,0.1	NOUN
ejpam-522	242	99	)	)	PUNCT
ejpam-522	242	100			PROPN
ejpam-522	242	101			PUNCT
ejpam-522	242	102	.	.	PUNCT
ejpam-522	243	1	let	let	VERB
ejpam-522	243	2	fuzzy	fuzzy	ADJ
ejpam-522	243	3	goals	goal	NOUN
ejpam-522	243	4	eg1	eg1	NOUN
ejpam-522	243	5	,	,	PUNCT
ejpam-522	243	6	eg2	eg2	NOUN
ejpam-522	243	7	and	and	CCONJ
ejpam-522	243	8	eg3	eg3	NOUN
ejpam-522	243	9	of	of	ADP
ejpam-522	243	10	player	player	NOUN
ejpam-522	243	11	i	i	PRON
ejpam-522	243	12	for	for	ADP
ejpam-522	243	13	the	the	DET
ejpam-522	243	14	three	three	NUM
ejpam-522	243	15	objectives	objective	NOUN
ejpam-522	243	16	be	be	AUX
ejpam-522	243	17	represented	represent	VERB
ejpam-522	243	18	by	by	ADP
ejpam-522	243	19	the	the	DET
ejpam-522	243	20	following	follow	VERB
ejpam-522	243	21	linear	linear	PROPN
ejpam-522	243	22	membership	membership	NOUN
ejpam-522	243	23	functions	function	NOUN
ejpam-522	243	24	:	:	PUNCT
ejpam-522	243	25	µeg(p	µeg(p	X
ejpam-522	243	26	)	)	PUNCT
ejpam-522	243	27	=	=	PUNCT
ejpam-522	244	1			PROPN
ejpam-522	244	2			PRON
ejpam-522	244	3			NOUN
ejpam-522	244	4	0	0	PUNCT
ejpam-522	245	1	i	i	PRON
ejpam-522	245	2	f	f	PROPN
ejpam-522	245	3	p1	p1	PROPN
ejpam-522	245	4	<	<	X
ejpam-522	245	5	−1	−1	NOUN
ejpam-522	245	6	p1	p1	NOUN
ejpam-522	245	7	+	+	PROPN
ejpam-522	245	8	1	1	NUM
ejpam-522	245	9	7.5	7.5	NUM
ejpam-522	246	1	i	i	NOUN
ejpam-522	246	2	f	f	NOUN
ejpam-522	246	3	−	−	PROPN
ejpam-522	246	4	1≤	1≤	PROPN
ejpam-522	246	5	p1	p1	PROPN
ejpam-522	246	6	≤	≤	NUM
ejpam-522	246	7	6.5	6.5	NUM
ejpam-522	246	8	1	1	NUM
ejpam-522	247	1	i	i	NOUN
ejpam-522	247	2	f	f	NOUN
ejpam-522	247	3	6.5	6.5	NUM
ejpam-522	247	4	<	<	X
ejpam-522	247	5	p1	p1	PROPN
ejpam-522	247	6			PROPN
ejpam-522	247	7			PROPN
ejpam-522	247	8			PROPN
ejpam-522	247	9	µeg(p	µeg(p	NOUN
ejpam-522	247	10	)	)	PUNCT
ejpam-522	247	11	=	=	PUNCT
ejpam-522	247	12			PROPN
ejpam-522	247	13			PRON
ejpam-522	247	14			NOUN
ejpam-522	247	15	0	0	PUNCT
ejpam-522	248	1	i	i	PRON
ejpam-522	248	2	f	f	PROPN
ejpam-522	248	3	p2	p2	X
ejpam-522	248	4	<	<	X
ejpam-522	248	5	−2	−2	NOUN
ejpam-522	248	6	p2	p2	X
ejpam-522	248	7	+	+	NOUN
ejpam-522	248	8	2	2	NUM
ejpam-522	248	9	7.5	7.5	NUM
ejpam-522	249	1	i	i	NOUN
ejpam-522	249	2	f	f	NOUN
ejpam-522	250	1	−	−	NUM
ejpam-522	250	2	2≤	2≤	NUM
ejpam-522	250	3	p2	p2	PROPN
ejpam-522	250	4	≤	≤	NUM
ejpam-522	250	5	5.5	5.5	NUM
ejpam-522	250	6	1	1	NUM
ejpam-522	251	1	i	i	NOUN
ejpam-522	251	2	f	f	PROPN
ejpam-522	251	3	5.5	5.5	NUM
ejpam-522	251	4	<	<	NOUN
ejpam-522	251	5	p2	p2	PROPN
ejpam-522	251	6			PROPN
ejpam-522	251	7			PROPN
ejpam-522	251	8			NOUN
ejpam-522	251	9	and	and	CCONJ
ejpam-522	251	10	µeg(p	µeg(p	NOUN
ejpam-522	251	11	)	)	PUNCT
ejpam-522	252	1	=	=	PUNCT
ejpam-522	252	2			PROPN
ejpam-522	252	3			PRON
ejpam-522	252	4			NOUN
ejpam-522	252	5	0	0	PUNCT
ejpam-522	253	1	i	i	PRON
ejpam-522	253	2	f	f	PROPN
ejpam-522	253	3	p3	p3	PROPN
ejpam-522	253	4	<	<	X
ejpam-522	253	5	−1	−1	NOUN
ejpam-522	253	6	p3	p3	NOUN
ejpam-522	253	7	+	+	PROPN
ejpam-522	253	8	1	1	NUM
ejpam-522	253	9	6.8	6.8	NUM
ejpam-522	254	1	i	i	NOUN
ejpam-522	254	2	f	f	NOUN
ejpam-522	254	3	−	−	PROPN
ejpam-522	254	4	1≤	1≤	NUM
ejpam-522	254	5	p3	p3	PROPN
ejpam-522	254	6	≤	≤	ADV
ejpam-522	254	7	5.8	5.8	NUM
ejpam-522	254	8	1	1	NUM
ejpam-522	255	1	i	i	PRON
ejpam-522	255	2	f	f	PROPN
ejpam-522	255	3	5.8	5.8	NUM
ejpam-522	255	4	<	<	X
ejpam-522	255	5	p3	p3	PROPN
ejpam-522	255	6			PROPN
ejpam-522	255	7			PROPN
ejpam-522	255	8			NOUN
ejpam-522	255	9	we	we	PRON
ejpam-522	255	10	computed	compute	VERB
ejpam-522	255	11	the	the	DET
ejpam-522	255	12	maximin	maximin	NOUN
ejpam-522	255	13	solution	solution	NOUN
ejpam-522	255	14	by	by	ADP
ejpam-522	255	15	the	the	DET
ejpam-522	255	16	algorithm	algorithm	NOUN
ejpam-522	255	17	and	and	CCONJ
ejpam-522	255	18	obtained	obtain	VERB
ejpam-522	255	19	following	follow	VERB
ejpam-522	255	20	solution	solution	NOUN
ejpam-522	255	21	:	:	PUNCT
ejpam-522	255	22	x1	x1	PROPN
ejpam-522	255	23	=	=	SYM
ejpam-522	255	24	0.4434	0.4434	NUM
ejpam-522	255	25	,	,	PUNCT
ejpam-522	255	26	x2	x2	NOUN
ejpam-522	255	27	=	=	SYM
ejpam-522	255	28	0.3178	0.3178	NUM
ejpam-522	255	29	,	,	PUNCT
ejpam-522	255	30	x3	x3	NOUN
ejpam-522	255	31	=	=	NOUN
ejpam-522	255	32	0.2388	0.2388	NUM
ejpam-522	255	33	y1	y1	NOUN
ejpam-522	255	34	=	=	SYM
ejpam-522	255	35	1	1	NUM
ejpam-522	255	36	,	,	PUNCT
ejpam-522	255	37	y2	y2	NOUN
ejpam-522	255	38	=	=	SYM
ejpam-522	255	39	0	0	NUM
ejpam-522	255	40	,	,	PUNCT
ejpam-522	255	41	y3	y3	NOUN
ejpam-522	255	42	=	=	SYM
ejpam-522	255	43	0	0	NUM
ejpam-522	255	44	(	(	PUNCT
ejpam-522	255	45	25	25	NUM
ejpam-522	255	46	)	)	PUNCT
ejpam-522	255	47	the	the	DET
ejpam-522	255	48	degree	degree	NOUN
ejpam-522	255	49	of	of	ADP
ejpam-522	255	50	attainment	attainment	NOUN
ejpam-522	255	51	of	of	ADP
ejpam-522	255	52	the	the	DET
ejpam-522	255	53	fuzzy	fuzzy	ADJ
ejpam-522	255	54	goal	goal	NOUN
ejpam-522	255	55	for	for	ADP
ejpam-522	255	56	the	the	DET
ejpam-522	255	57	maximin	maximin	NOUN
ejpam-522	255	58	solution	solution	NOUN
ejpam-522	255	59	was	be	AUX
ejpam-522	255	60	σ∗	σ∗	VERB
ejpam-522	255	61	=	=	PUNCT
ejpam-522	255	62	0.246059388	0.246059388	NUM
ejpam-522	255	63	.	.	PUNCT
ejpam-522	256	1	in	in	ADP
ejpam-522	256	2	algorithm	algorithm	NOUN
ejpam-522	256	3	,	,	PUNCT
ejpam-522	256	4	we	we	PRON
ejpam-522	256	5	set	set	VERB
ejpam-522	256	6	the	the	DET
ejpam-522	256	7	initial	initial	ADJ
ejpam-522	256	8	value	value	NOUN
ejpam-522	256	9	of	of	ADP
ejpam-522	256	10	y	y	PROPN
ejpam-522	256	11	as	as	ADP
ejpam-522	256	12	y1	y1	PROPN
ejpam-522	256	13	=	=	SYM
ejpam-522	256	14	0	0	NUM
ejpam-522	256	15	,	,	PUNCT
ejpam-522	256	16	y2	y2	NOUN
ejpam-522	256	17	=	=	SYM
ejpam-522	256	18	1	1	NUM
ejpam-522	256	19	,	,	PUNCT
ejpam-522	256	20	y3	y3	NOUN
ejpam-522	256	21	=	=	SYM
ejpam-522	256	22	0	0	NUM
ejpam-522	256	23	,	,	PUNCT
ejpam-522	256	24	and	and	CCONJ
ejpam-522	256	25	the	the	DET
ejpam-522	256	26	number	number	NOUN
ejpam-522	256	27	of	of	ADP
ejpam-522	256	28	iterations	iteration	NOUN
ejpam-522	256	29	was	be	AUX
ejpam-522	256	30	three	three	NUM
ejpam-522	256	31	.	.	PUNCT
ejpam-522	257	1	references	reference	NOUN
ejpam-522	257	2	116	116	NUM
ejpam-522	257	3	4	4	NUM
ejpam-522	257	4	.	.	PUNCT
ejpam-522	257	5	conclusion	conclusion	NOUN
ejpam-522	257	6	in	in	ADP
ejpam-522	257	7	this	this	DET
ejpam-522	257	8	paper	paper	NOUN
ejpam-522	257	9	we	we	PRON
ejpam-522	257	10	have	have	AUX
ejpam-522	257	11	considered	consider	VERB
ejpam-522	257	12	the	the	DET
ejpam-522	257	13	maximin	maximin	NOUN
ejpam-522	257	14	solutions	solution	NOUN
ejpam-522	257	15	with	with	ADP
ejpam-522	257	16	respect	respect	NOUN
ejpam-522	257	17	to	to	ADP
ejpam-522	257	18	a	a	DET
ejpam-522	257	19	degree	degree	NOUN
ejpam-522	257	20	of	of	ADP
ejpam-522	257	21	attainment	attainment	NOUN
ejpam-522	257	22	of	of	ADP
ejpam-522	257	23	the	the	DET
ejpam-522	257	24	fuzzy	fuzzy	ADJ
ejpam-522	257	25	goal	goal	NOUN
ejpam-522	257	26	and	and	CCONJ
ejpam-522	257	27	have	have	AUX
ejpam-522	257	28	presented	present	VERB
ejpam-522	257	29	the	the	DET
ejpam-522	257	30	computational	computational	ADJ
ejpam-522	257	31	method	method	NOUN
ejpam-522	257	32	for	for	ADP
ejpam-522	257	33	their	their	PRON
ejpam-522	257	34	solutions	solution	NOUN
ejpam-522	257	35	.	.	PUNCT
ejpam-522	258	1	we	we	PRON
ejpam-522	258	2	have	have	AUX
ejpam-522	258	3	used	use	VERB
ejpam-522	258	4	sakawa	sakawa	PROPN
ejpam-522	258	5	’s	’s	PART
ejpam-522	258	6	method	method	NOUN
ejpam-522	258	7	,	,	PUNCT
ejpam-522	258	8	the	the	DET
ejpam-522	258	9	dinkelbach	dinkelbach	NOUN
ejpam-522	258	10	algorithm	algorithm	NOUN
ejpam-522	258	11	,	,	PUNCT
ejpam-522	258	12	the	the	DET
ejpam-522	258	13	variable	variable	ADJ
ejpam-522	258	14	transformation	transformation	NOUN
ejpam-522	258	15	by	by	ADP
ejpam-522	258	16	charnes	charne	NOUN
ejpam-522	258	17	and	and	CCONJ
ejpam-522	258	18	cooper	cooper	NOUN
ejpam-522	258	19	and	and	CCONJ
ejpam-522	258	20	the	the	DET
ejpam-522	258	21	relaxation	relaxation	NOUN
ejpam-522	258	22	procedure	procedure	NOUN
ejpam-522	258	23	for	for	ADP
ejpam-522	258	24	minimax	minimax	NOUN
ejpam-522	258	25	problems	problem	NOUN
ejpam-522	258	26	by	by	ADP
ejpam-522	258	27	shimizu	shimizu	PROPN
ejpam-522	258	28	and	and	CCONJ
ejpam-522	258	29	aiyoshi	aiyoshi	NOUN
ejpam-522	258	30	for	for	ADP
ejpam-522	258	31	the	the	DET
ejpam-522	258	32	maximin	maximin	NOUN
ejpam-522	258	33	solutions	solution	NOUN
ejpam-522	258	34	of	of	ADP
ejpam-522	258	35	multiobjective	multiobjective	ADJ
ejpam-522	258	36	two	two	NUM
ejpam-522	258	37	-	-	PUNCT
ejpam-522	258	38	person	person	NOUN
ejpam-522	258	39	zero	zero	NUM
ejpam-522	258	40	-	-	PUNCT
ejpam-522	258	41	sum	sum	NOUN
ejpam-522	258	42	games	game	NOUN
ejpam-522	258	43	with	with	ADP
ejpam-522	258	44	fuzzy	fuzzy	ADJ
ejpam-522	258	45	payoffs	payoff	NOUN
ejpam-522	258	46	and	and	CCONJ
ejpam-522	258	47	fuzzy	fuzzy	ADJ
ejpam-522	258	48	goals	goal	NOUN
ejpam-522	258	49	.	.	PUNCT
ejpam-522	259	1	for	for	ADP
ejpam-522	259	2	multiobjective	multiobjective	ADJ
ejpam-522	259	3	two	two	NUM
ejpam-522	259	4	-	-	PUNCT
ejpam-522	259	5	person	person	NOUN
ejpam-522	259	6	zero	zero	NUM
ejpam-522	259	7	-	-	PUNCT
ejpam-522	259	8	sum	sum	NOUN
ejpam-522	259	9	games	game	NOUN
ejpam-522	259	10	,	,	PUNCT
ejpam-522	259	11	if	if	SCONJ
ejpam-522	259	12	membership	membership	NOUN
ejpam-522	259	13	functions	function	NOUN
ejpam-522	259	14	of	of	ADP
ejpam-522	259	15	the	the	DET
ejpam-522	259	16	fuzzy	fuzzy	ADJ
ejpam-522	259	17	goal	goal	NOUN
ejpam-522	259	18	and	and	CCONJ
ejpam-522	259	19	shape	shape	NOUN
ejpam-522	259	20	functions	function	NOUN
ejpam-522	259	21	of	of	ADP
ejpam-522	259	22	l	l	NOUN
ejpam-522	259	23	-	-	NOUN
ejpam-522	259	24	r	r	NOUN
ejpam-522	259	25	fuzzy	fuzzy	ADJ
ejpam-522	259	26	numbers	number	NOUN
ejpam-522	259	27	for	for	ADP
ejpam-522	259	28	fuzzy	fuzzy	ADJ
ejpam-522	259	29	payoffs	payoff	NOUN
ejpam-522	259	30	are	be	AUX
ejpam-522	259	31	linear	linear	ADJ
ejpam-522	259	32	,	,	PUNCT
ejpam-522	259	33	the	the	DET
ejpam-522	259	34	maximin	maximin	NOUN
ejpam-522	259	35	solution	solution	NOUN
ejpam-522	259	36	with	with	ADP
ejpam-522	259	37	respect	respect	NOUN
ejpam-522	259	38	to	to	ADP
ejpam-522	259	39	a	a	DET
ejpam-522	259	40	degree	degree	NOUN
ejpam-522	259	41	of	of	ADP
ejpam-522	259	42	attainment	attainment	NOUN
ejpam-522	259	43	of	of	ADP
ejpam-522	259	44	the	the	DET
ejpam-522	259	45	aggregated	aggregate	VERB
ejpam-522	259	46	fuzzy	fuzzy	ADJ
ejpam-522	259	47	goal	goal	NOUN
ejpam-522	259	48	presented	present	VERB
ejpam-522	259	49	with	with	ADP
ejpam-522	259	50	a	a	DET
ejpam-522	259	51	new	new	ADJ
ejpam-522	259	52	solution	solution	NOUN
ejpam-522	259	53	concept	concept	NOUN
ejpam-522	259	54	.	.	PUNCT
ejpam-522	260	1	finally	finally	ADV
ejpam-522	260	2	,	,	PUNCT
ejpam-522	260	3	a	a	DET
ejpam-522	260	4	numerical	numerical	ADJ
ejpam-522	260	5	example	example	NOUN
ejpam-522	260	6	has	have	AUX
ejpam-522	260	7	illustrated	illustrate	VERB
ejpam-522	260	8	the	the	DET
ejpam-522	260	9	proposed	propose	VERB
ejpam-522	260	10	method	method	NOUN
ejpam-522	260	11	and	and	CCONJ
ejpam-522	260	12	obtained	obtain	VERB
ejpam-522	260	13	the	the	DET
ejpam-522	260	14	same	same	ADJ
ejpam-522	260	15	solution	solution	NOUN
ejpam-522	260	16	with	with	ADP
ejpam-522	260	17	sakawa	sakawa	PROPN
ejpam-522	260	18	.	.	PUNCT
ejpam-522	261	1	references	reference	NOUN
ejpam-522	261	2	[	[	X
ejpam-522	261	3	1	1	NUM
ejpam-522	261	4	]	]	X
ejpam-522	261	5	j.p	j.p	PROPN
ejpam-522	261	6	.	.	PROPN
ejpam-522	261	7	aubin	aubin	PROPN
ejpam-522	261	8	,	,	PUNCT
ejpam-522	261	9	mathematical	mathematical	ADJ
ejpam-522	261	10	methods	method	NOUN
ejpam-522	261	11	of	of	ADP
ejpam-522	261	12	game	game	NOUN
ejpam-522	261	13	and	and	CCONJ
ejpam-522	261	14	economic	economic	ADJ
ejpam-522	261	15	theory	theory	NOUN
ejpam-522	261	16	(	(	PUNCT
ejpam-522	261	17	northholland	northholland	NOUN
ejpam-522	261	18	,	,	PUNCT
ejpam-522	261	19	amsterdam,1979	amsterdam,1979	NOUN
ejpam-522	261	20	)	)	PUNCT
ejpam-522	261	21	.	.	PUNCT
ejpam-522	262	1	[	[	X
ejpam-522	262	2	2	2	NUM
ejpam-522	262	3	]	]	X
ejpam-522	262	4	j.p	j.p	PROPN
ejpam-522	262	5	.	.	PROPN
ejpam-522	262	6	aubin	aubin	PROPN
ejpam-522	262	7	,	,	PUNCT
ejpam-522	262	8	cooperative	cooperative	ADJ
ejpam-522	262	9	fuzzy	fuzzy	ADJ
ejpam-522	262	10	game	game	NOUN
ejpam-522	262	11	,	,	PUNCT
ejpam-522	262	12	math	math	NOUN
ejpam-522	262	13	.	.	PUNCT
ejpam-522	263	1	of	of	ADP
ejpam-522	263	2	oper	oper	PROPN
ejpam-522	263	3	.	.	PUNCT
ejpam-522	264	1	res	re	NOUN
ejpam-522	264	2	.	.	PROPN
ejpam-522	264	3	6	6	NUM
ejpam-522	264	4	(	(	PUNCT
ejpam-522	264	5	1981	1981	NUM
ejpam-522	264	6	)	)	PUNCT
ejpam-522	264	7	1	1	NUM
ejpam-522	264	8	-	-	SYM
ejpam-522	264	9	13	13	NUM
ejpam-522	264	10	.	.	PUNCT
ejpam-522	265	1	[	[	X
ejpam-522	265	2	3	3	X
ejpam-522	265	3	]	]	X
ejpam-522	265	4	e.b	e.b	PROPN
ejpam-522	265	5	.	.	PROPN
ejpam-522	265	6	bajalinov	bajalinov	PROPN
ejpam-522	265	7	,	,	PUNCT
ejpam-522	265	8	linear	linear	ADJ
ejpam-522	265	9	-fractional	-fractional	ADJ
ejpam-522	265	10	programming	programming	NOUN
ejpam-522	265	11	theory	theory	NOUN
ejpam-522	265	12	,	,	PUNCT
ejpam-522	265	13	methods	method	NOUN
ejpam-522	265	14	,	,	PUNCT
ejpam-522	265	15	applications	application	NOUN
ejpam-522	265	16	and	and	CCONJ
ejpam-522	265	17	software	software	NOUN
ejpam-522	265	18	,	,	PUNCT
ejpam-522	265	19	[	[	X
ejpam-522	265	20	4	4	NUM
ejpam-522	265	21	]	]	PUNCT
ejpam-522	265	22	r.e.bellman	r.e.bellman	NOUN
ejpam-522	265	23	and	and	CCONJ
ejpam-522	265	24	l.a	l.a	PROPN
ejpam-522	265	25	.	.	PROPN
ejpam-522	265	26	zadeh	zadeh	PROPN
ejpam-522	265	27	,	,	PUNCT
ejpam-522	265	28	decision	decision	NOUN
ejpam-522	265	29	making	making	NOUN
ejpam-522	265	30	in	in	ADP
ejpam-522	265	31	a	a	DET
ejpam-522	265	32	fuzzy	fuzzy	ADJ
ejpam-522	265	33	environment	environment	NOUN
ejpam-522	265	34	,	,	PUNCT
ejpam-522	265	35	manag	manag	PROPN
ejpam-522	265	36	.	.	PUNCT
ejpam-522	266	1	sci	sci	PROPN
ejpam-522	266	2	.	.	PROPN
ejpam-522	267	1	17	17	NUM
ejpam-522	267	2	(	(	PUNCT
ejpam-522	267	3	1970	1970	NUM
ejpam-522	267	4	)	)	PUNCT
ejpam-522	267	5	209	209	NUM
ejpam-522	267	6	-	-	SYM
ejpam-522	267	7	215	215	NUM
ejpam-522	267	8	.	.	PUNCT
ejpam-522	268	1	[	[	X
ejpam-522	268	2	5	5	NUM
ejpam-522	268	3	]	]	PUNCT
ejpam-522	268	4	d.blackwell	d.blackwell	NOUN
ejpam-522	268	5	,	,	PUNCT
ejpam-522	268	6	an	an	DET
ejpam-522	268	7	analog	analog	NOUN
ejpam-522	268	8	of	of	ADP
ejpam-522	268	9	the	the	DET
ejpam-522	268	10	minimax	minimax	NOUN
ejpam-522	268	11	theorem	theorem	NOUN
ejpam-522	268	12	for	for	ADP
ejpam-522	268	13	vector	vector	NOUN
ejpam-522	268	14	payoffs	payoff	NOUN
ejpam-522	268	15	,	,	PUNCT
ejpam-522	268	16	pacific	pacific	PROPN
ejpam-522	268	17	j.	j.	PROPN
ejpam-522	268	18	math	math	PROPN
ejpam-522	268	19	.	.	PUNCT
ejpam-522	269	1	98	98	NUM
ejpam-522	269	2	(	(	PUNCT
ejpam-522	269	3	1956	1956	NUM
ejpam-522	269	4	)	)	PUNCT
ejpam-522	269	5	1	1	NUM
ejpam-522	269	6	-	-	SYM
ejpam-522	269	7	8	8	NUM
ejpam-522	269	8	.	.	PUNCT
ejpam-522	270	1	[	[	X
ejpam-522	270	2	6	6	NUM
ejpam-522	270	3	]	]	SYM
ejpam-522	270	4	d.butnariu	d.butnariu	ADV
ejpam-522	270	5	,	,	PUNCT
ejpam-522	270	6	fuzzy	fuzzy	ADJ
ejpam-522	270	7	games	game	NOUN
ejpam-522	270	8	:	:	PUNCT
ejpam-522	270	9	a	a	DET
ejpam-522	270	10	description	description	NOUN
ejpam-522	270	11	of	of	ADP
ejpam-522	270	12	the	the	DET
ejpam-522	270	13	concept	concept	NOUN
ejpam-522	270	14	,	,	PUNCT
ejpam-522	270	15	fuzzy	fuzzy	ADJ
ejpam-522	270	16	sets	set	NOUN
ejpam-522	270	17	and	and	CCONJ
ejpam-522	270	18	systems	system	NOUN
ejpam-522	270	19	1	1	NUM
ejpam-522	270	20	(	(	PUNCT
ejpam-522	270	21	1978	1978	NUM
ejpam-522	270	22	)	)	PUNCT
ejpam-522	270	23	181	181	NUM
ejpam-522	270	24	-	-	SYM
ejpam-522	270	25	192	192	NUM
ejpam-522	270	26	.	.	PUNCT
ejpam-522	271	1	[	[	X
ejpam-522	271	2	7	7	X
ejpam-522	271	3	]	]	SYM
ejpam-522	271	4	d.butnariu	d.butnariu	NOUN
ejpam-522	271	5	,	,	PUNCT
ejpam-522	271	6	stability	stability	NOUN
ejpam-522	271	7	and	and	CCONJ
ejpam-522	271	8	shapley	shapley	NOUN
ejpam-522	271	9	value	value	NOUN
ejpam-522	271	10	for	for	ADP
ejpam-522	271	11	n	n	CCONJ
ejpam-522	271	12	-	-	PUNCT
ejpam-522	271	13	person	person	NOUN
ejpam-522	271	14	fuzzy	fuzzy	ADJ
ejpam-522	271	15	game	game	NOUN
ejpam-522	271	16	,	,	PUNCT
ejpam-522	271	17	fuzzy	fuzzy	ADJ
ejpam-522	271	18	sets	set	NOUN
ejpam-522	271	19	and	and	CCONJ
ejpam-522	271	20	systems	system	NOUN
ejpam-522	271	21	4	4	NUM
ejpam-522	271	22	(	(	PUNCT
ejpam-522	271	23	1980	1980	NUM
ejpam-522	271	24	)	)	PUNCT
ejpam-522	271	25	63	63	NUM
ejpam-522	271	26	-	-	SYM
ejpam-522	271	27	72	72	NUM
ejpam-522	271	28	.	.	PUNCT
ejpam-522	272	1	[	[	X
ejpam-522	272	2	8	8	NUM
ejpam-522	272	3	]	]	SYM
ejpam-522	272	4	l.campos	l.campo	NOUN
ejpam-522	272	5	,	,	PUNCT
ejpam-522	272	6	fuzzy	fuzzy	ADJ
ejpam-522	272	7	linear	linear	ADJ
ejpam-522	272	8	programming	programming	NOUN
ejpam-522	272	9	models	model	NOUN
ejpam-522	272	10	to	to	PART
ejpam-522	272	11	solve	solve	VERB
ejpam-522	272	12	fuzzy	fuzzy	ADJ
ejpam-522	272	13	matrix	matrix	NOUN
ejpam-522	272	14	games	game	NOUN
ejpam-522	272	15	,	,	PUNCT
ejpam-522	272	16	fuzzy	fuzzy	ADJ
ejpam-522	272	17	sets	set	NOUN
ejpam-522	272	18	and	and	CCONJ
ejpam-522	272	19	systems	system	NOUN
ejpam-522	272	20	32	32	NUM
ejpam-522	272	21	(	(	PUNCT
ejpam-522	272	22	1989	1989	NUM
ejpam-522	272	23	)	)	PUNCT
ejpam-522	272	24	275	275	NUM
ejpam-522	272	25	-	-	SYM
ejpam-522	272	26	289	289	NUM
ejpam-522	272	27	.	.	PUNCT
ejpam-522	273	1	[	[	X
ejpam-522	273	2	9	9	NUM
ejpam-522	273	3	]	]	PUNCT
ejpam-522	273	4	a.charnes	a.charne	NOUN
ejpam-522	273	5	and	and	CCONJ
ejpam-522	273	6	w.	w.	PROPN
ejpam-522	273	7	cooper	cooper	PROPN
ejpam-522	273	8	,	,	PUNCT
ejpam-522	273	9	programming	program	VERB
ejpam-522	273	10	with	with	ADP
ejpam-522	273	11	linear	linear	ADJ
ejpam-522	273	12	fractional	fractional	ADJ
ejpam-522	273	13	function	function	NOUN
ejpam-522	273	14	,	,	PUNCT
ejpam-522	273	15	naval	naval	ADJ
ejpam-522	273	16	res	re	NOUN
ejpam-522	273	17	.	.	PUNCT
ejpam-522	274	1	logist	logist	NOUN
ejpam-522	274	2	.	.	PUNCT
ejpam-522	275	1	quart	quart	NOUN
ejpam-522	275	2	.	.	PUNCT
ejpam-522	276	1	9	9	NUM
ejpam-522	276	2	(	(	PUNCT
ejpam-522	276	3	1962	1962	NUM
ejpam-522	276	4	)	)	PUNCT
ejpam-522	276	5	181	181	NUM
ejpam-522	276	6	-	-	SYM
ejpam-522	276	7	186	186	NUM
ejpam-522	276	8	.	.	PUNCT
ejpam-522	277	1	[	[	X
ejpam-522	277	2	10	10	NUM
ejpam-522	277	3	]	]	PUNCT
ejpam-522	277	4	a.charnes	a.charne	NOUN
ejpam-522	277	5	,	,	PUNCT
ejpam-522	277	6	z.huang	z.huang	NUM
ejpam-522	277	7	,	,	PUNCT
ejpam-522	277	8	j.rousseau	j.rousseau	NOUN
ejpam-522	277	9	and	and	CCONJ
ejpam-522	277	10	q.	q.	PROPN
ejpam-522	277	11	wei	wei	PROPN
ejpam-522	277	12	,	,	PUNCT
ejpam-522	277	13	cone	cone	NOUN
ejpam-522	277	14	extremal	extremal	ADJ
ejpam-522	277	15	solutions	solution	NOUN
ejpam-522	277	16	of	of	ADP
ejpam-522	277	17	multi	multi	ADJ
ejpam-522	277	18	-	-	ADJ
ejpam-522	277	19	payoff	payoff	ADJ
ejpam-522	277	20	games	game	NOUN
ejpam-522	277	21	with	with	ADP
ejpam-522	277	22	cross	cross	ADJ
ejpam-522	277	23	-	-	ADJ
ejpam-522	277	24	constrained	constrained	ADJ
ejpam-522	277	25	strategy	strategy	NOUN
ejpam-522	277	26	set	set	NOUN
ejpam-522	277	27	,	,	PUNCT
ejpam-522	277	28	optimization	optimization	NOUN
ejpam-522	277	29	21	21	NUM
ejpam-522	277	30	(	(	PUNCT
ejpam-522	277	31	1990	1990	NUM
ejpam-522	277	32	)	)	PUNCT
ejpam-522	277	33	51	51	NUM
ejpam-522	277	34	-	-	SYM
ejpam-522	277	35	69	69	NUM
ejpam-522	277	36	.	.	PUNCT
ejpam-522	278	1	references	reference	NOUN
ejpam-522	278	2	117	117	NUM
ejpam-522	278	3	[	[	X
ejpam-522	278	4	11	11	NUM
ejpam-522	278	5	]	]	X
ejpam-522	278	6	i.	i.	PROPN
ejpam-522	278	7	olivtti	olivtti	PROPN
ejpam-522	278	8	and	and	CCONJ
ejpam-522	278	9	c.	c.	PROPN
ejpam-522	278	10	milano	milano	PROPN
ejpam-522	278	11	,	,	PUNCT
ejpam-522	278	12	a	a	DET
ejpam-522	278	13	decision	decision	NOUN
ejpam-522	278	14	model	model	NOUN
ejpam-522	278	15	under	under	ADP
ejpam-522	278	16	certainty	certainty	NOUN
ejpam-522	278	17	with	with	ADP
ejpam-522	278	18	multiple	multiple	ADJ
ejpam-522	278	19	payoffs	payoff	NOUN
ejpam-522	278	20	,	,	PUNCT
ejpam-522	278	21	in	in	ADP
ejpam-522	278	22	:	:	PUNCT
ejpam-522	278	23	a.	a.	NOUN
ejpam-522	278	24	mensch	mensch	PROPN
ejpam-522	278	25	,	,	PUNCT
ejpam-522	278	26	ed	ed	NOUN
ejpam-522	278	27	.	.	PROPN
ejpam-522	278	28	,	,	PUNCT
ejpam-522	278	29	theory	theory	NOUN
ejpam-522	278	30	of	of	ADP
ejpam-522	278	31	games	game	NOUN
ejpam-522	278	32	;	;	PUNCT
ejpam-522	278	33	techniques	technique	NOUN
ejpam-522	278	34	and	and	CCONJ
ejpam-522	278	35	applications	application	NOUN
ejpam-522	278	36	(	(	PUNCT
ejpam-522	278	37	american	american	PROPN
ejpam-522	278	38	elsevier	elsevier	PROPN
ejpam-522	278	39	,	,	PUNCT
ejpam-522	278	40	new	new	ADJ
ejpam-522	278	41	york,1966	york,1966	NOUN
ejpam-522	278	42	)	)	PUNCT
ejpam-522	278	43	50	50	NUM
ejpam-522	278	44	-	-	SYM
ejpam-522	278	45	63	63	NUM
ejpam-522	278	46	.	.	PUNCT
ejpam-522	279	1	[	[	X
ejpam-522	279	2	12	12	NUM
ejpam-522	279	3	]	]	X
ejpam-522	279	4	w.d	w.d	PROPN
ejpam-522	279	5	.	.	PROPN
ejpam-522	279	6	cook	cook	PROPN
ejpam-522	279	7	,	,	PUNCT
ejpam-522	279	8	zero	zero	NUM
ejpam-522	279	9	-	-	PUNCT
ejpam-522	279	10	sum	sum	NOUN
ejpam-522	279	11	games	game	NOUN
ejpam-522	279	12	with	with	ADP
ejpam-522	279	13	multiple	multiple	ADJ
ejpam-522	279	14	goals	goal	NOUN
ejpam-522	279	15	,	,	PUNCT
ejpam-522	279	16	naval	naval	ADJ
ejpam-522	279	17	res	re	NOUN
ejpam-522	279	18	.	.	PUNCT
ejpam-522	280	1	logist	logist	NOUN
ejpam-522	280	2	.	.	PUNCT
ejpam-522	281	1	quart	quart	NOUN
ejpam-522	281	2	.	.	PUNCT
ejpam-522	282	1	23	23	NUM
ejpam-522	282	2	(	(	PUNCT
ejpam-522	282	3	1976	1976	NUM
ejpam-522	282	4	)	)	PUNCT
ejpam-522	282	5	615	615	NUM
ejpam-522	282	6	-	-	SYM
ejpam-522	282	7	622	622	NUM
ejpam-522	282	8	[	[	SYM
ejpam-522	282	9	13	13	NUM
ejpam-522	282	10	]	]	PUNCT
ejpam-522	282	11	i.	i.	NOUN
ejpam-522	282	12	nishizaki	nishizaki	PROPN
ejpam-522	282	13	and	and	CCONJ
ejpam-522	282	14	m.sakawa	m.sakawa	PROPN
ejpam-522	282	15	,	,	PUNCT
ejpam-522	282	16	two	two	NUM
ejpam-522	282	17	-	-	PUNCT
ejpam-522	282	18	person	person	NOUN
ejpam-522	282	19	zero	zero	NUM
ejpam-522	282	20	-	-	PUNCT
ejpam-522	282	21	sum	sum	NOUN
ejpam-522	282	22	games	game	NOUN
ejpam-522	282	23	with	with	ADP
ejpam-522	282	24	multiple	multiple	ADJ
ejpam-522	282	25	fuzzy	fuzzy	ADJ
ejpam-522	282	26	goals	goal	NOUN
ejpam-522	282	27	,	,	PUNCT
ejpam-522	282	28	j.	j.	PROPN
ejpam-522	282	29	japan	japan	PROPN
ejpam-522	282	30	soc	soc	PROPN
ejpam-522	282	31	.	.	PUNCT
ejpam-522	283	1	fuzzy	fuzzy	ADJ
ejpam-522	283	2	theory	theory	NOUN
ejpam-522	283	3	systems	system	NOUN
ejpam-522	283	4	4	4	NUM
ejpam-522	283	5	(	(	PUNCT
ejpam-522	283	6	1992	1992	NUM
ejpam-522	283	7	)	)	PUNCT
ejpam-522	283	8	504	504	NUM
ejpam-522	283	9	-	-	SYM
ejpam-522	283	10	511	511	NUM
ejpam-522	283	11	.	.	PUNCT
ejpam-522	284	1	[	[	X
ejpam-522	284	2	14	14	NUM
ejpam-522	284	3	]	]	PUNCT
ejpam-522	284	4	i.	i.	NOUN
ejpam-522	284	5	nishizaki	nishizaki	PROPN
ejpam-522	284	6	and	and	CCONJ
ejpam-522	284	7	m.sakawa	m.sakawa	PROPN
ejpam-522	284	8	,	,	PUNCT
ejpam-522	284	9	fuzzy	fuzzy	ADJ
ejpam-522	284	10	and	and	CCONJ
ejpam-522	284	11	multiobjective	multiobjective	ADJ
ejpam-522	284	12	games	game	NOUN
ejpam-522	284	13	for	for	ADP
ejpam-522	284	14	conflict	conflict	NOUN
ejpam-522	284	15	resolution	resolution	NOUN
ejpam-522	284	16	,	,	PUNCT
ejpam-522	284	17	kluwer	kluwer	NOUN
ejpam-522	284	18	academic	academic	ADJ
ejpam-522	284	19	publishers	publisher	NOUN
ejpam-522	284	20	2003	2003	NUM
ejpam-522	284	21	.	.	PUNCT
ejpam-522	285	1	[	[	X
ejpam-522	285	2	15	15	NUM
ejpam-522	285	3	]	]	X
ejpam-522	285	4	i.	i.	NOUN
ejpam-522	285	5	nishizaki	nishizaki	PROPN
ejpam-522	285	6	and	and	CCONJ
ejpam-522	285	7	m.sakawa	m.sakawa	PROPN
ejpam-522	285	8	,	,	PUNCT
ejpam-522	285	9	equilibrium	equilibrium	NOUN
ejpam-522	285	10	solutions	solution	NOUN
ejpam-522	285	11	for	for	ADP
ejpam-522	285	12	multiobjective	multiobjective	ADJ
ejpam-522	285	13	bimatrix	bimatrix	NOUN
ejpam-522	285	14	games	game	NOUN
ejpam-522	285	15	incorporating	incorporate	VERB
ejpam-522	285	16	fuzzy	fuzzy	ADJ
ejpam-522	285	17	goals	goal	NOUN
ejpam-522	285	18	,	,	PUNCT
ejpam-522	285	19	journal	journal	NOUN
ejpam-522	285	20	of	of	ADP
ejpam-522	285	21	optimization	optimization	NOUN
ejpam-522	285	22	theory	theory	NOUN
ejpam-522	285	23	and	and	CCONJ
ejpam-522	285	24	applications	application	NOUN
ejpam-522	285	25	,	,	PUNCT
ejpam-522	285	26	86	86	NUM
ejpam-522	285	27	(	(	PUNCT
ejpam-522	285	28	1995	1995	NUM
ejpam-522	285	29	)	)	PUNCT
ejpam-522	285	30	433	433	NUM
ejpam-522	285	31	-	-	SYM
ejpam-522	285	32	457	457	NUM
ejpam-522	285	33	.	.	PUNCT
ejpam-522	286	1	[	[	X
ejpam-522	286	2	16	16	NUM
ejpam-522	286	3	]	]	PUNCT
ejpam-522	286	4	i.	i.	NOUN
ejpam-522	286	5	nishizaki	nishizaki	PROPN
ejpam-522	286	6	and	and	CCONJ
ejpam-522	286	7	m.sakawa	m.sakawa	PROPN
ejpam-522	286	8	,	,	PUNCT
ejpam-522	286	9	equilibrium	equilibrium	NOUN
ejpam-522	286	10	solutions	solution	NOUN
ejpam-522	286	11	in	in	ADP
ejpam-522	286	12	multiobjective	multiobjective	ADJ
ejpam-522	286	13	bimatrix	bimatrix	NOUN
ejpam-522	286	14	games	game	NOUN
ejpam-522	286	15	with	with	ADP
ejpam-522	286	16	fuzzy	fuzzy	ADJ
ejpam-522	286	17	payoffs	payoff	NOUN
ejpam-522	286	18	and	and	CCONJ
ejpam-522	286	19	fuzzy	fuzzy	ADJ
ejpam-522	286	20	goals	goal	NOUN
ejpam-522	286	21	,	,	PUNCT
ejpam-522	286	22	fuzzy	fuzzy	ADJ
ejpam-522	286	23	sets	set	NOUN
ejpam-522	286	24	and	and	CCONJ
ejpam-522	286	25	systems	system	NOUN
ejpam-522	286	26	,	,	PUNCT
ejpam-522	286	27	111	111	NUM
ejpam-522	286	28	(	(	PUNCT
ejpam-522	286	29	2000	2000	NUM
ejpam-522	286	30	)	)	PUNCT
ejpam-522	286	31	99	99	NUM
ejpam-522	286	32	-	-	SYM
ejpam-522	286	33	116	116	NUM
ejpam-522	286	34	.	.	PUNCT
ejpam-522	287	1	[	[	X
ejpam-522	287	2	17	17	NUM
ejpam-522	287	3	]	]	X
ejpam-522	287	4	m.sakawa	m.sakawa	PROPN
ejpam-522	287	5	and	and	CCONJ
ejpam-522	287	6	i.	i.	PROPN
ejpam-522	287	7	nishizaki	nishizaki	PROPN
ejpam-522	287	8	,	,	PUNCT
ejpam-522	287	9	max	max	PROPN
ejpam-522	287	10	-	-	PUNCT
ejpam-522	287	11	min	min	NOUN
ejpam-522	287	12	solutions	solution	NOUN
ejpam-522	287	13	for	for	ADP
ejpam-522	287	14	fuzzy	fuzzy	ADJ
ejpam-522	287	15	multiobjective	multiobjective	ADJ
ejpam-522	287	16	matrix	matrix	NOUN
ejpam-522	287	17	games	game	NOUN
ejpam-522	287	18	,	,	PUNCT
ejpam-522	287	19	fuzzy	fuzzy	ADJ
ejpam-522	287	20	sets	set	NOUN
ejpam-522	287	21	and	and	CCONJ
ejpam-522	287	22	systems	system	NOUN
ejpam-522	287	23	,	,	PUNCT
ejpam-522	287	24	67	67	NUM
ejpam-522	287	25	(	(	PUNCT
ejpam-522	287	26	1994	1994	NUM
ejpam-522	287	27	)	)	PUNCT
ejpam-522	287	28	53	53	NUM
ejpam-522	287	29	-	-	SYM
ejpam-522	287	30	69	69	NUM
ejpam-522	287	31	.	.	PUNCT
ejpam-522	288	1	[	[	X
ejpam-522	288	2	18	18	NUM
ejpam-522	288	3	]	]	PUNCT
ejpam-522	288	4	m.sakawa	m.sakawa	NOUN
ejpam-522	288	5	,	,	PUNCT
ejpam-522	288	6	interactive	interactive	ADJ
ejpam-522	288	7	computer	computer	NOUN
ejpam-522	288	8	program	program	NOUN
ejpam-522	288	9	for	for	ADP
ejpam-522	288	10	fuzzy	fuzzy	ADJ
ejpam-522	288	11	linear	linear	ADJ
ejpam-522	288	12	programming	programming	NOUN
ejpam-522	288	13	with	with	ADP
ejpam-522	288	14	multiple	multiple	ADJ
ejpam-522	288	15	objectives	objective	NOUN
ejpam-522	288	16	,	,	PUNCT
ejpam-522	288	17	int	int	NOUN
ejpam-522	288	18	.	.	PUNCT
ejpam-522	289	1	j.	j.	PROPN
ejpam-522	289	2	man	man	PROPN
ejpam-522	289	3	-	-	PUNCT
ejpam-522	289	4	machine	machine	NOUN
ejpam-522	289	5	studies	study	NOUN
ejpam-522	289	6	,	,	PUNCT
ejpam-522	289	7	18	18	NUM
ejpam-522	289	8	(	(	PUNCT
ejpam-522	289	9	1983	1983	NUM
ejpam-522	289	10	)	)	PUNCT
ejpam-522	289	11	489	489	NUM
ejpam-522	289	12	-	-	SYM
ejpam-522	289	13	503	503	NUM
ejpam-522	289	14	.	.	PUNCT
ejpam-522	290	1	[	[	X
ejpam-522	290	2	19	19	NUM
ejpam-522	290	3	]	]	X
ejpam-522	290	4	k.shimizu	k.shimizu	NOUN
ejpam-522	290	5	and	and	CCONJ
ejpam-522	290	6	e.aiyoshi	e.aiyoshi	ADJ
ejpam-522	290	7	,	,	PUNCT
ejpam-522	290	8	neccesary	neccesary	ADJ
ejpam-522	290	9	conditions	condition	NOUN
ejpam-522	290	10	for	for	ADP
ejpam-522	290	11	min	min	NOUN
ejpam-522	290	12	-	-	ADJ
ejpam-522	290	13	max	max	ADJ
ejpam-522	290	14	problems	problem	NOUN
ejpam-522	290	15	and	and	CCONJ
ejpam-522	290	16	algorithm	algorithm	NOUN
ejpam-522	290	17	by	by	ADP
ejpam-522	290	18	a	a	DET
ejpam-522	290	19	relaxation	relaxation	NOUN
ejpam-522	290	20	procedure	procedure	NOUN
ejpam-522	290	21	,	,	PUNCT
ejpam-522	290	22	ieee	ieee	NOUN
ejpam-522	290	23	trans	trans	PROPN
ejpam-522	290	24	.	.	PROPN
ejpam-522	290	25	automat	automat	PROPN
ejpam-522	290	26	.	.	PUNCT
ejpam-522	290	27	control	control	PROPN
ejpam-522	290	28	ac-25	ac-25	PUNCT
ejpam-522	291	1	(	(	PUNCT
ejpam-522	291	2	1980	1980	NUM
ejpam-522	291	3	)	)	PUNCT
ejpam-522	291	4	62	62	NUM
ejpam-522	291	5	-	-	SYM
ejpam-522	291	6	66	66	NUM
ejpam-522	291	7	.	.	PUNCT
ejpam-522	292	1	[	[	X
ejpam-522	292	2	20	20	NUM
ejpam-522	292	3	]	]	PUNCT
ejpam-522	292	4	m.zeleny	m.zeleny	VERB
ejpam-522	292	5	,	,	PUNCT
ejpam-522	292	6	games	game	NOUN
ejpam-522	292	7	with	with	ADP
ejpam-522	292	8	multiple	multiple	ADJ
ejpam-522	292	9	payoffs	payoff	NOUN
ejpam-522	292	10	,	,	PUNCT
ejpam-522	292	11	int	int	NOUN
ejpam-522	292	12	.	.	PUNCT
ejpam-522	293	1	j.	j.	PROPN
ejpam-522	293	2	game	game	PROPN
ejpam-522	293	3	theory	theory	NOUN
ejpam-522	293	4	4	4	NUM
ejpam-522	293	5	(	(	PUNCT
ejpam-522	293	6	1975	1975	NUM
ejpam-522	293	7	)	)	PUNCT
ejpam-522	293	8	179	179	NUM
ejpam-522	293	9	-	-	SYM
ejpam-522	293	10	191	191	NUM
ejpam-522	293	11	.	.	PUNCT
ejpam-522	294	1	[	[	X
ejpam-522	294	2	21	21	NUM
ejpam-522	294	3	]	]	X
ejpam-522	294	4	j.zhao	j.zhao	NOUN
ejpam-522	294	5	,	,	PUNCT
ejpam-522	294	6	the	the	DET
ejpam-522	294	7	equilibria	equilibrium	NOUN
ejpam-522	294	8	of	of	ADP
ejpam-522	294	9	a	a	DET
ejpam-522	294	10	multiple	multiple	ADJ
ejpam-522	294	11	objective	objective	ADJ
ejpam-522	294	12	game	game	NOUN
ejpam-522	294	13	,	,	PUNCT
ejpam-522	294	14	int	int	NOUN
ejpam-522	294	15	.	.	PUNCT
ejpam-522	295	1	j.	j.	PROPN
ejpam-522	295	2	game	game	PROPN
ejpam-522	295	3	theory	theory	NOUN
ejpam-522	295	4	20	20	NUM
ejpam-522	295	5	(	(	PUNCT
ejpam-522	295	6	1991	1991	NUM
ejpam-522	295	7	)	)	PUNCT
ejpam-522	295	8	171	171	NUM
ejpam-522	295	9	-	-	SYM
ejpam-522	295	10	182	182	NUM
ejpam-522	295	11	.	.	PUNCT