Multi-objective Fuzzy Bi-matrix Game Model: A Multicriteria Non-Linear Programming Approach

A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results of this paper are de...

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Published in:	Symmetry (Basel) Vol. 9; no. 8; p. 159
Main Authors:	Zhang, Wei, Xing, Yumei, Qiu, Dong
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 2017
Subjects:	Game theory Linear programming Mathematical analysis Mathematical models Mathematical programming Matrix methods Multiple objective analysis Nonlinear programming
ISSN:	2073-8994, 2073-8994
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Abstract	A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results of this paper are demonstrated through a numerical example.
AbstractList	A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results of this paper are demonstrated through a numerical example.
Author	Xing, Yumei Qiu, Dong Zhang, Wei
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Cites_doi	10.1023/B:JOTA.0000004867.66302.16 10.1109/IS.2008.4670407 10.1007/BF02192644 10.1016/0165-0114(78)90031-3 10.1016/S0377-2217(01)00384-8 10.1109/91.995123 10.1007/BF02192089 10.1109/TFUZZ.2013.2297153 10.1109/TFUZZ.2012.2203308 10.3390/sym9080130 10.1016/j.asoc.2014.10.020 10.1016/S0165-0114(96)00009-7 10.1016/0022-247X(64)90021-6 10.1007/978-94-015-8702-0 10.1016/j.engappai.2004.08.004 10.1007/s12597-012-0099-9 10.1016/S0165-0114(98)00455-2 10.1080/02533839.2002.9670676 10.2140/pjm.1956.6.1 10.1109/CIMCA.2008.214 10.1109/FUZZY.2010.5584733 10.1109/NAFIPS.2010.5548187 10.1016/j.amc.2006.01.083 10.5772/54677
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References	Garagic (ref_4) 2003; 118 Fernandez (ref_32) 1996; 89 Roy (ref_25) 2013; 7 Tan (ref_5) 2014; 22 Chakeri (ref_8) 2013; 21 ref_34 ref_11 ref_33 ref_10 Blackwell (ref_12) 1956; 6 Chen (ref_18) 2002; 19 Chen (ref_3) 2002; 10 Chen (ref_19) 2006; 181 Nishizaki (ref_15) 1992; 4 Angelov (ref_21) 1997; 86 Zimmermann (ref_35) 1978; 1 Mangasarian (ref_30) 1964; 9 Pal (ref_36) 2003; 144 Nishizaki (ref_17) 1995; 86 Das (ref_37) 2013; 50 Nishizaki (ref_16) 1993; 5 Ghosn (ref_24) 2016; 14 Roy (ref_14) 2007; 15 ref_20 Precup (ref_22) 2004; 17 Zadeh (ref_1) 1965; 8 Roy (ref_13) 2001; 30 Nishizaki (ref_31) 2000; 111 ref_2 ref_29 Kiran (ref_23) 2015; 26 ref_28 ref_27 ref_26 ref_9 ref_7 ref_6
References_xml	– volume: 118 start-page: 475 year: 2003 ident: ref_4 article-title: An approach to fuzzy noncooperative nash games publication-title: J. Optim. Theory Appl. doi: 10.1023/B:JOTA.0000004867.66302.16 – ident: ref_11 doi: 10.1109/IS.2008.4670407 – volume: 30 start-page: 56 year: 2001 ident: ref_13 article-title: An approach to multi-objective bimatrix games for Nash equilibrium solutions publication-title: Ric. Oper. – volume: 89 start-page: 115 year: 1996 ident: ref_32 article-title: Vector linear programming in zero-sum multicriteria matrix games publication-title: J. Optim. Theory Appl. doi: 10.1007/BF02192644 – volume: 1 start-page: 45 year: 1978 ident: ref_35 article-title: Fuzzy programming and linear programming with several objective functions publication-title: Fuzzy Sets Syst. doi: 10.1016/0165-0114(78)90031-3 – volume: 144 start-page: 480 year: 2003 ident: ref_36 article-title: A goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming publication-title: Eur. J. Oper. Res. doi: 10.1016/S0377-2217(01)00384-8 – volume: 10 start-page: 222 year: 2002 ident: ref_3 article-title: Fuzzy differential games for nonlinear stochastic systems: Suboptimal approach publication-title: IEEE Trans. Fuzzy Syst. doi: 10.1109/91.995123 – volume: 86 start-page: 433 year: 1995 ident: ref_17 article-title: Equilibrium solution for multiobjective bimatrix games incorporating fuzzy goals publication-title: J. Optim. Theory Appl. doi: 10.1007/BF02192089 – ident: ref_26 – volume: 22 start-page: 1489 year: 2014 ident: ref_5 article-title: A Banzhaf function for a fuzzy game publication-title: IEEE Trans. Fuzzy Syst. doi: 10.1109/TFUZZ.2013.2297153 – volume: 15 start-page: 141 year: 2007 ident: ref_14 article-title: Fuzzy programming approach to two-person multicriteria bimatrix games publication-title: J. Fuzzy Math. – volume: 21 start-page: 171 year: 2013 ident: ref_8 article-title: Fuzzy Nash equilibriums in crisp and fuzzy games publication-title: IEEE Trans. Fuzzy Syst. doi: 10.1109/TFUZZ.2012.2203308 – ident: ref_28 doi: 10.3390/sym9080130 – volume: 8 start-page: 338 year: 1965 ident: ref_1 article-title: Information and control publication-title: Fuzzy sets – volume: 26 start-page: 454 year: 2015 ident: ref_23 article-title: A directed artificial bee colony algorithm publication-title: Appl. Soft Comput. doi: 10.1016/j.asoc.2014.10.020 – volume: 86 start-page: 299 year: 1997 ident: ref_21 article-title: Optimization in an intuitionistic fuzzy environment publication-title: Fuzzy Sets Syst. doi: 10.1016/S0165-0114(96)00009-7 – volume: 9 start-page: 348 year: 1964 ident: ref_30 article-title: Two-person non-zero-sum games and quadratic programming publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(64)90021-6 – ident: ref_34 doi: 10.1007/978-94-015-8702-0 – volume: 17 start-page: 661 year: 2004 ident: ref_22 article-title: Optimisation criteria in development of fuzzy controllers with dynamics publication-title: Eng. Appl. Artif. Intel. doi: 10.1016/j.engappai.2004.08.004 – volume: 14 start-page: 130 year: 2016 ident: ref_24 article-title: A parallel genetic algorithm for the open-shop scheduling problem using deterministic and random moves publication-title: Eng. Appl. Artif. Intel. – volume: 50 start-page: 125 year: 2013 ident: ref_37 article-title: Fuzzy based GA to multi-objective entropy bimatrix game publication-title: Opsearch doi: 10.1007/s12597-012-0099-9 – volume: 111 start-page: 99 year: 2000 ident: ref_31 article-title: Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals publication-title: Fuzzy Sets Syst. doi: 10.1016/S0165-0114(98)00455-2 – volume: 19 start-page: 9 year: 2002 ident: ref_18 article-title: An alternative approach to the bimatrix non-cooperative game with fuzzy multiple objectives publication-title: J. Chin. Inst. Eng. doi: 10.1080/02533839.2002.9670676 – volume: 6 start-page: 1 year: 1956 ident: ref_12 article-title: An analog of the minimax theorem for vector payoffs publication-title: Pac. J. Math. doi: 10.2140/pjm.1956.6.1 – ident: ref_29 – ident: ref_33 – ident: ref_27 – ident: ref_2 – volume: 7 start-page: 108 year: 2013 ident: ref_25 article-title: Multicriteria entropy bimatrix goal game: A Fuzzy programming approach publication-title: J. Uncertain Syst. – ident: ref_10 doi: 10.1109/CIMCA.2008.214 – ident: ref_7 doi: 10.1109/FUZZY.2010.5584733 – volume: 5 start-page: 505 year: 1993 ident: ref_16 article-title: Max-min solution for fuzzy multi-objective matrix games publication-title: J. Japan Soc. Fuzzy Theory Syst. – ident: ref_6 doi: 10.1109/NAFIPS.2010.5548187 – volume: 4 start-page: 504 year: 1992 ident: ref_15 article-title: Two-person zero-sum games with multiple fuzzy goals publication-title: J. Japan Soc. Fuzzy Theory Syst. – ident: ref_20 – volume: 181 start-page: 1139 year: 2006 ident: ref_19 article-title: Fuzzy multi-stage de-novo programming problem publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2006.01.083 – ident: ref_9 doi: 10.5772/54677
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SubjectTerms	Game theory Linear programming Mathematical analysis Mathematical models Mathematical programming Matrix methods Multiple objective analysis Nonlinear programming
Title	Multi-objective Fuzzy Bi-matrix Game Model: A Multicriteria Non-Linear Programming Approach
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