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 demonstrated through a numerical example.

[1]  Ichiro Nishizaki,et al.  Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals , 2000, Fuzzy Sets Syst..

[2]  Yuh-Wen Chen AN ALTERNATIVE APPROACH TO THE BIMATRIX NON-COOPERATIVE GAME WITH FUZZY MULTIPLE OBJECTIVES , 2002 .

[3]  Bijay Baran Pal,et al.  A goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming , 2003, Eur. J. Oper. Res..

[4]  F. Sheikholeslam,et al.  Linguisitc representation of Nash equilibriums in fuzzy games , 2010, 2010 Annual Meeting of the North American Fuzzy Information Processing Society.

[5]  Nasser Sadati,et al.  Nash Equilibrium Strategies in Fuzzy Games , 2013 .

[6]  Ching-Chih Tsai,et al.  A new partition law of information which governs systems , 2002 .

[7]  H. Carter Fuzzy Sets and Systems — Theory and Applications , 1982 .

[8]  Plamen P. Angelov,et al.  Optimization in an intuitionistic fuzzy environment , 1997, Fuzzy Sets Syst..

[9]  Sankar Kumar Roy,et al.  An Approach to Multi-objective Bimatrix Games for Nash Equilibrium Solutions , 2000 .

[10]  O. Mangasarian,et al.  Two-person nonzero-sum games and quadratic programming , 1964 .

[11]  M. Sakawa,et al.  Equilibrium solutions for multiobjective bimatrix games incorporating fuzzy goals , 1995 .

[12]  Bor-Sen Chen,et al.  Fuzzy differential games for nonlinear stochastic systems: suboptimal approach , 2002, IEEE Trans. Fuzzy Syst..

[13]  Sankar Kumar Roy,et al.  Multicriteria Entropy Bimatrix Goal Game : A Fuzzy Programming Approach , 2013 .

[14]  Alireza Chakeri,et al.  Fuzzy Nash Equilibriums in Crisp and Fuzzy Games , 2013, IEEE Transactions on Fuzzy Systems.

[15]  Stef Tijs,et al.  Pareto equilibria in multiobjective games , 1988 .

[16]  F. R. Fernandez,et al.  Vector linear programming in zero-sum multicriteria matrix games , 1996 .

[17]  C. R. Bector,et al.  Fuzzy Mathematical Programming and Fuzzy Matrix Games , 2005 .

[18]  W. A. Rosenblith Information and Control in Organ Systems , 1959 .

[19]  Sankar Kumar Roy,et al.  Fuzzy based GA to multi-objective entropy bimatrix game , 2013 .

[20]  C. Lucas,et al.  How can fuzzy logic determine game equilibriums better? , 2008, 2008 4th International IEEE Conference Intelligent Systems.

[21]  Haidar M. Harmanani,et al.  A parallel genetic algorithm for the open-shop scheduling problem using deterministic and random moves , 2009, SpringSim '09.

[22]  Stefan Preitl,et al.  Optimisation criteria in development of fuzzy controllers with dynamics , 2004, Eng. Appl. Artif. Intell..

[23]  D. Blackwell An analog of the minimax theorem for vector payoffs. , 1956 .

[24]  Oguz Findik,et al.  A directed artificial bee colony algorithm , 2015, Appl. Soft Comput..

[25]  Ichiro Nishizaki,et al.  Fuzzy and Multiobjective Games for Conflict Resolution , 2001 .

[26]  H. Zimmermann Fuzzy programming and linear programming with several objective functions , 1978 .

[27]  Jafar Habibi,et al.  Fuzzy Type-2 Nash Equilibrium , 2008, 2008 International Conference on Computational Intelligence for Modelling Control & Automation.

[28]  Ichiro Nishizaki,et al.  Max-Min Solutions for Fuzzy Multiobjective Matrix Games , 1993 .

[29]  Zhong-Zhong Jiang,et al.  A Banzhaf Function for a Fuzzy Game , 2014, IEEE Transactions on Fuzzy Systems.

[30]  Yuh-Wen Chen,et al.  Fuzzy multi-stage De-Novo programming problem , 2006, Appl. Math. Comput..

[31]  H.-J. Zimmermann,et al.  Fuzzy set theory—and its applications (3rd ed.) , 1996 .

[32]  Nasser Sadati,et al.  Fuzzy Nash equilibrium in fuzzy games using ranking fuzzy numbers , 2010, International Conference on Fuzzy Systems.

[33]  Dong Qiu,et al.  Solving Multi-Objective Matrix Games with Fuzzy Payoffs through the Lower Limit of the Possibility Degree , 2017, Symmetry.

[34]  J. B. Cruz,et al.  An Approach to Fuzzy Noncooperative Nash Games , 2003 .