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Max-min solution approach for multiobjective matrix game with fuzzy goals

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In this paper, we consider a multi-objective two person zero-sum matrix game with fuzzy goals, assuming that each player has a fuzzy goal for each of the payoffs. The max-min solution is formulated for this multi-objective game model, in which the optimization problem for each player is a linear programming problem. Every developed model for each player is demonstrated through a numerical example. | Yugoslav Journal of Operations Research 26 (2016), Number 1, 51-60 DOI: 10.2298/YJOR140415008K MAX-MIN SOLUTION APPROACH FOR MULTIOBJECTIVE MATRIX GAME WITH FUZZY GOALS Sandeep KUMAR Department of Mathematics C.C.S.University, Meerut-250004 India drsandeepmath@gmail.com Received: April 2014 / Accepted: January 2015 Abstract: In this paper, we consider a multi-objective two person zero-sum matrix game with fuzzy goals, assuming that each player has a fuzzy goal for each of the payoffs. The max-min solution is formulated for this multi-objective game model, in which the optimization problem for each player is a linear programming problem. Every developed model for each player is demonstrated through a numerical example. Keywords: Multi-objective matrix game, Fuzzy goal, Max-min solution. MSC: 90C29, 91A05. 1. INTRODUCTION Game theory is concerned with decision making problem where two or more autonomous decision makers have conflicting interests. They are usually referred to as players who act strategically to find out a compromise solution. On the other hand, in multi-objective optimization problems, a single decision maker optimizes the solution among the conflicting objectives. Multi-objective matrix games are capable of dealing with both types of conflicts. When interest of one player is completely against the interest of others, matrix game is determined as two person zero-sum matrix game. Fuzziness in game problems may occur in goals and payoffs. Such types of game were first studied by Campos [8]. His approach was based on ranking of fuzzy numbers. Afterwards, Sakawa and Nishizaki [17] studied single and multi-objective matrix games with fuzzy goals and fuzzy payoffs by using max-min principle of game theory. Bector et al. [5, 6], and Vijay et al. [18] proved that a two person zero-sum matrix game with fuzzy goals and fuzzy payoffs is equivalent to a pair of linear programming problems, which are dual to each other in fuzzy sense. Their methodology was .