Fuzzy Systems

Shakti Nath Mondal ¹, Sankar Kumar Roy ¹

Affiliations
1 Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, IN

Abstract

Conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. We present a new methodology for the analysis of random fuzzy payoffs matrix games. The main difficulty then appears in the study of these games is the comparison between the payoff values associated to the strategies of the players because these payoffs are random fuzzy quantities. The purpose of this paper is to introduce a two-person zero-sum matrix game in which the elements of payoff are characterized as random fuzzy variables. Based on expected value operator, an expected minmax equilibrium strategy to the proposed game is defined and the existence of the strategy is proved. Finally, an example is given to illustrate the effectiveness of the proposed game.

Keywords

Matrix Game, Random Fuzzy Variable, Minmax Equilibrium Strategy.

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Sankar Kumar Roy ¹, Prasanta Mula ², Shakti Nath Mondal ³

Affiliations
1 Department of Applied Mathematics with Oceaniology and Computer Progarnmming, Vidyasagar University, IN
2 ISRO Satellite Centre, Bangalore, IN
3 Department of Applied Mathematics with Oceanology and Computer Programming, V.U. , Midnapore, West Bengal, IN

Abstract

This paper presents the two-person zero-sum game in which the elements of the payoff matrix are characterized by fuzzy variables. This type of game is called credibilistic game. To analyze the credibilistic game, we introduced the concept of credibility measure by credibility theory. Using credibility theory, the fuzzy constraints is converted into equivalent deterministic constraints. Mainly we have discussed the credibilistic game under the light of linear programming, which depends upon the confidence level due to incomplete information. Lastly a numerical example is presented to illustrate the methodology.

Keywords

Fuzzy Variable, Fuzzy Constraint, Credibilistic Game, Credibility Measure, Linear Programming.

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