Two Person zero-sum fuzzy matrix games and extensions

TL;DR

This paper explores fuzzy linear programming within two-person zero-sum fuzzy matrix games, extending existing models with I-fuzzy sets, and provides MATLAB tools for solving various fuzzy game types.

Contribution

It introduces the application of I-fuzzy sets to fuzzy matrix games and offers MATLAB codes for solving different fuzzy game scenarios.

Findings

Verification of solutions through numerical examples

Extension of fuzzy game theory with I-fuzzy goals

Provision of MATLAB codes for practical implementation

Abstract

In this work, fuzzy Linear programming problems (FLPP) and their implementations is being done in two person zero-sum fuzzy matrix game theory, based on Bector, Chandra and Vijay [2] model. Verification of solution of all possible type of two person zero-sum game is done by solving examples by numerical method. Generalized fuzzy set first introduced by Atanassov (1986) which is called I-fuzzy set has been studied and using this knowledge, application in (FLPP) and two person zero-sum matrix game with I-fuzzy goals is given. At the end I gave useful MATLAB codes for solving all three type of two person zero-sum fuzzy matrix games, with fuzzy goals, with fuzzy pay-offs and with both fuzzy goals and fuzzy pay-offs.