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A Novel Approach to the Solution of Matrix Games with Payoffs Expressed by Trapezoidal Intuitionistic Fuzzy Numbers

Verma T., Kumar A., Kacprzyk J.

Journal of Automation Mobile Robotics and Intelligent Systems

2015

Vol. 9, No. 3

25--46

We propose a novel approach to the solution of fuzzy matrix games with payoffs given as trapezoidal intuitionistic fuzzy numbers. We extend Li’s [36, Chapter 9] work based on a cut-set based method for finding an optimal solution to overcome the fact that the assumptions and properties assumed therein do not guarantee in general, first, the very existence of an optimal solution, and second, its attainment via a mathematical programming formulation proposed. We first briefly mention those problems in Li’s [36] approach, and then propose a new, corrected and general method, called the Mehar mehod, based on a modified mathematical pro- gramming formulation of a matrix game with payoffs represented by trapezoid intuitionistic fuzzy numbers. For illustration, we solve Li’s [36] example, and compare his and our results.