On the analysis of interval data based game theoretical problem under various symmetric fuzzy environments

Abstract

In a real world environment, the payoffs of a matrix game are varying between two fixed values because of uncertainty. This type of payoffs may not be defined as a crisp numbers. In order to model such uncertainty, the payoffs can be represented as interval numbers. A matrix game with payoffs of such interval numbers are called interval data based matrix game. This work takes an initiative to solve the interval data based matrix game in an uncertain environment. In order to find the optimum solution of the interval matrix game without the knowledge of interval arithmetic, the fuzzy set theory is used in various symmetric environments. Finally the analysis is made on the solutions obtained through various symmetric fuzzy environments with the help of different shapes of fuzzy numbers.