Fuzzy Game with Qualitative Payoffs in Linguistic Terms

Abstract

Game strategies are vital in Economics, Business Administration, Sociology, Social sciences, Military operations, etc. The fuzzy set theory offers a background and a better foundation for studying game theory problems in which fuzzy numbers represent the payoffs to address the qualitative data. This paper deals with game theory problems with qualitative payoffs in linguistic terms. The fuzzy numbers represent the qualitative data irrespective of their linear or non-linear membership functions. The mean value of the horizontal points on the left-right membership functions of the fuzzy numbers justifies their order. Ordering the qualitative payoffs provides scope for solving the game theory problems using the saddle point method. Finally, the technique is illustrated numerically.