Solving I-fuzzy two person zero-sum matrix games: Tanaka and Asai approach

Abstract

This paper aims to design a method for solving a two person zero-sum matrix game with I-fuzzy goals and I-fuzzy pay-offs, where the symmetric triangular I-fuzzy numbers prescribe the entries of the pay-offs matrix. The most common approaches in the literature to solve matrix games with fuzzy goals and fuzzy pay-offs employ ranking function or defuzzification technique, like in Bector and Chandra (Fuzzy mathematical programming and fuzzy matrix games, vol 169. Springer, Berlin, 2005) and Vijay et al. (Fuzzy Optim Decis Making 6:299–314, 2007). Our proposed approach in this work differs from the existing approaches in the sense that it is devoid of ranking or defuzzification function. It also provides precise degrees of belief and disbelief in achieving the goals set by each player. An essential concept of ‘almost positive I-fuzzy number’ introduced by Aggarwal et al. (Notes Intuit Fuzzy Sets 23:85–101, 2017) is employed to study matrix games in I-fuzzy setting. Solving such a game is shown to be equivalent to solving a pair of crisp non-linear programming problem. In this way, our approach is unique for solving such a game. Some numerical examples are included to illustrate the proposed approach.