Jagdambika Method for Solving Matrix Games with Fuzzy Payoffs

Abstract

Li (IEEE Trans Cybern 43:610-621, 2013) [1] recently proposed a method for solving matrix games with fuzzy payoffs and claimed that the obtained minimum expected gain of Player I and maximum expected loss of Player II, will be identical. Chandra and Aggarwal (Eur J Oper Res 2015. https://doi.org/10.1016/j.ejor.2015.05.011) [2], in their recent paper, pointed out the shortcomings of Li’s approach and overcome the shortcomings of Li’s approach. Chandra and Aggarwal, transformed the fuzzy mathematical programming problem into a multiobjective programming problem and obtained its result by using GAMS software. In this paper, it is pointed out that Chandra and Aggarwal have not considered some necessary constraints for the value of game to be a fuzzy number. Further, a new method (named as Jagdambika method) is proposed to overcome the limitations of existing method and to obtain the solution of matrix games with fuzzy payoffs. To illustrate the proposed Jagdambika method, an existing numerical problem of matrix games with fuzzy payoffs is solved by the proposed Jagdambika method.