Pareto-optimal security strategies in matrix games with fuzzy payoffs

Abstract

We present a new methodology for the analysis of fuzzy payoff matrix games. The main difficulty that appears in the study of these games is the comparison between the payoff values associated to the strategies of the players because these payoffs are fuzzy quantities. Our approach does not transform the fuzzy payoffs to crisp numbers via standard defuzzyfication but we use standard fuzzy orders which allows us to find solutions within the same space of fuzzy numbers. Moreover, we provide a method to solve these games finding equivalent fuzzy linear programs whose maximal solutions give the solutions of the games.