A New Decomposition Linear Programming Model to Solve Zero Sum Two Person Matrix Game in Fully Fuzzy Trapezoidal Environment

Abstract

This article targets to unriddle the problem of a non-cooperative fully fuzzified ’Zero Sum Two Person Matrix Game’ (ZSTPMG) with payoff matrix equipped with Trapezoidal fuzzy numbers (TrFNs). To achieve the target a unique and novel decomposition technique has been introduced. First, we develop two auxiliaries fully fuzzified linear programming problem (FFLPP) models for both the players and then we decompose these two FFLPP models into four linear programming (LP) models each, for both the players. These eight LP models are then solved by using the software TORA-2.0. The solutions of these eight LP models ascertain the optimal strategies and the optimal value of the fully fuzzified ZSTPMG for both the players. Our technique has an advantage over the existing ones as it can solve fully fuzzified ZSTPMG with all kind of TrFNs such as symmetric, asymmetric, positive or negative TrFNs. To establish this fact, the proposed methodology has been illustrated by taking three numericals equipped with various kinds of TrFNs.