Solution of Rectangular Fuzzy Games by Principle of Dominance Using LR-type Trapezoidal Fuzzy Numbers

TL;DR

This paper presents a method for solving rectangular fuzzy games using dominance principles and LR-type trapezoidal fuzzy numbers, extending classical game theory to handle imprecise pay-offs.

Contribution

It introduces an algebraic approach to solve fuzzy games with mixed strategies and pay-offs as fuzzy numbers, including a dominance reduction technique.

Findings

Pay-off matrices can be simplified using dominance methods.

The approach effectively handles fuzzy pay-offs without saddle points.

Numerical example demonstrates the method's practicality.

Abstract

Fuzzy Set Theory has been applied in many fields such as Operations Research, Control Theory, and Management Sciences etc. In particular, an application of this theory in Managerial Decision Making Problems has a remarkable significance. In this Paper, we consider a solution of Rectangular Fuzzy game with pay-off as imprecise numbers instead of crisp numbers viz., interval and LR-type Trapezoidal Fuzzy Numbers. The solution of such Fuzzy games with pure strategies by minimax-maximin principle is discussed. The Algebraic Method to solve Fuzzy games without saddle point by using mixed strategies is also illustrated. Here, pay-off matrix is reduced to pay-off matrix by Dominance Method. This fact is illustrated by means of Numerical Example.