Solving Triangular Intuitionistic Fuzzy Matrix Game by Applying the Accuracy Function Method

Yumei Xing,Dong Qiu

doi:10.3390/sym11101258

Abstract

In this paper, the matrix game based on triangular intuitionistic fuzzy payoff is put forward. Then, we get a conclusion that the equilibrium solution of this game model is equivalent to the solution of a pair of the primal–dual single objective intuitionistic fuzzy linear optimization problems ( I F L O P 1 ) and ( I F L O D 1 ) . Furthermore, by applying the accuracy function, which is linear, we transform the primal–dual single objective intuitionistic fuzzy linear optimization problems ( I F L O P 1 ) and ( I F L O D 1 ) into the primal–dual discrete linear optimization problems ( G L O P 1 ) and ( G L O D 1 ) . The above primal–dual pair ( G L O P 1 ) – ( G L O D 1 ) is symmetric in the sense the dual of ( G L O D 1 ) is ( G L O P 1 ) . Thus the primal–dual discrete linear optimization problems ( G L O P 1 ) and ( G L O D 1 ) are called the symmetric primal–dual discrete linear optimization problems. Finally, the technique is illustrated by an example.

Highlights

Since the 1940s [1,2], game theory has been extensively studied in a systematic and axiomatic way.This is an important milestone in the development of game theory
A matrix game model of payoffs based on intuitionistic fuzzy sets is proposed in [20]
By applying the accuracy function, which is linear, and utilizing problems IFLOP, LOP and Theorem 2, we find that the problems ( IFLOP1) and ( IFLOD1) are equivalent to problems GLOP1 and GLOD1, respectively

Summary

Introduction

Since the 1940s [1,2], game theory has been extensively studied in a systematic and axiomatic way. A matrix game model of payoffs based on intuitionistic fuzzy sets is proposed in [20]. Seikh et al [28] presented a model for studying bi-matrix games based on intuitionistic fuzzy goals. In this paper, we put forward a new model of a matrix game based on triangular intuitionistic fuzzy numbers. We utilize the accuracy function method [31] and single intuitionistic fuzzy optimization method [32] to solve the new model of matrix game based on the triangular intuitionistic fuzzy payoff. The framework of this paper is as follows: Section 2 briefly depicts the basic knowledge of crisp matrix game models, intuitionistic fuzzy sets and the intuitionistic fuzzy optimization theory.

Preliminaries

A Matrix Game Based on Triangular Intuitionistic Fuzzy Payoff

Example

Conclusions