Solving Multi-Objective Matrix Games with Fuzzy Payoffs through the Lower Limit of the Possibility Degree

Abstract

Abstract:In this article, we put forward the multi-objective matrix game model based on fuzzy payoffs. In order to solve the game model, we first discuss the relationship of two fuzzy numbers via the lower limit− 1 2 of the possibility degree. Then, utilizing this relationship, we conclude that the equilibrium solution of this game model and the optimal solution of multicriteria linear optimization problems are of equal value. Finally, to illustrate the effectiveness and correctness of the obtained model, an example is provided.

Multi-objective Fuzzy Bi-matrix Game Model: A Multicriteria Non-Linear Programming Approach

“…Nishizaki et al [17] studied an equilibrium solution of multi-objective bi-matrix games. Qiu et al [28] discussed the relationship of two fuzzy numbers via the lower limit− 1 2 of the possibility degree. They also concluded that the equilibrium solution of multiple objective fuzzy games and the optimal solution of multi-objective linear optimization problems are of equal value.…”

On Characterizations of Directional Derivatives and Subdifferentials of Fuzzy Functions

“…Later, Zadeh proposed the fuzzy number [2][3][4] and put forward the theory of the fuzzy numerical function together with Chang [5]. These theories and those associated with optimization theory have been extensively studied in some fields, such as economics, engineering, the stock market, greenhouse gas emissions and management science [6][7][8][9][10][11][12][13][14].…”