Abstract
The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.
Highlights
As conflicting interests appear between different decision-makers, and within each individual, the study of multi-criteria matrix games becomes vital in recent years
We study multi-criteria zero-sum matrix games with intuitionistic fuzzy set (IFS) goals in which the goals of players are represented with IFSs, and payoffs of both players are real numbers
The proposed approach is based on IFS, and it is evident that IFS suitably reflects the hesitation and uncertainty of human thinking; so, it provides more flexibility to the decision makers while expressing their decision
Summary
Game theory is a mathematical tool to study the conflict and cooperation among intelligent, rational decision makers. Decision making in competitive environments is known to be a critical process. Game theory has been extensively applied in several fields, such as behavioral science, economics [1], pattern recognizers, complex engineering, biology, business modeling, politics and investment management, etc. The zero sum multi-criteria matrix game is an extension of the standard zero sum two person game model. The zero sum multi-criteria game is defined as the multi-objective matrix game as it involves two or more than two decision-makers and can be expressed by multiple payoffs. As conflicting interests appear between different decision-makers, and within each individual, the study of multi-criteria matrix games becomes vital in recent years
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