Analytical Hierarchy Process in modeling and solving matrix games in neutrosophic environment and its application in military problems

Abstract

Objective: The war environment is a conflict situation and operations research is one of the used techniques to make decisions in different battle conditions. In this article, game theory is used to model the conflict situation, which is one of the widely used methods in the military field.Method: In this article, after modeling the problem as a matrix game, a hierarchical analysis method is proposed to determine the payoffs and prioritize the outputs of the game. On the other hand, due to the fact that in the real world information is presented in an imprecise and ambiguous way, Neutrosaphic collections have been used to express this information. A method of solving the hierarchical analysis problem with Neutrosaphic data is proposed and then solving the game problem with the outputs of the hierarchical analysis method is discussed.Findings: To solve the matrix game problem with neutrosaphic payoffs, the concept of nearest interval approximation of the generalized triangular neutrosaphic fuzzy number is used and the game model is written as a problem with interval payoffs. In the following, a method is proposed to solve this game problem. Finally, the solution of a practical example in military problems has been investigated with the proposed method. To solve this problem, two optimistic and pessimistic problems have been proposed for each player, and by solving these problems, the optimal solutions of the players are obtained in two optimistic and pessimistic states.Conclusion: Efficiency and simplicity in the problem solving method as well as the ability to develop the proposed method to game problems with interval-type payoffs are among the results of this research.

Keywords

• game theory
• analysis hierarchy
• neutrosophic fuzzy set
• military decision making