Analysis of a novel method for finding solutions of interval game problems via fuzzy approaches

Game theory has significant importance in various domains as it is a powerful tool that helps the rational decision-makers to understand and assess strategic interactions. It develops mathematical models to depict these strategic engagements in competitive environments. Given the inherent uncertainty in real-world problems, obtaining exact values of payoffs for a matrix game can be difficult. In many instances, however, these payoffs vary within certain ranges, which makes in-terval numbers the best form to represent them. This results in the creation of a specialized category of game problem which is referred to as the interval-valued matrix game (IVMG). According to the literature, various methodologies exist to identify the optimal strategies and game value for IVMGs. However, many of these methods possess some shortcomings dis-cussed in the paper, highlighting the requirement for a novel approach. Therefore, in the present study, we propose a novel method to find solutions to game problems with interval payoffs, utilizing the fuzzy concept. Since operations and comparisons on interval numbers are not well-defined, we transform the elements of payoff matrix into a fuzzy represen-tation. Utilizing ranking function for defuzzification of these fuzzy payoffs, we transform them to crisp form. The solu-tion for the subsequent crisp matrix game is obtained using a graphical technique or linear programming problem ap-proach. Additionally, numerical examples are provided for validation of the presented method. The game values for these examples are also obtained using methods presented by other researchers in the literature, and comparisons with these methods are made, highlighting the limitations of the methods in the existing literature and significance of the presented method. Finally, conclusions with shortcomings and future scope of research based on the paper are described.

کلیدواژه ها:

Generalized Pentagonal Fuzzy Number ، Generalized Hexagonal Fuzzy Number ، fuzzification ، ranking function ، Two person zero-sum game ، Value of game