A non-linear mathematical approach for solving matrix games with picture fuzzy payoffs with application to cyberterrorism attacks

Abstract

Numerous expansions of fuzzy sets have been proposed to manage uncertain information in real-world problems. Unlike fuzzy sets and intuitionistic fuzzy sets, picture fuzzy sets independently consider membership, non-membership, and indeterminacy. They have been extensively employed to delineate decision-makers’ perspectives when knowledge is lacking and have found application in numerous domains. However, little research has been conducted on uncertain matrix games in picture-fuzzy environments. This paper proposes an approach to resolving a matrix game with picture-fuzzy payoffs. Two non-linear mathematical programming models equipped with multi-objective functions are formulated and converted into crisp linear programming models by applying the weighted average approach. The reduced problems are solved using the LINGO platform, yielding optimal solutions. An illustrative example demonstrates how an information security agency can select the most effective strategies to combat cyberterrorism. Finally, comparing the presented methodology’s outcomes and existing work establishes its dependability and efficacy.