Optimal Defense Strategies for Security Agencies: A Dual Hesitant Fuzzy Matrix Game Approach

Up till now, Game theory has been modified with the concepts of various kinds of uncertainties. Dual Hesitant Fuzzy Set (DHFS) provides a noteworthy tool for expressing the uncertain quantitative aspects effectively in two-player zero-sum matrix game problems (TMGPs) with uncertain pay-offs. In the present work, we deal with TMGP with pay-offs given by DHFSs. For solving such problems, first, we transform a dual hesitant fuzzy element into a Dual Hesitant Fuzzy Element with Possibility (DHFEP) for equating the lengths of two dual hesitant fuzzy element. Then, we define value and ambiguity functions for these elements with comparative laws. Further, four-steps algorithm is developed to solve dual hesitant fuzzy matrix game problem based on the suggested value and ambiguity functions. To demonstrate the relevance of the proposed work, a real-world event-based problem-how to counter a terrorist attack is considered in order to calculate the optimal defense strategies for the security agencies.