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Adversarial decision making is a particular type of decision making problemwhere the gain a decision maker obtains as a result of his decisions isaffected by the actions taken by others. Representation of alternatives'evaluations and methods to find the optimal alternative are two importantaspects in the adversarial decision making. The aim of this study is to developa general framework for solving the adversarial decision making issue underuncertain environment. By combining fuzzy set theory, game theory and D numberstheory (DNT), a DNT based game-theoretic framework for adversarial decisionmaking under fuzzy environment is presented. Within the proposed framework ormodel, fuzzy set theory is used to model the uncertain evaluations of decisionmakers to alternatives, the non-exclusiveness among fuzzy evaluations are takeninto consideration by using DNT, and the conflict of interests among decisionmakers is considered in a two-person non-constant sum game theory perspective.An illustrative application is given to demonstrate the effectiveness of theproposed model. This work, on one hand, has developed an effective frameworkfor adversarial decision making under fuzzy environment; One the other hand, ithas further improved the basis of DNT as a generalization of Dempster-Shafertheory for uncertainty reasoning.

D numbers theory based game-theoretic framework in adversarial decision making under fuzzy environment