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

Adversarial decision making is a particular type of decision making problem where the gain a decision maker obtains as a result of his decisions is affected by the actions taken by others. Representation of evaluation of alternatives and methods to find the optimal alternative are two important aspects in adversarial decision making. The aim of this study is to develop a general framework for solving the adversarial decision making problem under an uncertain environment. By combining fuzzy set theory, game theory and D number theory (DNT), we present a DNT-based game-theoretic framework for adversarial decision making under a fuzzy environment. Within the proposed framework or model, fuzzy set theory is used to model uncertain evaluations by decision makers of alternatives, the non-exclusiveness among fuzzy evaluations is taken into account by use of DNT, and the conflict of interests among decision makers is considered by means of a two-person non-constant sum game. An illustrative application is given to demonstrate the effectiveness of the proposed model. This work, on the one hand, has developed an effective framework for adversarial decision making under a fuzzy environment and, on the other hand, has further improved the basis of DNT as a generalization of Dempster–Shafer theory for uncertainty reasoning.