D numbers theory based game-theoretic framework in adversarial decision
  making under 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 alternatives'
evaluations and methods to find the optimal alternative are two important
aspects in the adversarial decision making. The aim of this study is to develop
a general framework for solving the adversarial decision making issue under
uncertain environment. By combining fuzzy set theory, game theory and D numbers
theory (DNT), a DNT based game-theoretic framework for adversarial decision
making under fuzzy environment is presented. Within the proposed framework or
model, fuzzy set theory is used to model the uncertain evaluations of decision
makers to alternatives, the non-exclusiveness among fuzzy evaluations are taken
into consideration by using DNT, and the conflict of interests among decision
makers is considered in a two-person non-constant sum game theory perspective.
An illustrative application is given to demonstrate the effectiveness of the
proposed model. This work, on one hand, has developed an effective framework
for adversarial decision making under fuzzy environment; One the other hand, it
has further improved the basis of DNT as a generalization of Dempster-Shafer
theory for uncertainty reasoning.
