Decision Making Based On The Basic Probability Assignment In D-S Evidence Theory

Target-identification was an uncertain decision problem under complex background. The well-known conclusion of the decision theory is: If the uncertainty in the natural states can be represented by a probability distribution, then the decision would be consistent(Coherent).The mathematical rigor of decision theory is beyond doubt, but from the application point of view, it is relatively demanding. It requires that decision makers must provide a precise proba-bility distribution. Existing research shows that the requirement to decision makers of providing an exact probability distribution usually is not only difficult, but also is not absolutely necessary. The Basic Probability Assignment(BPA) of D-S evidence theory distributes on the power set of propositions, this feature enables the BPA represent and handle uncertain information more effectively than the probability distribution which only distributes on the singletons of propositions. So BPA has been widely applied in the field of information fusion and artificial intelligence with uncertain reasoning. But decision-making based on BPA is still a problem to be solved. To solve this problem, it is reasonable to transform BPA to probability function. For the issues that making decision based on BPA, we focus on the correlation representation of BPA and the algorithm design of transforming BPA to probability distribution optimally in this paper. A new correlation coefficient is proposed to efficiently measure the degree of evidence association; A new probability transformation method that utilizes the information contained in the belief function and plausibility function of the propositions in the D-S evidence theory is proposed; Then a new probabilistic transformation based on the dispersion in the distribution of Basic Probability Assignment is presented, which achieves the reasonable transformation from BPA to probability. And then the above transformation methods are compared to existing transformation, such as pignistic probability transform and the plausibility function transform. It can more effectively use the information that known. And we illustrate the effectiveness of the proposed method with the numerical examples.