Basic probability assignment to probability distribution function based on the Shapley value approach

Abstract

In Dempster–Shafer evidence theory, how to use the basic probability assignment (BPA) in decision-making is a significant issue. The transformation of BPA into a probability distribution function is one of the common and feasible schemes. To overcome the problems of the existing methods, we propose a marginal probability transformation method based on the Shapley value approach. The proposed method allocates BPA values in terms of how much an element contributes to a set, which is an equitable and effective distribution mechanism. Furthermore, we use probabilistic information content to evaluate the effect of each transformation method. Moreover, some numerical examples are used to demonstrate the efficiency and feasibility of the proposed method. Further, two applications, target recognition, fault diagnosis are used to verify the superiority and effectiveness of the proposed method in practice.