A Study on Properties of Dempster-Shafer Theory to Probability Theory transformations

In this paper, five conditions that have been proposed by Cobb and Shenoy are studied for nine different mappings from the Dempster-Shafer theory to the probability theory. After comparing these mappings, one of the considerable results indicates that none of the mappings satisfies the condition of invariance with respect to the marginalization process. In more details, the main reason for this defect is that the classic projection process in DST loses some probabilistic information. Therefore, as regards this subject, a solution is presented for solving this problem for two mappings: the pignistic probability and the normalized plausibility transformation.