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

Abstract: 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. For solving this problem, the modified pignistic probability and the modified normalized plausibility transformation which are invariance under marginalization are proposed. The two modified mappings are utilized in two ambiguity measures in Dempster-Shafer theory. Then, similar to the mutual information in the probability theory, these measures are used for computing the dependency of the variables of a social bliss problem on the personʹs happiness value