Inverse pignistic probability transforms

In some information fusion processes, the incomplete information set can be naturally mapped into a belief theory information set and a Bayesian probability theory information set. For decision making, the mapping of the belief theory fusion results represented by the basic belief assignment to a probability set is accomplished via a pignistic probability transform. This article introduces the inverse pignistic probability transforms (IPPT) that map the posteriori probabilities into the belief function theories, basic belief assignments. Also introduced are two infinite classes and some finite classes of mapping the posteriori probability results to the basic belief assignment of the belief theory.