A method to obtain a probability distribution from a unimodal possibility distribution

The probability and possibility theories are two particular cases of the more general theory of evidence, and probability and possibility distributions are two different, though complementary ways, to represent incomplete information. To fully achieve the advantages of these two representations, mathematical transformations to move from probability to possibility distributions and vice versa are needed. While different methods can be found in the literature to transform a probability distribution into a corresponding possibility distribution, no satisfactory methods are available to transform a possibility distribution into a probability one. This paper is aimed at overcoming this problem. It initially develops a general method to transform an asymmetric unimodal probability distribution into a possibility distribution preserving the mode of the probability distribution. Then a method to obtain a probability distribution starting from a possibility distribution is proposed. Finally, the results of simulations are presented to prove the validity of the proposed algorithms.