Obtaining 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 distribution and possibility distribution (PD) are two different, though complementary ways, to represent the incomplete information. To fully achieve the advantages of these two representations, mathematical transformations to move from probability distribution to PD and vice versa are needed. While different methods can be found in the literature to transform a probability distribution into a corresponding PD, no satisfactory methods are available to transform a PD into a probability one. This article is aimed at overcoming this problem. It initially develops a general method to transform an asymmetric unimodal probability distribution into a PD preserving the mode of the probability distribution. Then, a method to obtain a probability distribution starting from a PD is proposed. Moreover, the results of simulations are presented to demonstrate the working principle of the algorithm, and finally, the experimental results prove the validity of the proposed method.