A generalization of the symmetrical and optimal probability-to-possibility transformations

Abstract: Possibility and probability theories are alternative and complementary ways to deal with uncertainty, which has motivated over the last years an interest for the study of ways to transform probability distributions into possibility distributions and conversely. This paper studies the advantages and shortcomings of two well-known discrete probability to possibility transformations: the optimal transformation and the symmetrical transformation, and presents a novel parametric family of probability to possibility transformations which generalizes them and alleviate their shortcomings, showing a big potential for practical application. The paper also introduces a novel fuzzy measure of specificity for probability distributions based on the concept of fuzzy subsethood and presents a empirical validation of the generalized transformation usefulness applying it to the text authorship attribution problem.