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

TL;DR

This paper introduces a new parametric family of probability-to-possibility transformations that generalizes existing methods, addressing their limitations and demonstrating practical utility in text authorship attribution.

Contribution

It proposes a novel generalized transformation method and a fuzzy measure of specificity, enhancing the conversion between probability and possibility theories.

Findings

The generalized transformation outperforms traditional methods in specific scenarios.

The fuzzy measure effectively quantifies the specificity of probability distributions.

Empirical validation shows improved accuracy in authorship attribution.

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.