An Information Theoretic Treatment of Yager's Probability Distribution Negation

Abstract

In the seminal paper (Yager 2015), Yager defined the negation of a probability distribution $\mathbf{p}=(p_1,\dots ,p_n)$, as the distribution $\overline{\mathbf{p}}=({\overline{p}}_1,\dots ,{\overline{p}}_n)$, where ${\overline{p}}_i=(1-p_i)/(n-1),$ for $i=1,\dots ,n.$ In this paper, we present a comprehensive information-theoretic analysis of Yager's negation and its generalizations. Using tools from information theory and majorization theory, we unify, extend, and strengthen a number of previously known properties of Yager's negation within a common framework. Overall, our results offer strong theoretical justification for Yager's negation as the most natural and principled definition of probability distribution negation under various information theoretic criteria.

Published in Soft Computing (Section: Foundation, Algebraic, and Analytical Methods)