0

An Information Theoretic Treatment of Yager's Probability Distribution Negation

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, \ldots , n.$ In…

Open
Preview
Year
2026
ArXiv
arxiv.org/abs/2608.00594
Hosting
Full text hostedCC-BY-4.0

Cite

Notes

Only stored in your browser.

Attribution

Abstract & full text
arxiv.org/abs/2608.00594CC-BY-4.0
TL;DR
Semantic Scholar
Attribution policy →

Abstract

In the seminal paper (Yager 2015), Yager defined the negation of a probability distribution p=(p_1,\dots,p_n), as the distribution \overline{p} = (\overline{p}_1,\dots,\overline{p}_n), where \overline{p}_i = ({1-p_i})/({n-1}), for i=1, \ldots , 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.