An Information Theoretic Treatment of Yager's Probability Distribution Negation

2026-08-01

AI Summary

This work rigorously defines the negation of probability distributions from an information-theoretic perspective. Building upon Yager’s negation operator, it introduces—for the first time—a systematic analysis grounded in information theory and majorization theory, establishing a unified theoretical framework. This framework not only elucidates the naturalness and principled character of Yager’s negation under multiple information-theoretic criteria but also strengthens and unifies the theoretical foundations of its known properties. By providing robust mathematical justification, the study underscores the distinctive role of this negation operation within the space of probability transformations.

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, \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.

Problem

• probability distribution negation
• information theory
• Yager's negation
• majorization theory
• theoretical justification

Innovation

• information theory
• Yager negation
• probability distribution
• majorization theory
• distribution negation