An Information Theoretic Treatment of Yager's Probability Distribution Negation

2026/08/01 by Roberto Bruno, Ugo Vaccaro
Computer Science · Mathematics · #cs.IT #cs.AI #math.IT #math.PR

paper · pdf · doi:10.1007/s00500-026-11413-9

published as Soft Computing, 2026 · Published in Soft Computing (Section: Foundation, Algebraic, and Analytical Methods)

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

In the seminal paper (Yager 2015), Yager defined the negation of a probability distribution p=(p₁,…,p_n), as the distribution p = (p₁,…,p_n), where p_i = (1-p_i)/(n-1), for i=1, … , 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.

Citations

• Extension of Yager's negation of probability distribution based on uncertainty measures
• Contracting and Involutive Negations of Probability Distributions
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