An Information Theoretic Treatment of Yager's Probability Distribution Negation

In the seminal paper (Yager 2015), Yager defined the negation of a probability distribution p=(p1,dots,pn), as the distribution overlinep = (overlinep1,dots,overlinepn), where overlinepi = (1-pi)/(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.