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,⋯,pn), as the distribution p¯=(p¯1,⋯,p¯n), where p¯i=(1-pi)/(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.