An information theoretic treatment of Yager’s probability distribution negation

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