In the seminal paper (Yager 2015), Yager defined the negation of a probability distribution \(\textbf{p}=(p_1,\dots ,p_n)\) , as the distribution \(\overline{\textbf{p}} = (\overline{p}_1,\dots ,\overline{p}_n)\) , 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.
