Contracting and Involutive Negations of Probability Distributions

A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently it was shown that Yager's negator plays a crucial role in the definition of pd-independent linear negators: any linear negator is a function of Yager's negator. Here, we prove that the sequence of multiple negations of pd generated by a linear negator converges to the uniform distribution with maximal entropy. We show that any pd-independent negator is non-involutive, and any nontrivial linear negator is strictly contracting. Finally, we introduce an involutive negator in the class of pddependent negators that generates an involutive negation of probability distributions. Keywords: Probability distribution, contracting negation, involutive negation 1. Introduction The concept of the negation of a probability distribution (pd) was introduced by Yager [1].