Negations of Probability Distributions: A Survey

Authors

Ildar Z. Baryrshin, Instituto Politecnico NacionalFollow
Nailya I. Kubysheva, Kazan Federal University
Venera R. Bayrasheva, Kazan Federal University
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

12-1-2021

Comments

Technical Report: UTEP-CS-21-106

Published in Computacion y Sistemas, 2021, Vol. 25, No. 4, pp. 775–781.

Abstract

In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-by-element PD into a negation of PD. Negators are non-increasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager's negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager's negator and uniform negator. Involutivity of negations is important in logic, and such involutive negator is considered in the paper. We propose a new simple definition of the class of linear negators generalizing Yager's negator. Different examples illustrate properties of negations of PD. Finally, we consider some open problems in the analysis of negations of probability distributions.