Generating Negations of Probability Distributions

TL;DR

This paper introduces a general framework for generating negations of probability distributions using decreasing functions called negators, providing a systematic way to construct and analyze such negations.

Contribution

It proposes a unified method for creating negations of probability distributions through negators and characterizes linear negators as convex combinations of Yager and uniform negators.

Findings

Developed a general method for generating negators of probability distributions.

Characterized linear negators as convex combinations of Yager and uniform negators.

Studied properties of the proposed negation transformations.

Abstract

Recently it was introduced a negation of a probability distribution. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example, HIGH PROFIT or HIGH PRICE can be considered. The application of this negation in Dempster-Shafer theory was considered in many works. Although several negations of probability distributions have been proposed, it was not clear how to construct other negations. In this paper, we consider negations of probability distributions as point-by-point transformations of pd using decreasing functions defined on [0,1] called negators. We propose the general method of generation of negators and corresponding negations of pd, and study their properties. We give a characterization of linear negators as a convex combination of Yager and uniform negators.