Generating negations of probability distributions

Recently, the notation of a negation of a probability distribution was introduced. 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's and uniform negators.

Automated summary

The paper introduces the notion of negation of a probability distribution, emphasizing the need for such a negation in knowledge-based systems. The study focuses on transforming probability distributions point by point using decreasing functions defined on [0,1]. The characterization of linear negators is presented as a convex combination of Yager's and uniform negators.