Generating Negations of Probability Distributions
This work addresses a specific theoretical issue in probability and Dempster-Shafer theory for knowledge-based systems, but it appears incremental as it builds on existing negation concepts.
The paper tackles the problem of generating negations of probability distributions, which are needed for knowledge-based systems using terms like NOT HIGH, by proposing a general method to construct negators as decreasing functions on [0,1] and characterizing linear negators as convex combinations of Yager and uniform negators.
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.