Generating Negations of Probability Distributions
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.
Keywords
Cite
@article{arxiv.2103.14986,
title = {Generating Negations of Probability Distributions},
author = {Ildar Batyrshin and Luis Alfonso Villa-Vargas and Marco Antonio Ramirez-Salinas and Moises Salinas-Rosales and Nailya Kubysheva},
journal= {arXiv preprint arXiv:2103.14986},
year = {2021}
}
Comments
10 pages, 1 figure