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....

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Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 25; no. 12; pp. 7929 - 7935
Main Authors Batyrshin, Ildar, Villa-Vargas, Luis Alfonso, Ramírez-Salinas, Marco Antonio, Salinas-Rosales, Moisés, Kubysheva, Nailya
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Subjects
Artificial Intelligence
Codes
Computational Intelligence
Control
Engineering
Entropy
Focus
Knowledge based systems
Mathematical functions
Mathematical Logic and Foundations
Mechatronics
Probability distribution
Robotics
Negation
Probability distribution
Dempster–Shafer theory
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Summary: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.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-021-05802-5