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Axioms 2017, 6(1), 5; doi:10.3390/axioms6010005

Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case

Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia
Academic Editor: Humberto Bustince
Received: 30 January 2017 / Accepted: 1 March 2017 / Published: 3 March 2017
View Full-Text   |   Download PDF [294 KB, uploaded 9 March 2017]

Abstract

The main aim of this contribution is to define the notions of Kullback-Leibler divergence and conditional mutual information in fuzzy probability spaces and to derive the basic properties of the suggested measures. In particular, chain rules for mutual information of fuzzy partitions and for Kullback-Leibler divergence with respect to fuzzy P-measures are established. In addition, a convexity of Kullback-Leibler divergence and mutual information with respect to fuzzy P-measures is studied. View Full-Text
Keywords: fuzzy probability space; fuzzy partition; Shannon’s entropy; Kullback-Leibler divergence; mutual information; conditional mutual information fuzzy probability space; fuzzy partition; Shannon’s entropy; Kullback-Leibler divergence; mutual information; conditional mutual information
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Markechová, D. Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case. Axioms 2017, 6, 5.

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