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Kullback–Leibler Divergence and Mutual Information of Partitions in Product MV Algebras

1
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia
2
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia
3
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(6), 267; https://doi.org/10.3390/e19060267
Received: 11 May 2017 / Revised: 5 June 2017 / Accepted: 7 June 2017 / Published: 10 June 2017
(This article belongs to the Section Information Theory, Probability and Statistics)
The purpose of the paper is to introduce, using the known results concerning the entropy in product MV algebras, the concepts of mutual information and Kullback–Leibler divergence for the case of product MV algebras and examine algebraic properties of the proposed measures. In particular, a convexity of Kullback–Leibler divergence with respect to states in product MV algebras is proved, and chain rules for mutual information and Kullback–Leibler divergence are established. In addition, the data processing inequality for conditionally independent partitions in product MV algebras is proved. View Full-Text
Keywords: product MV algebra; partition; Shannon’s entropy; Kullback–Leibler divergence; mutual information; conditional mutual information product MV algebra; partition; Shannon’s entropy; Kullback–Leibler divergence; mutual information; conditional mutual information
MDPI and ACS Style

Markechová, D.; Riečan, B. Kullback–Leibler Divergence and Mutual Information of Partitions in Product MV Algebras. Entropy 2017, 19, 267.

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