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

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 Kullbac...

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Main Author: Dagmar Markechová
Format: Article
Language:English
Published: MDPI AG 2017-03-01
Series:Axioms
Subjects:
Online Access:http://www.mdpi.com/2075-1680/6/1/5
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spelling doaj-449a80ab9cfb4f9bb3565a2b0de577702020-11-24T23:11:57ZengMDPI AGAxioms2075-16802017-03-0161510.3390/axioms6010005axioms6010005Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy CaseDagmar Markechová0Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, SlovakiaThe 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.http://www.mdpi.com/2075-1680/6/1/5fuzzy probability spacefuzzy partitionShannon’s entropyKullback-Leibler divergencemutual informationconditional mutual information
collection DOAJ
language English
format Article
sources DOAJ
author Dagmar Markechová
spellingShingle Dagmar Markechová
Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case
Axioms
fuzzy probability space
fuzzy partition
Shannon’s entropy
Kullback-Leibler divergence
mutual information
conditional mutual information
author_facet Dagmar Markechová
author_sort Dagmar Markechová
title Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case
title_short Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case
title_full Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case
title_fullStr Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case
title_full_unstemmed Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case
title_sort kullback-leibler divergence and mutual information of experiments in the fuzzy case
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2017-03-01
description 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.
topic fuzzy probability space
fuzzy partition
Shannon’s entropy
Kullback-Leibler divergence
mutual information
conditional mutual information
url http://www.mdpi.com/2075-1680/6/1/5
work_keys_str_mv AT dagmarmarkechova kullbackleiblerdivergenceandmutualinformationofexperimentsinthefuzzycase
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