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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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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1725603229520101376 |