R -Norm Entropy and R -Norm Divergence in Fuzzy Probability Spaces

In the presented article, we define the -norm entropy and the conditional -norm entropy of partitions of a given fuzzy probability space and study the properties of the suggested entropy measures. In addition, we introduce the concept of -norm divergence of fuzzy P-measures and we derive fundamental...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2018-04, Vol.20 (4), p.272
Main Authors: Markechová, Dagmar, Mosapour, Batool, Ebrahimzadeh, Abolfazl
Format: Article
Language:English
Subjects:
conditional R-norm entropy
Constraining
Divergence
Entropy
Entropy (Information theory)
fuzzy measurable space
fuzzy P-measure
fuzzy partition
fuzzy probability space
Partitions
Quantum theory
R-norm divergence
R-norm entropy
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Summary:In the presented article, we define the -norm entropy and the conditional -norm entropy of partitions of a given fuzzy probability space and study the properties of the suggested entropy measures. In addition, we introduce the concept of -norm divergence of fuzzy P-measures and we derive fundamental properties of this quantity. Specifically, it is shown that the Shannon entropy and the conditional Shannon entropy of fuzzy partitions can be derived from the -norm entropy and conditional -norm entropy of fuzzy partitions, respectively, as the limiting cases for going to 1; the Kullback-Leibler divergence of fuzzy P-measures may be inferred from the -norm divergence of fuzzy P-measures as the limiting case for going to 1. We also provide numerical examples that illustrate the results.
ISSN:1099-4300
1099-4300
DOI:10.3390/e20040272