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R-Norm Entropy and R-Norm Divergence in Fuzzy Probability Spaces
Dagmar Markechová1, Batool Mosapour2, Abolfazl Ebrahimzadeh3
1Department of Mathematics, Faculty of Natural Sciences, Constantine The Philosopher University in Nitra, A. Hlinku 1, Nitra SK-949 01, Slovakia.
Abstract:
In the presented article, we define the R-norm entropy and the conditional R-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 R-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 R-norm entropy and conditional R-norm entropy of fuzzy partitions, respectively, as the limiting cases for R going to 1; the Kullback-Leibler divergence of fuzzy P-measures may be inferred from the R-norm divergence of fuzzy P-measures as the limiting case for R going to 1. We also provide numerical examples that illustrate the results.
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