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

• Main Authors: Dagmar Markechová, Batool Mosapour, Abolfazl Ebrahimzadeh
• Format: Article
• Language: English
• Published: MDPI AG 2018-04-01
• Series: Entropy
• Subjects: fuzzy measurable space; fuzzy P-measure; fuzzy probability space; fuzzy partition; R-norm entropy; conditional R-norm entropy; R-norm divergence
• Online Access: http://www.mdpi.com/1099-4300/20/4/272

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.