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

Dagmar Markechová, Batool Mosapour, Abolfazl Ebrahimzadeh
2018 Entropy  
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
more » ... m 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.
doi:10.3390/e20040272 pmid:33265363 fatcat:dkuwejsbnfcypfz3uelstk4w7a