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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.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512788 | PMC |
| http://dx.doi.org/10.3390/e20040272 | DOI Listing |
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