Tsallis entropy of fuzzy dynamical systems
type: Item
instance of: scholarly article
title: Tsallis entropy of fuzzy dynamical systems
zbMATH Open document ID: 1408.37015
author: Dagmar Markechová
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order \(q,\) where \(q\) is a positive real number not equal to 1, of fuzzy partitions are introduced and their mathematical behavior is described. As an important result, we showed that the Tsallis entropy of fuzzy partitions of order \(q > 1\) satisfies the property of sub-additivity. This property permits the definition of the Tsallis entropy of order \(q > 1\) of a fuzzy dynamical system. It was shown that Tsallis entropy is an invariant under isomorphisms of fuzzy dynamical systems; thus, we acquired a tool for distinguishing some non-isomorphic fuzzy dynamical systems. Finally, we formulated a version of the Kolmogorov-Sinai theorem on generators for the case of the Tsallis entropy of a fuzzy dynamical system. The obtained results extend the results provided by the author and \textit{B. Riečan} in [``Entropy of fuzzy partitions and entropy of fuzzy dynamical systems'', Entropy 18, No. 1, Paper No. 19, 10 p. (2016; doi:10.3390/e18010019)], which are particularized to the case of logical entropy.
Mathematics Subject Classification ID: 37A35
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 6994867
zbMATH Keywords: fuzzy set
zbMATH Keywords: fuzzy partition
zbMATH Keywords: Tsallis entropy
zbMATH Keywords: conditional Tsallis entropy
zbMATH Keywords: fuzzy dynamical system
zbMATH Keywords: isomorphism
zbMATH Keywords: generators
MaRDI profile type: Publication
full work available at URL: math6110264
OpenAlex ID: W2901919977
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DOI: 10.3390/MATH6110264
description: scientific article; zbMATH DE number 6994867