Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems

Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems

In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entrop...

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Main Authors: Dagmar Markechová, Beloslav Riečan
Format: Article
Language:English
Published: MDPI AG 2016-01-01
Series:Entropy
Subjects:
probability space
fuzzy set
fuzzy partition
entropy
fuzzy dynamical system
Online Access:http://www.mdpi.com/1099-4300/18/1/19
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spelling doaj-636ee2bf468a4ce7afcf58f9f3a39a8b2020-11-25T00:33:36ZengMDPI AGEntropy1099-43002016-01-011811910.3390/e18010019e18010019Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical SystemsDagmar Markechová0Beloslav Riečan1Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Trieda A. Hlinku 1, Nitra 949 01, SlovakiaDepartment of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, Banská Bystrica 974 01, SlovakiaIn the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.http://www.mdpi.com/1099-4300/18/1/19probability spacefuzzy setfuzzy partitionentropyfuzzy dynamical system
collection DOAJ
language English
format Article
sources DOAJ
author Dagmar Markechová
Beloslav Riečan
spellingShingle Dagmar Markechová
Beloslav Riečan
Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
Entropy
probability space
fuzzy set
fuzzy partition
entropy
fuzzy dynamical system
author_facet Dagmar Markechová
Beloslav Riečan
author_sort Dagmar Markechová
title Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
title_short Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
title_full Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
title_fullStr Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
title_full_unstemmed Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
title_sort entropy of fuzzy partitions and entropy of fuzzy dynamical systems
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2016-01-01
description In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.
topic probability space
fuzzy set
fuzzy partition
entropy
fuzzy dynamical system
url http://www.mdpi.com/1099-4300/18/1/19
work_keys_str_mv AT dagmarmarkechova entropyoffuzzypartitionsandentropyoffuzzydynamicalsystems
AT beloslavriecan entropyoffuzzypartitionsandentropyoffuzzydynamicalsystems
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