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Entropy 2016, 18(1), 19; doi:10.3390/e18010019

Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems

1
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Trieda A. Hlinku 1, Nitra 949 01, Slovakia
2
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, Banská Bystrica 974 01, Slovakia
3
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, Bratislava 814 73, Slovakia
*
Author to whom correspondence should be addressed.
Academic Editors: J.A. Tenreiro Machado and Kevin H. Knuth
Received: 10 September 2015 / Revised: 27 November 2015 / Accepted: 25 December 2015 / Published: 18 January 2016
(This article belongs to the Section Complexity)
View Full-Text   |   Download PDF [218 KB, uploaded 18 January 2016]

Abstract

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. View Full-Text
Keywords: probability space; fuzzy set; fuzzy partition; entropy; fuzzy dynamical system probability space; fuzzy set; fuzzy partition; entropy; fuzzy dynamical system
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Markechová, D.; Riečan, B. Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems. Entropy 2016, 18, 19.

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