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Mathematics 2017, 5(1), 4;

Logical Entropy of Dynamical Systems—A General Model

Department of Mathematics, Zahedan Branch, Islamic Azad University, +98-9816883673 Zahedan, Iran
Department of Mathematics, Sirjan Branch, Islamic Azad University, 7815778989 Sirjan, Iran
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia
Author to whom correspondence should be addressed.
Academic Editor: Indranil SenGupta
Received: 11 November 2016 / Revised: 23 December 2016 / Accepted: 27 December 2016 / Published: 6 January 2017
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In the paper by Riečan and Markechová (Fuzzy Sets Syst. 96, 1998), some fuzzy modifications of Shannon’s and Kolmogorov-Sinai’s entropy were studied and the general scheme involving the presented models was introduced. Our aim in this contribution is to provide analogies of these results for the case of the logical entropy. We define the logical entropy and logical mutual information of finite partitions on the appropriate algebraic structure and prove basic properties of these measures. It is shown that, as a special case, we obtain the logical entropy of fuzzy partitions studied by Markechová and Riečan (Entropy 18, 2016). Finally, using the suggested concept of entropy of partitions we define the logical entropy of a dynamical system and prove that it is the same for two dynamical systems that are isomorphic. View Full-Text
Keywords: logical entropy; logical mutual information; m-preserving transformation; dynamical system; isomorphism logical entropy; logical mutual information; m-preserving transformation; dynamical system; isomorphism
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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Ebrahimzadeh, A.; Giski, Z.E.; Markechová, D. Logical Entropy of Dynamical Systems—A General Model. Mathematics 2017, 5, 4.

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