Logical Entropy of Dynamical Systems—A General Model

Abolfazl Ebrahimzadeh, Zahra Eslami Giski and Dagmar Markechová
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Abolfazl Ebrahimzadeh: Department of Mathematics, Zahedan Branch, Islamic Azad University, +98-9816883673 Zahedan, Iran
Zahra Eslami Giski: Department of Mathematics, Sirjan Branch, Islamic Azad University, 7815778989 Sirjan, Iran
Dagmar Markechová: Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia

Mathematics, 2017, vol. 5, issue 1, 1-17

Abstract: In the paper by Rie?an 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 Rie?an (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.

Keywords: logical entropy; logical mutual information; m -preserving transformation; dynamical system; isomorphism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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