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Entropy 2016, 18(4), 157; doi:10.3390/e18040157

Logical Entropy of Fuzzy Dynamical Systems

1
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia
2
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia
3
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia
*
Author to whom correspondence should be addressed.
Academic Editors: J. A. Tenreiro Machado and Kevin H. Knuth
Received: 23 February 2016 / Revised: 23 March 2016 / Accepted: 12 April 2016 / Published: 23 April 2016
(This article belongs to the Section Complexity)
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Abstract

Recently the logical entropy was suggested by D. Ellerman (2013) as a new information measure. The present paper deals with studying logical entropy and logical mutual information and their properties in a fuzzy probability space. In particular, chain rules for logical entropy and for logical mutual information of fuzzy partitions are established. Using the concept of logical entropy of fuzzy partition we define the logical entropy of fuzzy dynamical systems. Finally, it is proved that the logical entropy of fuzzy dynamical systems is invariant under isomorphism of fuzzy dynamical systems. View Full-Text
Keywords: fuzzy probability space; fuzzy partition; logical entropy; logical mutual information; fuzzy dynamical system fuzzy probability space; fuzzy partition; logical entropy; logical mutual information; 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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Markechová, D.; Riečan, B. Logical Entropy of Fuzzy Dynamical Systems. Entropy 2016, 18, 157.

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