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Open AccessArticle

Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case

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.
Entropy 2017, 19(8), 429; https://doi.org/10.3390/e19080429
Received: 4 July 2017 / Revised: 6 August 2017 / Accepted: 17 August 2017 / Published: 21 August 2017
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, we define the logical entropy of an IF-dynamical system. It is shown that the logical entropy of IF-dynamical systems is invariant under isomorphism. Finally, an analogy of the Kolmogorov–Sinai theorem on generators for IF-dynamical systems is proved. View Full-Text
Keywords: intuitionistic fuzzy set; IF-partition; logical entropy; conditional logical entropy; logical mutual information; IF-dynamical system; isomorphism intuitionistic fuzzy set; IF-partition; logical entropy; conditional logical entropy; logical mutual information; IF-dynamical system; isomorphism
MDPI and ACS Style

Markechová, D.; Riečan, B. Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case. Entropy 2017, 19, 429.

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