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

Dagmar Markechová; Beloslav Riečan

doi:10.3390/e19080429

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

Entropy (Basel). 2017 Aug 21;19(8):429. doi: 10.3390/e19080429.

Authors

Dagmar Markechová¹, Beloslav Riečan^{2

3}

Affiliations

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.

PMID: 33535368
DOI: 10.3390/e19080429

Abstract

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.

Keywords: IF-dynamical system; IF-partition; conditional logical entropy; intuitionistic fuzzy set; isomorphism; logical entropy; logical mutual information.