Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/8/429 |
| _version_ | 1817996195391340544 |
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| author | Dagmar Markechová Beloslav Riečan |
| author_facet | Dagmar Markechová Beloslav Riečan |
| author_sort | Dagmar Markechová |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T02:18:39Z |
| format | Article |
| id | doaj.art-6ac1468b7a1d4f1a8321d7431bb86f46 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T02:18:39Z |
| publishDate | 2017-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-6ac1468b7a1d4f1a8321d7431bb86f462022-12-22T02:18:06ZengMDPI AGEntropy1099-43002017-08-0119842910.3390/e19080429e19080429Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy CaseDagmar Markechová0Beloslav Riečan1Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, SlovakiaDepartment of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, SlovakiaIn 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.https://www.mdpi.com/1099-4300/19/8/429intuitionistic fuzzy setIF-partitionlogical entropyconditional logical entropylogical mutual informationIF-dynamical systemisomorphism |
| spellingShingle | Dagmar Markechová Beloslav Riečan Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case Entropy intuitionistic fuzzy set IF-partition logical entropy conditional logical entropy logical mutual information IF-dynamical system isomorphism |
| title | Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case |
| title_full | Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case |
| title_fullStr | Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case |
| title_full_unstemmed | Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case |
| title_short | Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case |
| title_sort | logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case |
| topic | intuitionistic fuzzy set IF-partition logical entropy conditional logical entropy logical mutual information IF-dynamical system isomorphism |
| url | https://www.mdpi.com/1099-4300/19/8/429 |
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