| Title of paper:
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φ–entropy of IF-partitions
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| Author(s):
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| Beloslav Riečan
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Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica
Mathematical Institute of Slovak Acad. of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia
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| beloslav.riecan@umb.sk
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| Dagmar Markechová
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| Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia
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| dmarkechova@ukf.sk
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| Published in:
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"Notes on IFS", Volume 23, 2017, Number 3, pages 9—16
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| Download:
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 PDF (157 Kb Kb, File info)
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| Abstract:
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In the paper a common formulation is given for two types of entropy of partitions in the intuitionistic fuzzy case: the Shannon-Kolmogorov-Sinai entropy ([6]) and the logical entropy ([4]).
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| Keywords:
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Intuitionistic fuzzy set, IF-partition, Shannon’s entropy, Logical entropy, Subadditive generator.
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| AMS Classification:
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03E72
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| References:
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- Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Physic Verlag, Heidelberg,.
- Ďurica, M. (2007) Entropy on IF events. Notes on Intuitionistic Fuzzy Sets, 13(4), 30–40.
- Ebrahimzadeh, A. (2016) Logical entropy of quantum dynamical systems. Open Physics, 14, 1–5.
- Ellerman, D. (2013) An introduction to logical entropy and its relation to Shannon entropy. Int. J. Seman. Comput., 7, 121–145.
- Gray, R. M. (2009) Entropy and Information Theory. Springer: Berlin/Heidelberg, Germany.
- Kolmogorov, A. N. (1958) New metric invariant of transitive dynamical systems and
automorphisms of Lebesgue spaces. Dokl. Russ. Acad. Sci., 119, 861–864.
- Markechová, D. (1992) The entropy of fuzzy dynamical systems and generators. Fuzzy Sets Syst., 48, 351–363.
- Markechová, D., & Riečan, B. (2016) Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems. Entropy, 18 (19), doi:10.3390/e18010019.
- Markechová, D., & Riečan, B. (2016) Logical Entropy of Fuzzy Dynamical Systems. Entropy, Vol. 18 (157), doi: 10.3390/e18040157.
- Markechová, D., & Riečan, B. Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case. Entropy (under review).
- Mesiar, R., & Rybárik, J. (1998) Entropy of Fuzzy Partitions – A General Model. Fuzzy Sets Syst., 99, 73–79.
- Riečan, B. (2015) On finitely additive IF-states. Proceedings of the 7th IEEE International Conference Intelligent Systems IS’2014, Warsaw, Poland, 24-26 September 2014; Volume 1: Mathematical Foundations, Theory, Analysis (P. Angelov et al. eds.), Springer, Switzerland; 149–156.
- Shannon, C. E. (1948) Mathematical theory of communication. Bell Syst. Tech. J., 27, 379–423.
- Sinai, Y. G. (1990) Ergodic theory with applications to dynamical systems and statistical mechanics. Springer, Berlin.
- Szmidt, E., & Kacprzyk, J. (2001) Entropy of intuitionistic fuzzy sets. Fuzzy Sets Syst., 118, 467–477.
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