8-9 October 2020 • Burgas, Bulgaria

Submission: 15 May 2020 • Notification: 31 May 2020 • Final Version: 15 June 2020

Issue:φ–entropy of IF-partitions

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Title of paper: φ–entropy of IF-partitions
Author(s):
Beloslav Riečan
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
beloslav.riecanAt sign.pngumb.sk
Dagmar Markechová
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia
dmarkechovaAt sign.pngukf.sk
Published in: "Notes on IFS", Volume 23, 2017, Number 3, pages 9—16
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Abstract: 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]).
Keywords: Intuitionistic fuzzy set, IF-partition, Shannon’s entropy, Logical entropy, Subadditive generator.
AMS Classification: 03E72
References:
  1. Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Physic Verlag, Heidelberg,.
  2. Ďurica, M. (2007) Entropy on IF events. Notes on Intuitionistic Fuzzy Sets, 13(4), 30–40.
  3. Ebrahimzadeh, A. (2016) Logical entropy of quantum dynamical systems. Open Physics, 14, 1–5.
  4. Ellerman, D. (2013) An introduction to logical entropy and its relation to Shannon entropy. Int. J. Seman. Comput., 7, 121–145.
  5. Gray, R. M. (2009) Entropy and Information Theory. Springer: Berlin/Heidelberg, Germany.
  6. Kolmogorov, A. N. (1958) New metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces. Dokl. Russ. Acad. Sci., 119, 861–864.
  7. Markechová, D. (1992) The entropy of fuzzy dynamical systems and generators. Fuzzy Sets Syst., 48, 351–363.
  8. Markechová, D., & Riečan, B. (2016) Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems. Entropy, 18 (19), doi:10.3390/e18010019.
  9. Markechová, D., & Riečan, B. (2016) Logical Entropy of Fuzzy Dynamical Systems. Entropy, Vol. 18 (157), doi: 10.3390/e18040157.
  10. Markechová, D., & Riečan, B. Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case. Entropy (under review).
  11. Mesiar, R., & Rybárik, J. (1998) Entropy of Fuzzy Partitions – A General Model. Fuzzy Sets Syst., 99, 73–79.
  12. 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.
  13. Shannon, C. E. (1948) Mathematical theory of communication. Bell Syst. Tech. J., 27, 379–423.
  14. Sinai, Y. G. (1990) Ergodic theory with applications to dynamical systems and statistical mechanics. Springer, Berlin.
  15. Szmidt, E., & Kacprzyk, J. (2001) Entropy of intuitionistic fuzzy sets. Fuzzy Sets Syst., 118, 467–477.
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