Abstract
In this paper, we define a type of Yager entropy for continuous dynamical systems on compact metric spaces. The concept of k-ergodic decomposition is introduced and applied to represent the new concept in terms of the Yager entropy in the sense of Riečan.
This is a preview of subscription content, log in via an institution to check access.
Access this article
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Similar content being viewed by others
References
Breiman, L.: The individual theorem of information theory. Ann. Math. Stat. 28, 809–811 (1957), errata 31, 809–810 (1960)
Brin, M., Katok, A.: On Local Entropy in Geometric Dynamics. Lecture Notes in Mathematics 1007. Springer, New York (1983)
Chen, X., Dai, W.: Maximum entropy principle for uncertain variables. Int. J. Fuzzy Syst. 13(3), 234 (2011)
Chiu, C.H., Wang, W.J.: Simple calculation for the entropy of the fuzzy number in addition and extension principle. Int. J. Fuzzy Syst. 2, 256–266 (2000)
Dumitrescu, D.: Measure-Preserving Transformation and the Entropy of a Fuzzy Partition. In: 13th Linz seminar on fuzzy set theory (Linz, 1991), 25–27 (1991)
Dumitrescu, D.: Fuzzy measures and the entropy of fuzzy partitions. J. Math. Anal. Appl. 176, 359–373 (1993)
Dumitrescu, D.: Entropy of a fuzzy process. Fuzzy Sets Syst. 55, 169–177 (1993)
Dumitrescu, D.: Entropy of fuzzy dynamical systems. Fuzzy Sets Syst. 70, 45–57 (1995)
Kolmogorov, A.N.: New metric invariant of transitive dynamical systems and endomorphisms of Lebesgue spaces. Dokl. Russ. Acad. Sci. 119(N5), 861–864 (1958)
Mañé, R.: Ergodic Theory and Differentiable Dynamics. Springer, Berlin (1987)
Markechová, D.: The entropy on F-quantum spaces. Math. Slovaca 40, 177–190 (1990)
Markechová, D.: The entropy of fuzzy dynamical systems and generators. Fuzzy Sets Syst. 48, 351–363 (1992)
Markechová, D.: Entropy of complete fuzzy partitions. Math. Slovaca 43(1), 1–10 (1993)
Markechová, D.: A note to the Kolmogorov-Sinaj entropy of fuzzy dynamical systems. Fuzzy Sets Syst. 64, 87–90 (1994)
McMillan, B.: The basic theorems of information theory. Ann. Math. Stat. 24, 196–219 (1953)
Mesiar, R., Rybárik, J.: Entropy of fuzzy partitions: a general model. Fuzzy Sets Syst. 99, 73–79 (1998)
Rahimi, M., Riazi, A.: On local entropy of fuzzy partitions. Fuzzy Sets Syst. 234, 97–108 (2014)
Riečan, B.: On a type of entropy of dynamical systems. Tatra Mt. Math. Publ. 1, 135–140 (1992)
Riečan, B., Markechová, D.: The entropy of fuzzy dynamical systems, general scheme and generators. Fuzzy Sets Syst. 96, 191–199 (1998)
Riečan, B.: On the Yager entropy of dynamical systems. Acta Math. Nitra 5, 1–14 (2002)
Rybárik, J.: The entropy of the Q-F-dynamical systems. Busefal 48, 24–26 (1991)
Rybarik, J.: The entropy based on pseudoarithmetical operations. Tatra Mt. Math. Publ. 6, 157–164 (1995)
Pesin, Y.: Characteristic Lyapunov exponents and smooth ergodic theory. Russ. Math. Surv. 32, 54–114 (1977)
Phelps, R.: Lectures on Choquet’s Theorem. Van Nostrand, Princeton (1966)
Ruelle, D.: An inequality for the entropy of differential maps. Bol. Soc. Bras. de Mat. 9, 83–87 (1978)
Shannon, C.: A mathematical theory of communication. Bell Syst. Tech. J. 27(379–423), 623–656 (1948)
Sinai, Y.G.: On the notion of entropy of a dynamical system. Dokl. Russ. Acad. Sci. 124, 768–771 (1959)
Walters, P.: An Introduction to Ergodic Theory. Springer, New York (1982)
Acknowledgments
The authors would like to thank the referees for their comprehensive and useful comments which helped the improvement of this work to the present form.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rahimi, M., Assari, A. & Ramezani, F. A Local Approach to Yager Entropy of Dynamical Systems. Int. J. Fuzzy Syst. 18, 98–102 (2016). https://doi.org/10.1007/s40815-015-0062-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-015-0062-z