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m-Generators of Fuzzy Dynamical Systems

Yıl 2012, Cilt: 9 Sayı: 2, - , 01.04.2012

Öz

In this paper we prove that the entropy of a fuzzy measure preserving transformation
with respect to a sub-σ-algebra having finite atoms is affine and then we extend
the method of computing the entropy of a finite sub-σ-algebra to a sub-σ-algebra having
countable atoms, and we investigate the ergodic properties of fuzzy probability dynamical
systems. At the end by using this notion, a version of Kolmogorov-Sinai proposition [6, 9,
10] is given.

Kaynakça

  • [1] D. Dumitrescu, C. H˘aloiu and A. Dumitrescu, Generators of fuzzy dynamical systems, Fuzzy Sets and Systems 113 (2000), 447–452.
  • [2] D. Dumitrescu, Entropy of a fuzzy dynamical system, Fuzzy Sets and Systems 70 (1995), 45–57.
  • [3] D. Dumitrescu, Entropy of a fuzzy process, Fuzzy Sets and Systems 55 (1993), 169–177.
  • [4] M. Ebrahimi, Generators of probability dynamical systems, Differential Geometry-Dynamical Systems 8 (2006), 90–97.
  • [5] M. Ebrahimi and N. Mohamadi, The entropy function on an algebraic structure with infinite partition and m-preserving transformation generators, Applied Sciences 12 (2010), 48–63.
  • [6] A. N. Kolmogorov, Entropy per unit time as a metric invariant of automorphism, Doklady of Russian Academy of Sciences 124 (1959), 754–755.
  • [7] P. Serivastava, M. Khare and Y. K. Srivastava, A fuzzy measure algebra on a metric space,Fuzzy Sets and Systems 79 (1996), 395–400.
  • [8] P. Serivastava, M. Khare and Y. K. Srivastava, m-Equivalence, entropy and F-dynamical systems, Fuzzy Sets and Systems 121 (2001), 275–283.
  • [9] Ya. Sinai, On the notion of entropy of a dynamical system, Doklady ofRussian Academy of Sciences 124 (1959), 768–771.
  • [10] P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, 1982.
Yıl 2012, Cilt: 9 Sayı: 2, - , 01.04.2012

Öz

Kaynakça

  • [1] D. Dumitrescu, C. H˘aloiu and A. Dumitrescu, Generators of fuzzy dynamical systems, Fuzzy Sets and Systems 113 (2000), 447–452.
  • [2] D. Dumitrescu, Entropy of a fuzzy dynamical system, Fuzzy Sets and Systems 70 (1995), 45–57.
  • [3] D. Dumitrescu, Entropy of a fuzzy process, Fuzzy Sets and Systems 55 (1993), 169–177.
  • [4] M. Ebrahimi, Generators of probability dynamical systems, Differential Geometry-Dynamical Systems 8 (2006), 90–97.
  • [5] M. Ebrahimi and N. Mohamadi, The entropy function on an algebraic structure with infinite partition and m-preserving transformation generators, Applied Sciences 12 (2010), 48–63.
  • [6] A. N. Kolmogorov, Entropy per unit time as a metric invariant of automorphism, Doklady of Russian Academy of Sciences 124 (1959), 754–755.
  • [7] P. Serivastava, M. Khare and Y. K. Srivastava, A fuzzy measure algebra on a metric space,Fuzzy Sets and Systems 79 (1996), 395–400.
  • [8] P. Serivastava, M. Khare and Y. K. Srivastava, m-Equivalence, entropy and F-dynamical systems, Fuzzy Sets and Systems 121 (2001), 275–283.
  • [9] Ya. Sinai, On the notion of entropy of a dynamical system, Doklady ofRussian Academy of Sciences 124 (1959), 768–771.
  • [10] P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, 1982.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Mohammad Ebrahimi Bu kişi benim

Uosef Mohamadi Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 9 Sayı: 2

Kaynak Göster

APA Ebrahimi, M., & Mohamadi, U. (2012). m-Generators of Fuzzy Dynamical Systems. Cankaya University Journal of Science and Engineering, 9(2).
AMA Ebrahimi M, Mohamadi U. m-Generators of Fuzzy Dynamical Systems. CUJSE. Nisan 2012;9(2).
Chicago Ebrahimi, Mohammad, ve Uosef Mohamadi. “M-Generators of Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering 9, sy. 2 (Nisan 2012).
EndNote Ebrahimi M, Mohamadi U (01 Nisan 2012) m-Generators of Fuzzy Dynamical Systems. Cankaya University Journal of Science and Engineering 9 2
IEEE M. Ebrahimi ve U. Mohamadi, “m-Generators of Fuzzy Dynamical Systems”, CUJSE, c. 9, sy. 2, 2012.
ISNAD Ebrahimi, Mohammad - Mohamadi, Uosef. “M-Generators of Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering 9/2 (Nisan 2012).
JAMA Ebrahimi M, Mohamadi U. m-Generators of Fuzzy Dynamical Systems. CUJSE. 2012;9.
MLA Ebrahimi, Mohammad ve Uosef Mohamadi. “M-Generators of Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering, c. 9, sy. 2, 2012.
Vancouver Ebrahimi M, Mohamadi U. m-Generators of Fuzzy Dynamical Systems. CUJSE. 2012;9(2).