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m-Generators of Fuzzy Dynamical Systems

Year 2012, Volume: 9 Issue: 2, - , 01.04.2012

Abstract

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.

References

  • [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.
Year 2012, Volume: 9 Issue: 2, - , 01.04.2012

Abstract

References

  • [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.
There are 10 citations in total.

Details

Journal Section Articles
Authors

Mohammad Ebrahimi This is me

Uosef Mohamadi This is me

Publication Date April 1, 2012
Published in Issue Year 2012 Volume: 9 Issue: 2

Cite

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. April 2012;9(2).
Chicago Ebrahimi, Mohammad, and Uosef Mohamadi. “M-Generators of Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering 9, no. 2 (April 2012).
EndNote Ebrahimi M, Mohamadi U (April 1, 2012) m-Generators of Fuzzy Dynamical Systems. Cankaya University Journal of Science and Engineering 9 2
IEEE M. Ebrahimi and U. Mohamadi, “m-Generators of Fuzzy Dynamical Systems”, CUJSE, vol. 9, no. 2, 2012.
ISNAD Ebrahimi, Mohammad - Mohamadi, Uosef. “M-Generators of Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering 9/2 (April 2012).
JAMA Ebrahimi M, Mohamadi U. m-Generators of Fuzzy Dynamical Systems. CUJSE. 2012;9.
MLA Ebrahimi, Mohammad and Uosef Mohamadi. “M-Generators of Fuzzy Dynamical Systems”. Cankaya University Journal of Science and Engineering, vol. 9, no. 2, 2012.
Vancouver Ebrahimi M, Mohamadi U. m-Generators of Fuzzy Dynamical Systems. CUJSE. 2012;9(2).