Journal of Mathematical Sciences

, Volume 157, Issue 3, pp 466–479 | Cite as

Modelling and studying fuzzy dynamical systems

  • A. S. Bychkov


The goal of this paper is to further develop the Yu. P. Pyt'ev fuzzy set theory. Based on this, the author suggests a new class of differential equations for describing fuzzy dynamics.


Closed Interval Lipschitz Condition Fuzzy Variable Independent Increment Perceptive Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Buckley and T. Feuring, “Fuzzy differential equations,” Fuzzy Sets Syst., 110, No. 1, 43–54 (2000).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. S. Bychkov, “Differential equations; a possibility-theoretic approach,” In: 7th Creamean International Mathematical School, September 11–18, 2004. Abstracts of Reports [in Russian], p. 33.Google Scholar
  3. 3.
    A. S. Bychkov, “Constructing of the integral of a fuzzy walk process,” Visn. Kiivsogo Univ., Ser.: Fiz.-Mat. Nauki, No. 4, 125–133 (2005).Google Scholar
  4. 4.
    A. I. Chulikov, Mathematical Models of Nonlinear Dynamics [in Russian], Fizmatlit, Moscow (2000).Google Scholar
  5. 5.
    O. Kaleva, “Fuzzy differential equations,” Fuzzy Sets Syst., 24, No. 3, 301–317 (1987).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    P. E. Kloeden, “Fuzzy Dynamical Systems,” Fuzzy Sets Syst., 19, No. 7, 275–296 (1982).CrossRefMathSciNetGoogle Scholar
  7. 7.
    M. G. Merkur'ev “On a certain approach to the definition of the integral of fuzzy walk,” Visn. Kiivsogo Univ., Ser.: Fiz.-Mat. Nauki, No. 2, 224–230 (2006).Google Scholar
  8. 8.
    Yu. P. Pyt'ev, Possibiity. Elements of Theory and Applications [in Russian], URSS, Moscow (1990).Google Scholar
  9. 9.
    L. A. Zade, “Foundations of a new approach to analysis of complicated systems,” In: Mathematics Today [in Russian], Znanie, Moscow (1974).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Taras Shevchenko Kiev National UniversityKievUkraine

Personalised recommendations