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Transformation Lemma on Analytical Modeling Via Takagi-Sugeno Fuzzy System and Its Applications

  • Jacek Kluska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)

Abstract

The work presents some applications of the transformation lemma on analytical modeling using the Takagi-Sugeno fuzzy rule-based system [7], which can be used for exact fuzzy modeling of some class of conventional systems. The examples are based on recent author’s theorems [5], which provide necessary and sufficient conditions for transformation of fuzzy rules into the crisp model of the system and vice-versa. The fuzzy model represents the widely used Takagi-Sugeno fuzzy system with linear membership functions. The main attention is paid for usability of the results for control engineering community.

Keywords

Fuzzy System Fuzzy Rule Fuzzy Control Nonlinear Dynamical System Linear Membership Function 
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.

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References

  1. 1.
    Cassillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.): Interpretability Issues in Fuzzy Modeling. Studies in Fuzziness and Soft Computing. Vol. 128. Springer, Berlin (2003)Google Scholar
  2. 2.
    Dubois, D., Nguyen, H.T., Prade, H., Sugeno, M.: Fuzzy Systems: Modeling and Control. In: Nguyen, H.T., Sugeno, M. (eds.) Introduction: The real contribution of fuzzy systems, pp. 1–17. Kluwer Academic Publishers, Norwell (1998)Google Scholar
  3. 3.
    Galichet, S., Boukezzoula, R., Foulloy, L.: Explicit analytical formulation and exact inversion of decomposable fuzzy systems with singleton consequents. Fuzzy Sets and Systems 146, 421–436 (2004)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kluska, J.: Fuzzy Control (in Polish), ZNPRz, Rzeszów 12 (104) (1992)Google Scholar
  5. 5.
    Kluska, J.: New results in Analytical Modeling Using Takagi-Sugeno Expert System. In: Hryniewicz, O., Kacprzyk, J., Koronacki, J., Wierzchoń, S.T. (eds.) Issues in Intelligent Systems Paradigms, EXIT, pp. 79–94 (2005)Google Scholar
  6. 6.
    Kluska, J.: Exact fuzzy modeling of conventional control systems. Proc. of the 12th Zittau Fuzzy Colloquium, Sep. 21-23, Wissenschaftliche Berichte, Heft 84/2005, No 2090-2131, 113-125 (2005)Google Scholar
  7. 7.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Systems, Man, Cybernet SMC-15(1), 116–132 (1985)MATHGoogle Scholar
  8. 8.
    Wang, L.X.: A Course in Fuzzy Systems and Control. Prentice-Hall, Upper Saddle River (1997)MATHGoogle Scholar
  9. 9.
    Wygralak, M.: Cardinality of Fuzzy Sets. Springer, Heidelberg (2003)Google Scholar
  10. 10.
    Ying, H.: Theory and application of a novel fuzzy PID controller using a simplified Takagi-Sugeno rule-scheme. Information Sciences 123, 281–293 (2000)CrossRefGoogle Scholar
  11. 11.
    Ying, H.: Fuzzy control and modeling. In: Analytical foundations and applications, IEEE Press, New York (2000)Google Scholar
  12. 12.
    Ying, H.: Structure and Stability Analysis of General Mamdani Fuzzy Dynamic Models. Int. J. of Intelligent Systems 20, 103–125 (2005)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jacek Kluska
    • 1
  1. 1.Faculty of Electrical and Computer EngineeringRzeszow University of TechnologyRzeszowPoland

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