Advertisement

Generalized Parametric Conjunction Operations in Fuzzy Modeling

  • Ildar Batyrshin
Part of the Advances in Soft Computing book series (AINSC, volume 6)

Abstract

An approach to construct optimal fuzzy models based on an optimization of parameters of generalized conjunction operations is discussed. Several approaches to construct parametric classes of conjunction operations simpler than known parametric classes of T-norms are considered. These approaches are based on elimination of associativity and commutativity properties from definition of conjunction operation. A new simplest generalized parametric conjunction operation is introduced. Different approaches to approximation of real valued function by fuzzy models based on optimization of parameters of membership functions and parameters of operations are compared by numerical examples. It is shown that fuzzy models based on new conjunction operation have better performance than previous ones.

Keywords

Membership Function Fuzzy Rule Fuzzy Model Parametric Classis Generalize Conjunction 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alsina, C., Trillas, E., Valverde, L.: On Some Logical Connectives for Fuzzy Sets Theory. J. Math. Anal. Appl. 93 (1983) 15–26MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Batyrshin, I., Bikbulatov, A.: Construction of Optimal Fuzzy Models Based on the Tuning of Fuzzy Operations. In: Proceedings of 6th Zittau Fuzzy Colloquium. Zittau (1998) 33–38Google Scholar
  3. 3.
    Batyrshin, I., Bikbulatov, A., Kaynak, O., Rudas, I.: Functions Approximation Based on the Tuning of Generalized Connectives. In: Proceedings of EUROFUSE - SIC ‘89. Budapest (1999) 556–561Google Scholar
  4. 4.
    Batyrshin, I., Kaynak, O.: Parametric Classes of Generalized Conjunction and Disjunction Operations for Fuzzy Modeling. IEEE Trans. Fuzzy Syst. 7 (1999) 586–596CrossRefGoogle Scholar
  5. 5.
    Batyrshin, I., Kaynak, O., Rudas, I.: Generalized Conjunction and Disjunction Operations for Fuzzy Control. In: Proceeding of 6th European Congress on Intelligent Technignes & Soft Computing, EUFIT’98, Vol. 1. Aachen (1998) 52–57Google Scholar
  6. 6.
    Cervinka, O.: Automatic Tuning of Parametric T-norms and T-conorms in Fuzzy Modeling. In: Proceedings of 7th IFSA World Congress, Vol. 1. ACADEMIA, Prague (1997) 416–421Google Scholar
  7. 7.
    Jang, J.-S. R., Sun, C. T., Mizutani, E.: Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence. Prentice-Hall International, New York (1997)Google Scholar
  8. 8.
    Kosko, B.: Fuzzy Engineering. Prentice-Hall, New Jersey (1997)MATHGoogle Scholar
  9. 9.
    Mitaim, S., Kosko, B.: What is the Best Shape for a Fuzzy Set in Function Approximation? In: Proceeding of 5’h IEEE Int. Conf. Fuzzy Systems, FUZZ-96, Vol. 2. (1996) 1237–1243Google Scholar
  10. 10.
    Sugeno, M., Kang, G.T.: Structure Identification of Fuzzy Model. Fuzzy Sets and Systems 28 (1988) 15–33MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Zadeh, L.A.: A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges. Journal of Cybernetics 2 (1972) 4–34MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ildar Batyrshin
    • 1
  1. 1.Kazan State Technological UniversityKazanRepublic of Tatarstan, Russia

Personalised recommendations