On Designing of Flexible Neuro-Fuzzy Systems for Nonlinear Modelling

  • Krzysztof Cpałka
  • Olga Rebrova
  • Robert Nowicki
  • Leszek Rutkowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6743)


In the paper the evolutionary strategy is used for learning of neuro-fuzzy structures of a Mamdani type applied to modelling of nonlinear systems. In the process of evolution we determine parameters of fuzzy membership functions, specific t-norm in a fuzzy inference, specific t-norm for aggregation of antecedents in each rule, and specific t-conorm describing an aggregation operator. The method is tested using well known approximation benchmarks.


Fuzzy System Fuzzy Membership Function Aggregation Operator Temporary Population Triangular Norm 
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.
    Casillas, J., Cordon, O., Herrera, F., Magdalena, L. (eds.): Interpretability Issues in Fuzzy Modeling. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  2. 2.
    Cpałka, K.: A New Method for Design and Reduction of Neuro-Fuzzy Classification Systems. IEEE Transactions on Neural Networks 20(4), 701–714 (2009)CrossRefGoogle Scholar
  3. 3.
    Cpałka, K.: On evolutionary designing and learning of flexible neuro-fuzzy structures for nonlinear classification. In: Nonlinear Analysis Series A: Theory, Methods & Applications, vol. 71. Elsevier, Amsterdam (2009)Google Scholar
  4. 4.
    Czogała, E., Łęski, J.: Fuzzy and Neuro-Fuzzy Intelligent Systems. Physica-Verlag. A Springer Company, Heidelberg, New York (2000)CrossRefzbMATHGoogle Scholar
  5. 5.
    Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, 3rd edn. IEEE Press, Piscataway (2006)zbMATHGoogle Scholar
  6. 6.
    Gabryel, M., Rutkowski, L.: Evolutionary Learning of Mamdani-Type Neuro-fuzzy Systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 354–359. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)CrossRefzbMATHGoogle Scholar
  8. 8.
    Kumar, M., Stoll, R., Stoll, N.: A robust design criterion for interpretable fuzzy models with uncertain data. IEEE Trans. Fuzzy Syst. 14(2), 314–328 (2006)CrossRefGoogle Scholar
  9. 9.
    Łęski, J.: A Fuzzy If-Then Rule-Based Nonlinear Classifier. Int. J. Appl. Math. Comput. Sci. 13(2), 215–223 (2003)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Rutkowski, L.: Computational Intelligence. Springer, Heidelberg (2007)Google Scholar
  11. 11.
    Rutkowski, L., Cpałka, K.: Flexible neuro-fuzzy systems. IEEE Trans. Neural Networks 14(3), 554–574 (2003)CrossRefGoogle Scholar
  12. 12.
    Sivanandam, S.N., Deepa, S.N.: Introduction to Genetic Algorithms. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  13. 13.
    Sugeno, M., Yasukawa, T.: A fuzzy logic based approach to qualitative modeling. IEEE Trans. on Fuzzy Systems 1, 7–31 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Krzysztof Cpałka
    • 1
    • 2
  • Olga Rebrova
    • 3
  • Robert Nowicki
    • 1
    • 2
  • Leszek Rutkowski
    • 1
    • 2
  1. 1.Department of Computer EngineeringCzestochowa University of TechnologyPoland
  2. 2.Institute of Information TechnologyAcademy of Management (SWSPiZ)Poland
  3. 3.Institute of PharmaeconomicsThe Russian State Medical UniversityRussia

Personalised recommendations