The Equality of Inference Results Using Fuzzy Implication and Conjunctive Interpretations of the If-Then Rules Under Defuzzification

  • E. Czogała
  • N. Henzel
  • J. Łeski
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 6)


A specific type of equivalence of inference results under defuzzification between logical implication interpretation and conjunctive interpretation of the fuzzy if-then rules has been considered in this paper. The theoretical considerations are illustrated by means of numerical examples in the field of fuzzy modeling.


Inference System Inference Algorithm Aggregation Operation Inference Result Approximate Reasoning 
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.
    O.Cordon, F. Herrera, A. Peregrin: Applicability of the fuzzy operators in the design of fuzzy logic controllers, Fuzzy Sets and Systems 86 (1997)15–41Google Scholar
  2. 2.
    E.Czogala, J.Leski: An equivalence of approximate reasoning under defuzzification, BUSEFAL 74 (1998) 83–92Google Scholar
  3. 3.
    E. Czogala, R. Kowalczyk: Investigation of selected fuzzy operations and implications in engineering, Fifth IEEE Int. Conf. on Fuzzy Systems (1996) 879–885Google Scholar
  4. 4.
    D. Dubois, H. Prade: Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions, Fuzzy Sets and Systems 40 (1991) 143–202MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    D. Dubois, H. Prade: What are fuzzy rules and how to use them, Fuzzy Sets and Systems 84 (1996) 169–185MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    J.C. Fodor: On fuzzy implication operators, Fuzzy Sets and Systems 42 (1991) 293–300MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    E. Kerre: A comparative study of the behavior of some popular fuzzy implication operators on the generalized modus ponens, in: L. Zadeh and J. Kacprzyk, Eds., Fuzzy Logic for the Management of Uncertainty, Wiley, New York (1992) 281–295Google Scholar
  8. 8.
    H.Maeda: An investigation on the spread of fuzziness in multi-fold multi-stage approximate reasoning by pictorial representation - under sup-min composition and triangular type membership function, Fuzzy Sets and Systems 80 (1996) 133MathSciNetCrossRefGoogle Scholar
  9. 9.
    S. Weber: A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms, Fuzzy Sets and Systems 11 (1983) 115–134MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    R. R. Yager: On the interpretation of fuzzy if-then rules, Applied Intelligence 6 (1996) 141–151CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • E. Czogała
    • 1
  • N. Henzel
    • 1
  • J. Łeski
    • 1
  1. 1.Institute of ElectronicsTechnical University of SilesiaGliwicePoland

Personalised recommendations