Chaining syllogism applied to fuzzy IF-THEN rules and rule bases

  • Christian Igel
  • Karl-Heinz Temme
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1226)

Abstract

This paper presents a new approach to show the validity of the chaining syllogism for fuzzy IF-THEN rules and rule bases. Based on this approach new conditions are given on which the investigated deduction scheme holds.

Keywords

Fuzzy Rule Rule Base Fuzzy Rule Base Syllogistic Reasoning Deduction Scheme 
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.
    B. Cappelle, Etienne E. Kerre, Ruan Da, and F. R. Vanmassenhove. Characterization of binary operations on the unit interval satisfying the general modus ponens inference rule. Mathematica Pannonica, 2(1):105–121, 1991.Google Scholar
  2. 2.
    Ruan Da and Etienne E. Kerre. Extended Fuzzy Chaining Syllogismus. In ISFA '95-Sixth International Fuzzy System Assocition World Congress, volume 1, pages 145–148, São Paulo, Brazil, Juli 1995.Google Scholar
  3. 3.
    Didier Dubois and Henri Prade. Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions. Fuzzy Sets and Systems, 40:143–202, 1991.Google Scholar
  4. 4.
    Siegfried Gottwald. Fuzzy Sets and Fuzzy Logic. Vieweg Verlag, Braunschweig, 1993.Google Scholar
  5. 5.
    Siegfried Gottwald. On the Chainability of Fuzzy if-then Rules. In IPMU '96-Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, volume 2, pages 997–1001, Granada, Spain, Juli 1996.Google Scholar
  6. 6.
    Masaharu Mizumoto and Hans-Jürgen Zimmermann. Comparison of fuzzy reasoning methods. Fuzzy Sets and Systems, 8:253–283, 1982.Google Scholar
  7. 7.
    Karl-Heinz Temme and Helmut Thiele. On the Correctness of the Priciples FATI and FITA and their Equivalence. In IFSA '95—Sixth International Fuzzy System Assocition World Congress, volume 2, pages 475–478, São Paulo, Brasil, Juli 1995.Google Scholar
  8. 8.
    Karl-Heinz Temme and Helmut Thiele. On the Chaining of If-Then Rule Bases Interpreted by the Principle FATI. In Proceedings of Symposium on Qualitative System Modelling, Qualitative Fault Diagnosis and Fuzzy Logic and Control, pages 143–152, Budapest and Balantonfüret, April 1996. Further references may be found in the bibliography of this paper.Google Scholar
  9. 9.
    Karl-Heinz Temme and Helmut Thiele. On the Chaining of If-Then Rule Bases Interpreted by the Principle FITA. In EUFIT '96—Fourth European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, September 1996.Google Scholar
  10. 10.
    Helmut Thiele. On the calculus of fuzzy if-then rules. In Intelligent Technologies and Soft Computing, Mangalia, Romania, September 1995.Google Scholar
  11. 11.
    Lotfi A. Zadeh. Syllogistic reasoning in fuzzy logic and its application to reasoning with dispositions. IEEE Trans. on Systems, Man and Cybernetics, pages 754–763, 1985.Google Scholar
  12. 12.
    Lotfi A. Zadeh. The Calculus of Fuzzy If-Then Rules. In T. Terano, M. Sugeno, M. Mukaidono, and K. Shigemasu, editors, Fuzzy Engineering toward Human Friendly Systems-Proceedings of the International Fuzzy Engineering Symposium '91, volume 1, pages 11–12, Yokohama, Japan, November 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Christian Igel
    • 1
  • Karl-Heinz Temme
    • 1
  1. 1.Department of Computer Science IUniversity of DortmundDortmundGermany

Personalised recommendations