Skip to main content

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

  • Conference paper
Fuzzy Control

Part of the book series: Advances in Soft Computing ((AINSC,volume 6))

  • 331 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  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)15–41

    Google Scholar 

  2. E.Czogala, J.Leski: An equivalence of approximate reasoning under defuzzification, BUSEFAL 74 (1998) 83–92

    Google Scholar 

  3. E. Czogala, R. Kowalczyk: Investigation of selected fuzzy operations and implications in engineering, Fifth IEEE Int. Conf. on Fuzzy Systems (1996) 879–885

    Google Scholar 

  4. D. Dubois, H. Prade: Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions, Fuzzy Sets and Systems 40 (1991) 143–202

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Dubois, H. Prade: What are fuzzy rules and how to use them, Fuzzy Sets and Systems 84 (1996) 169–185

    Article  MathSciNet  MATH  Google Scholar 

  6. J.C. Fodor: On fuzzy implication operators, Fuzzy Sets and Systems 42 (1991) 293–300

    Article  MathSciNet  MATH  Google Scholar 

  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) 281–295

    Google Scholar 

  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) 133

    Article  MathSciNet  Google Scholar 

  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) 115–134

    Article  MathSciNet  MATH  Google Scholar 

  10. R. R. Yager: On the interpretation of fuzzy if-then rules, Applied Intelligence 6 (1996) 141–151

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Czogała, E., Henzel, N., Łeski, J. (2000). The Equality of Inference Results Using Fuzzy Implication and Conjunctive Interpretations of the If-Then Rules Under Defuzzification. In: Hampel, R., Wagenknecht, M., Chaker, N. (eds) Fuzzy Control. Advances in Soft Computing, vol 6. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1841-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1841-3_6

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1327-2

  • Online ISBN: 978-3-7908-1841-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics