Skip to main content

Part of the book series: Advances in Soft Computing ((AINSC,volume 33))

Abstract

Nowadays, it is not necessary to advocate in favor of systems of fuzzy IFTHEN rules, because they are widely used in applications of fuzzy set theory such that fuzzy control, identification of dynamic systems, prediction of dynamic systems, decision-making, etc. The reason is in the fact that these systems can be effectively used as an instrument for representation of continuous dependencies. Therefore, the continuity property of a model of fuzzy IF-THEN rules is expected.

This paper has been partially supported by grants IAA1187301 of the GA AV ČR, 201/04/1033 of the GA ČR, and by the Deutsche Forschungsgemeinschaft as part of the Collaborative Research Center “Computational Intelligence” (531).

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
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.

References

  1. Gottwald S (1993) Fuzzy Sets and Fuzzy Logic. The Foundations of Application — from a Mathematical Point of View. Vieweg, Braunschweig

    Google Scholar 

  2. Höhle U (1995) Commutative residuated l-monoids. In: Höhle U, Klement E P (eds) Non-Classical Logics and Their Applications to Fuzzy Subsets. A Handbook of the Mathematical Foundations of Fuzzy Set Theory. Kluwer, Dordrecht, 53–106

    Google Scholar 

  3. Lehmke S, Reusch B, Temme K H, Thiele H (2003) Mathematical Foundations of Fuzzy Inference. In: Schwefel H P, Wegener I, Weinert K (eds) Advances in Computational Intelligence. Springer-Verlag, Berlin

    Google Scholar 

  4. Mamdani A, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man-Machine Studies 7:1–13

    Article  MATH  Google Scholar 

  5. Perfilieva I (2003) Solvability of a System of Fuzzy Relation Equations: Easy to Check Conditions. Neural Network World 13:571–580

    Google Scholar 

  6. Perfilieva I, Tonis A (2000) Compatibility of systems of fuzzy relation equations. Internat. J. General Systems 29:511–528

    Article  MATH  MathSciNet  Google Scholar 

  7. Sanchez E (1976) Resolution of composite fuzzy relation equations. Information and Control 30:38–48.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Perfilieva, I., Lehmke, S. (2005). Safe Modelling of Fuzzy If-Then Rules. In: Reusch, B. (eds) Computational Intelligence, Theory and Applications. Advances in Soft Computing, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31182-3_20

Download citation

  • DOI: https://doi.org/10.1007/3-540-31182-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22807-3

  • Online ISBN: 978-3-540-31182-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics