Skip to main content

Approximation of Fuzzy Functions by Extended Fuzzy Transforms

  • Conference paper
Computational Intelligence, Theory and Applications

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

  • 763 Accesses

Abstract

A fuzzy approximation method called fuzzy transforms for approximation of continuous function is presented in this paper. It is shown how can be fuzzy transforms naturally generalized for functions with more variables. A fuzzy function as an approximated mapping is considered. This leads to an extension of fuzzy transforms for fuzzy function as well as to an extension of generalized fuzzy transforms for fuzzy functions with more variables. It is shown how the proposed method can be used as so called learning to obtain a fuzzy rule base for fuzzy control.

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. Perfilieva I (2004) Fuzzy Transforms. In: Dubois D, Grzymala-Buse J, Inuiguchi M, Polkowski L (eds) Fuzzy Sets and Rough Sets, Lecture Notes in Computer Science. Springer, Heidelberg, to appear

    Google Scholar 

  2. Perfilieva I (2003) Fuzzy Approach to Solution of Differential Equations with Imprecise Data: Application to Reef Growth Problem. In: Demicco R V, Klir G J (eds) Fuzzy Logic in Geology. Academic Press, Amsterdam

    Google Scholar 

  3. Daňková M (2002) Representation of Logic Fromulas by Normal Forms, Kybernetika 38:717–728

    MathSciNet  Google Scholar 

  4. Perfilieva I, Chaldeeva E (2001) Proc of the 4th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty:116–124

    Google Scholar 

  5. Perfilieva I (2004) Normal Forms in BL and ŁΠ Algebras of Functions, Soft Computing 8:291–298

    MATH  Google Scholar 

  6. Štěpnička M (2003) Fuzzy Transformation and Its Applications in A/D Converter, Journal of Electrical Engineering Vol. 54, NO. 12/s:72–75

    Google Scholar 

  7. Štěpnička M, Valášek R (2004) Fuzzy Transforms and Their Application on Wave Equation, Journal of Electrical Engineering, to appear

    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

Štěpnička, M., Lehmke, S. (2005). Approximation of Fuzzy Functions by Extended Fuzzy Transforms. 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_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-31182-3_16

  • 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