Skip to main content
SpringerLink
Log in
Book cover

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2010: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications pp 402–411Cite as

Trapezoidal Approximation of Fuzzy Numbers Based on Sample Data

  • Conference paper

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 81))

Abstract

The idea of the membership functions construction form a data sample is suggested. The proposed method is based on the trapezoidal approximation of fuzzy numbers.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abbasbandy, S., Asady, B.: The nearest approximation of a fuzzy quantity in parametric form. Applied Mathematics and Computation 172, 624–632 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Abbasbandy, S., Amirfakhrian, M.: The nearest trapezoidal form of a generalized LR fuzzy number. International Journal of Approximate Reasoning 43, 166–178 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ban, A.: Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets and Systems 159, 1327–1344 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9, 613–626 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  5. Grzegorzewski, P.: Metrics and orders in space of fuzzy numbers. Fuzzy Sets and Systems 97, 83–94 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Grzegorzewski, P.: Trapezoidal approximations of fuzzy numbers preserving the expected interval - algorithms and properties. Fuzzy Sets and Systems 159, 1354–1364 (2008)

    MATH  MathSciNet  Google Scholar 

  7. Grzegorzewski, P.: New algorithms for trapezoidal approximation of fuzzy numbers preserving the expected interval. In: Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L. (eds.) Proceedings of the Twelfth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2008, Spain, Torremolinos, Málaga, pp. 117–123 (2008)

    Google Scholar 

  8. Grzegorzewski, P.: Algorithms for trapezoidal approximations of fuzzy numbers preserving the expected interval. In: Bouchon-Meunier, B., Magdalena, L., Ojeda-Aciego, M., Verdegay, J.-L., Yager, R.R. (eds.) Foundations of Reasoning under Uncertainty, pp. 85–98. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Grzegorzewski, P., Mrówka, E.: Trapezoidal approximations of fuzzy numbers. Fuzzy Sets and Systems 153, 115–135 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Grzegorzewski, P., Mrówka, E.: Trapezoidal approximations of fuzzy numbers - revisited. Fuzzy Sets and Systems 158, 757–768 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  12. Pedrycz, W.: Why triangular membership functions? Fuzzy Sets and Systems 64, 21–30 (1994)

    Article  MathSciNet  Google Scholar 

  13. Yeh, C.T.: Trapezoidal and triangular approximations preserving the expected interval. Fuzzy Sets and Systems 159, 1345–1353 (2008)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski

  2. Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland

    Przemysław Grzegorzewski

Authors
  1. Przemysław Grzegorzewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, (Germany)

    Frank Hoffmann

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grzegorzewski, P. (2010). Trapezoidal Approximation of Fuzzy Numbers Based on Sample Data. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14058-7_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14057-0

  • Online ISBN: 978-3-642-14058-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation