Skip to main content
SpringerLink
Log in

Approximation of Fuzzy Numbers by F-Transform

  • Conference paper
Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 299))

Abstract

The fuzzy transform setting (F-transform) is proposed as a tool for representation and approximation of type-1 and type-2 fuzzy numbers; the inverse F-transform on appropriate fuzzy partition of the membership interval [0,1] is used to characterize spaces of fuzzy numbers in such a way that arithmetic operations are defined and expressed in terms of the F-transform of the results. A type-2 fuzzy number is represented as a particular fuzzy-valued function and it is expressed in terms of a two-dimensional F-transform where the first dimension represents the universe domain and the second dimension represents the membership domain. Operators on two dimensional F-transform are then proposed to approximate arithmetic operations with type 2 fuzzy numbers.

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

Access this chapter

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Di Martino, F., Loia, V., Sessa, S.: Fuzzy transforms method and attribute dependency in data analysis. Information Sciences 180, 493–505 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Di Martino, F., Loia, V., Sessa, S.: Fuzzy transforms for compression and decompression of color videos. Information Sciences 180, 3914–3931 (2010)

    Article  MathSciNet  Google Scholar 

  3. Perfilieva, I.: Fuzzy Transforms: Theory and Applications. Fuzzy Sets and Systems 157, 993–1023 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Perfilieva, I.: Fuzzy Transforms: A Challenge to conventional transforms. In: Hawkes, P.W. (ed.) Advances in Images and Electron Physics, vol. 147, pp. 137–196. Elsevier Academic Press (2007)

    Google Scholar 

  5. Perfilieva, I.: Fuzzy Transforms and Their Applications to Image Compression. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 19–31. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Perfilieva, I., Dankova, M.: Image fusion on the basis of fuzzy transform. In: Ruan, D., et al. (eds.) Computational Intelligence in Decision and Control, pp. 471–476. World Scientific (2008)

    Google Scholar 

  7. Perfilieva, I., De Baets, B.: Fuzzy transforms of monotone functions with applications to image compression. Information Sciences 180, 3304–3315 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Perfilieva, I., Novak, V., Dvorak, A.: Fuzzy transform in the analysis of data. International Journal of Approximate Reasoning 48, 36–46 (2008)

    Article  MATH  Google Scholar 

  9. Stefanini, L.: Differential Evolution methods for LU-fuzzy Arithmetic. In: Proceedings EUSFLAT 2007, Ostrawa (September 2007)

    Google Scholar 

  10. Stefanini, L.: Fuzzy Transform with Parametric LU-Fuzzy Partitions. In: Ruan, D., et al. (eds.) Computational Intelligence in Decision and Control, pp. 399–404. World Scientific (2008)

    Google Scholar 

  11. Stefanini, L.: Fuzzy Transform and Smooth Functions. In: Carvalho, J.P., Dubois, D., Kaymak, U., Sousa, J.M.C. (eds.) Proceeding of the IFSA-EUSFLAT 2009 Conference, Lisbon, pp. 579–584 (2009)

    Google Scholar 

  12. Stefanini, L.: F-Transform with Parametric Generalized Fuzzy Partitions. Fuzzy Sets and Systems 180, 98–120 (2011), doi:10.1016/j.fss.2011.01.017

    Article  MathSciNet  MATH  Google Scholar 

  13. Stepnicka, M., Polakovic, O.: A neural network approach to the fuzzy transform. Fuzzy Sets and Systems 160, 1037–1047 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Stepnicka, M., Valasek, R.: Fuzzy Transforms for functions of two variables. In: Ramik, J., Novak, V. (eds.) Methods for Decision Support in Environment with Uncertainty, University of Ostrava, IRAFM, pp. 96–102 (2003)

    Google Scholar 

  15. Stepnicka, M., Valasek, R.: Numerical solution of partial differential equations with help of fuzzy transforms. In: Proceedings of the FUZZ-IEE 2005 Conference, Reno, Nevada (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DESP - Department of Economics, Society and Politics, University of Urbino ”Carlo Bo”, Italy

    Luciano Stefanini & Laerte Sorini

Authors
  1. Luciano Stefanini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laerte Sorini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stefanini, L., Sorini, L. (2012). Approximation of Fuzzy Numbers by F-Transform. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31718-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31717-0

  • Online ISBN: 978-3-642-31718-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation