Skip to main content
SpringerLink
Log in

On sup — * Compositions of Fuzzy Implications

  • Conference paper
Book cover Neural Networks and Soft Computing

Part of the book series: Advances in Soft Computing ((AINSC,volume 19))

Abstract

Recently we have examined properties of sup-min compositions of fuzzy implications [3]. However, in many applications, another connectives are used for composition of fuzzy implications. Now, we generalize these results to the case of sup —* composition with a triangular norm *.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Baczynski, M., Drewniak, J. (1999): Conjugacy classes of fuzzy implication, In: Reusch, B. (Eds.): Computational Intelligence: Theory and Applications, Springer-Verlag, Berlin, (LNCS Vol. 1625), 287–298.

    Google Scholar 

  2. Baczylíski, M., Drewniak, J. (2000): Monotonic fuzzy implications, In: Szczepaniak, P., Lisboa, P., Kacprzyk, J. (Eds.): Fuzzy Systems in Medicine, PhysicaVerlag, Heidelberg, (Studies in Fuzzines and Soft Computing, Vol. 41), 90–111.

    Google Scholar 

  3. Baczynski, M., Drewniak, J., Sobera, J. (2001): Semigroups of fuzzy implications, Tatra Mt. Math. Publ. 21, 61–71.

    MathSciNet  MATH  Google Scholar 

  4. Baldwin, J.F., Pilsworth, B.W. (1980): Axiomatic approach to implication for approximate reasoning with fuzzy logic, Fuzzy Sets Syst. 3, 193–219.

    Article  MathSciNet  MATH  Google Scholar 

  5. Drewniak, J., Kula, K. (2002): Generalized compositions of fuzzy relations, Presented in FSTA 2002, Liptovsky Jan, Slovakia.

    Google Scholar 

  6. Cordon, O., Herrera, F., Peregrin, A. (1997): Applicability of the fuzzy operators in the design of fuzzy logic controllers, Fuzzy Sets Syst. 86, 15–41.

    Article  MATH  Google Scholar 

  7. Fodor, J.C., Roubens, M.C. (1994): Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht.

    Book  MATH  Google Scholar 

  8. Goguen, J.A. (1967): L-fuzzy sets, J. Math. Anal. Appl. 18, 145–174.

    Article  MathSciNet  MATH  Google Scholar 

  9. Klement, E.P., Mesiar, R., Pap, E. (2000): Triangular Norms, Kluwer, Dordrecht.

    MATH  Google Scholar 

  10. Schweizer, B., Sklar, A. (1961): Associative functions and statistical triangle inequalities, Publ. Math. Debrecen 8, 169–186.

    MathSciNet  MATH  Google Scholar 

  11. Zadeh, L.A. (1965): Fuzzy sets, Inform. Control 8, 338–353.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Silesia, 40-007, Katowice, ul., Bankowa 14, Poland

    Michał Baczyński, Józef Drewniak & Jolanta Sobera

  2. Institute of Mathematics, University of Rzeszów, 35-310, Rzeszów, ul., Rejtana 16a, Poland

    Józef Drewniak

Authors
  1. Michał Baczyński
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Józef Drewniak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jolanta Sobera
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Engineering, Technical University Częstochowa, Al. Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski

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

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baczyński, M., Drewniak, J., Sobera, J. (2003). On sup — * Compositions of Fuzzy Implications. In: Rutkowski, L., Kacprzyk, J. (eds) Neural Networks and Soft Computing. Advances in Soft Computing, vol 19. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1902-1_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1902-1_39

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0005-0

  • Online ISBN: 978-3-7908-1902-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation