Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Generalized cardinal numbers and their ordering

  • 3. Fuzzy Sets
  • Conference paper
  • First Online:
Uncertainty in Knowledge Bases (IPMU 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 521))

  • 145 Accesses

Abstract

In this paper a general theory of power for hardly characterizable objects as well as related generalized cardinal numbers are presented. The attention is focused on the questions of order. Łukasiewicz logic is used as a supporting logic. The theory refers both to fuzzy sets and twofold fuzzy sets, partial sets, rough sets, etc.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BLANCHARD N. (1981). Theories cardinale et ordinale des ensembles flous, Thesis, Claude-Bernard University, Lyon.

    Google Scholar 

  2. GOTTWALD S. (1969). Konstruktion von Zahlbereichen und die Grundlagen der Inhaltstheorie in einer mehrwertigen Mengenlehre, Thesis, Leipzig.

    Google Scholar 

  3. KLAUA D. (1969). Partielle Mengen und Zahlen, Monatsber. Deut. Akad. Wiss. Berlin, 11, 585–599.

    Google Scholar 

  4. KLAUA D. (1972). Zum Kardinalzahlbegriff in der mehrwertigen Mengenlehre. In Theory of Sets and Topology (Asser G., Flachsmeyer J., Rinow W., Eds.), Deut. Verlag Wiss., 313–325.

    Google Scholar 

  5. ŠOSTAK A. (1989). Fuzzy cardinals and cardinalities of fuzzy sets. In Algebra and Discrete Mathematics, Latvian State University, 137–144 (in Russian).

    Google Scholar 

  6. TARSKI A. (1924). Sur quelques théorémes qui équivalent a l'axiome de choix, Fund. Math., 5, 147–154.

    Google Scholar 

  7. WYGRALAK M. (1986). Fuzzy cardinals based on the generalized equality of fuzzy subsets, Fuzzy Sets and Systems, 18, 143–158.

    Article  Google Scholar 

  8. WYGRALAK M. (1988). Fuzzy sets, twofold fuzzy sets and their cardinality. In Proc. 1st Joint IFSA-EC & EURO-WG Workshop on Progress in Fuzzy Sets in Europe (Kacprzyk J., Straszak A., Eds.), Warsaw, 369–374.

    Google Scholar 

  9. WYGRALAK M., On the power of a rough set, Fasc. Math., in print.

    Google Scholar 

  10. WYGRALAK M., Fuzzy sets — their powers and cardinal numbers. In Proc. 10th Inter. Seminar on Fuzzy Set Theory, Linz, 1988, in print.

    Google Scholar 

  11. WYGRALAK M., On HCH-objects and the proper choice of basic operations, In Proc. 3rd Polish Symp. IFM, Poznan, 1989, in print.

    Google Scholar 

  12. WYGRALAK M., Powers and generalized cardinal numbers for HCH-objects — basic notions, Math. Pann., submitted.

    Google Scholar 

  13. WYGRALAK M., Powers and generalized cardinal numbers for HCH-objects — operations, Fuzzy Sets and Systems, submitted.

    Google Scholar 

  14. WYGRALAK M., Generalized cardinal numbers for lattice valued HCH-objects, in preparation.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, A. Mickiewicz University, PL-60-769, Matejki 48/49, Poznań

    Maciej Wygralak

Authors
  1. Maciej Wygralak
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wygralak, M. (1991). Generalized cardinal numbers and their ordering. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Uncertainty in Knowledge Bases. IPMU 1990. Lecture Notes in Computer Science, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028103

Download citation

  • DOI: https://doi.org/10.1007/BFb0028103

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54346-6

  • Online ISBN: 978-3-540-47580-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation