Advertisement

Hard and Soft Sets

  • Zdzislaw Pawlak
Part of the Workshops in Computing book series (WORKSHOPS COMP.)

Abstract

In this paper I would like to make some remarks on the concept of a set in the context of some recent developments concerning vagueness, imprecision and uncertainty.

Keywords

Membership Function Membership Problem Notre Dame Journal Indiscernibility Relation Negative Membership 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    W.D. Blizard, (1989a). Multiset Theory, Notre Dame Journal of Formal Logic, 30, pp. 36–66.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    W.D. Blizard, (1989b). Real-valued Multisets and Fuzzy Sets, Fuzzy Sets and Systems, 33, pp. 77–79.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    W.D. Blizard, (1990). Negative Membership, Notre Dame Journal of Formal Logic, 31, pp. 346–368.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    E. Bryniarski, (1993). Formal Concept of Rough Set (in polish). Ph.D. Dissertation.Google Scholar
  5. [5]
    Z. Pawlak, S.K.M Wong and W. Ziarko, (1988). Rough Sets: Probabilistic Versus Deterministic Approach, Int. J. Man-Machine Studies, 29, pp. 81–95MATHGoogle Scholar
  6. [6]
    Z. Pawlak, (1991). Rough Sets-Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers.Google Scholar
  7. [7]
    Z. Pawlak, (1982). Rough Sets, hit. J. of Inf. and Comp. Sci., 11, 5, pp. 341–356.MATHMathSciNetGoogle Scholar
  8. [8]
    Z. Pawlak, (1985). Rough Sets and Fuzzy Sets, J. of Fuzzy Sets and Systems, 17, pp. 99–102.CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    Z. Pawlak, (1988). Hard Sets and Soft Sets, Bull. Pol. Acad. Sci. Tech., 36, 1–2, pp. 119–123.Google Scholar
  10. [10]
    Z. Pawlak, and A. Skowron, (1993). Rough Membership Function: a Tool for Reasoning with Uncertainty. Algebraic Methods in Logic and Computer Science, Banach Center Publications Vol. 28, Polish Academy of Sciences, Warsaw, 1993, 135–150.MathSciNetGoogle Scholar
  11. [11]
    L. Zadeh, (1965). Fuzzy Sets, Information and Control 8, pp. 338–353.MATHMathSciNetGoogle Scholar

Copyright information

© British Computer Society 1994

Authors and Affiliations

  • Zdzislaw Pawlak
    • 1
  1. 1.Institute of Computer ScienceWarsaw University of TechnologyWarsawPoland

Personalised recommendations