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Hard and Soft Sets

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Rough Sets, Fuzzy Sets and Knowledge Discovery

Part of the book series: Workshops in Computing ((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.

“Apart from the known and the unknown, what else is there?”

Harold Pinter in The Homecoming

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References

  1. W.D. Blizard, (1989a). Multiset Theory, Notre Dame Journal of Formal Logic, 30, pp. 36–66.

    Article  MATH  MathSciNet  Google Scholar 

  2. W.D. Blizard, (1989b). Real-valued Multisets and Fuzzy Sets, Fuzzy Sets and Systems, 33, pp. 77–79.

    Article  MATH  MathSciNet  Google Scholar 

  3. W.D. Blizard, (1990). Negative Membership, Notre Dame Journal of Formal Logic, 31, pp. 346–368.

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Bryniarski, (1993). Formal Concept of Rough Set (in polish). Ph.D. Dissertation.

    Google Scholar 

  5. Z. Pawlak, S.K.M Wong and W. Ziarko, (1988). Rough Sets: Probabilistic Versus Deterministic Approach, Int. J. Man-Machine Studies, 29, pp. 81–95

    MATH  Google Scholar 

  6. Z. Pawlak, (1991). Rough Sets-Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers.

    Google Scholar 

  7. Z. Pawlak, (1982). Rough Sets, hit. J. of Inf. and Comp. Sci., 11, 5, pp. 341–356.

    MATH  MathSciNet  Google Scholar 

  8. Z. Pawlak, (1985). Rough Sets and Fuzzy Sets, J. of Fuzzy Sets and Systems, 17, pp. 99–102.

    Article  MATH  MathSciNet  Google Scholar 

  9. Z. Pawlak, (1988). Hard Sets and Soft Sets, Bull. Pol. Acad. Sci. Tech., 36, 1–2, pp. 119–123.

    Google Scholar 

  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.

    MathSciNet  Google Scholar 

  11. L. Zadeh, (1965). Fuzzy Sets, Information and Control 8, pp. 338–353.

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Warsaw University of Technology, ul. Nowowiejska 15/19, 00 665, Warsaw, Poland

    Zdzislaw Pawlak

Authors
  1. Zdzislaw Pawlak
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Wojciech P. Ziarko MSc, PhD

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© 1994 British Computer Society

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Pawlak, Z. (1994). Hard and Soft Sets. In: Ziarko, W.P. (eds) Rough Sets, Fuzzy Sets and Knowledge Discovery. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3238-7_15

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  • DOI: https://doi.org/10.1007/978-1-4471-3238-7_15

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19885-7

  • Online ISBN: 978-1-4471-3238-7

  • eBook Packages: Springer Book Archive

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