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Algebraic Structures of Rough Sets

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Rough Sets, Fuzzy Sets and Knowledge Discovery

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

Abstract

This paper deals with some algebraic and set-theoretical properties of rough sets. Our considerations are based on the original conception of rough sets formulated by Pawlak [4, 5]. Let U be any fixed non-empty set traditionally called the universe and let R be an equivalence relation on U. The pair A = (U, R) is called the approximation space. We will call the equivalence classes of the relation R the elementary sets. We denote the family of elementary sets by U/R. We assume that the empty set is also an elementary set. Every union of elementary sets will be called a composed set. We denote the family of composed sets by ComR. We can characterize each set X ⊆ U using the composed sets [5].

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References

  1. Z. Bonikowski, A Certain Conception of the Calculus of Rough Sets, Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 412–421.

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  2. E. Bryniarski, A calculus of rough sets of the first order, Bull.Pol.Ac.: Math., vol. 37 (1989), pp. 71–78.

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  4. Z. Pawlak, Information systems. Theoretical foundations., WNT, Warszawa, 1983 (in Polish).

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  5. Z. Pawlak, Rough Sets. Theoretical Aspects of Reasoning about Data., Kluwer Academic Publisher, Dordrecht, 1991.

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  6. J. Pomykala, J.A. Pomykala, The Stone Algebra of Rough Sets, Bull. Pol.Ac.:Math., vol. 36 (1988), pp. 495–508.

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  7. H. Rasiowa, R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa, 1970.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Applied Logic, University of Opole, Opole, Poland

    Zbigniew Bonikowski

Authors
  1. Zbigniew Bonikowski
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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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Cite this paper

Bonikowski, Z. (1994). Algebraic Structures of Rough 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_29

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  • DOI: https://doi.org/10.1007/978-1-4471-3238-7_29

  • 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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