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On Convergence of Rough Sets

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Part of the book series: Theory and Decision Library ((TDLD,volume 11))

Abstract

Various considerations of analysis of knowledge by means of rough sets lead to the following situation: we are given a universe U along with a descending sequence of equivalence relations. We propose metrics for rough sets that make them into a complete metric space; the metric convergence encompasses and generalizes approximative convergence studied by Marek, Pawlak and Marek, Rasiowa.

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References

  1. Hausdorff F., Grundzuge der Mengenlehre, Leipzig (Vien), 1914.

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  2. Kuratowski K., Topology I, Warszawa, 1966.

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  3. Marek W., Pawlak Z., Information systems and rough sets, Fund.Inform.VIII (1984), 105–115.

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  4. Marek W., Rasiowa H., Approximating sets with equivalence relations, Theoretical Computer Sc. 48 (1986), 145–152

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  5. Pawlak Z., Rough sets: Theoretical Aspects of Reasoning About Data, Kluver 1991.

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  6. Pawlak Z., Rough sets, International J. Computer and Information Sciences 11 (1982), 341–356

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© 1992 Springer Science+Business Media Dordrecht

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Polkowski, L.T. (1992). On Convergence of Rough Sets. In: Słowiński, R. (eds) Intelligent Decision Support. Theory and Decision Library, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7975-9_19

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  • DOI: https://doi.org/10.1007/978-94-015-7975-9_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4194-4

  • Online ISBN: 978-94-015-7975-9

  • eBook Packages: Springer Book Archive

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