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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hausdorff F., Grundzuge der Mengenlehre, Leipzig (Vien), 1914.
Kuratowski K., Topology I, Warszawa, 1966.
Marek W., Pawlak Z., Information systems and rough sets, Fund.Inform.VIII (1984), 105–115.
Marek W., Rasiowa H., Approximating sets with equivalence relations, Theoretical Computer Sc. 48 (1986), 145–152
Pawlak Z., Rough sets: Theoretical Aspects of Reasoning About Data, Kluver 1991.
Pawlak Z., Rough sets, International J. Computer and Information Sciences 11 (1982), 341–356
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
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