Topological Structures of Rough Sets Induced by Equivalence Relations

Michiro Kondo; Wieslaw A. Dudek

doi:10.20965/jaciii.2006.p0621

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JACIII Vol.10 No.5 pp. 621-624

doi: 10.20965/jaciii.2006.p0621

(2006)

Paper:

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Topological Structures of Rough Sets Induced by Equivalence Relations

Michiro Kondo^* and Wieslaw A. Dudek^**

^*School of Information Environment, Tokyo Denki University, Inzai 270-1382, Japan

^**Institute of Mathematics, Wroclaw University of Technology, Wroclaw 50-370, Poland

Received:

January 20, 2006

Accepted:

February 24, 2006

Published:

September 20, 2006

Keywords:

rough sets, topology

Abstract

In this paper we consider some fundamental topological properties of rough sets induced by equivalence relations and show that 1. Every approximation space is retrieval. 2. For every approximation space X=(X,θ), X is strongly connected if and only if θ=X×X. Moreover we consider topological properties of generalized rough sets.

Cite this article as:

M. Kondo and W. Dudek, “Topological Structures of Rough Sets Induced by Equivalence Relations,” J. Adv. Comput. Intell. Intell. Inform., Vol.10, No.5, pp. 621-624, 2006.

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References

[1] R. Biwas and S. Nandas, “Rough groups and rough subgroups,” Bull. Pol. Ac. Math., Vol.42, pp. 251-254, 1994.
[2] W. A. Dudek, Y. B. Jun, and H. S. Kim, “Rough set theory applied to BCI-algebras,” Quasigroups and Related Systems, Vol.9, pp. 45-54, 2002.
[3] T. B. Iwinski, “Algebraic approach to rough sets,” Bull. Pol. Ac. Math., Vol.35, pp. 673-683, 1987.
[4] N. Kuroki, “Rough ideals in semigroups,” Information Sciences, Vol.100, pp. 139-163, 1997.
[5] N. Kuroki and J. N. Mordeson, “Structures of rough sets and rough groups,” Jour. Fuzzy Math., Vol.5, pp. 183-191, 1997.
[6] Z. Pawlak, “Rough sets,” Int. J. Inform. Comp. Sci., Vol.11, pp. 341-356, 1982.

[1] [1] R. Biwas and S. Nandas, “Rough groups and rough subgroups,” Bull. Pol. Ac. Math., Vol.42, pp. 251-254, 1994.

[2] [2] W. A. Dudek, Y. B. Jun, and H. S. Kim, “Rough set theory applied to BCI-algebras,” Quasigroups and Related Systems, Vol.9, pp. 45-54, 2002.

[3] [3] T. B. Iwinski, “Algebraic approach to rough sets,” Bull. Pol. Ac. Math., Vol.35, pp. 673-683, 1987.

[4] [4] N. Kuroki, “Rough ideals in semigroups,” Information Sciences, Vol.100, pp. 139-163, 1997.

[5] [5] N. Kuroki and J. N. Mordeson, “Structures of rough sets and rough groups,” Jour. Fuzzy Math., Vol.5, pp. 183-191, 1997.

[6] [6] Z. Pawlak, “Rough sets,” Int. J. Inform. Comp. Sci., Vol.11, pp. 341-356, 1982.

Topological Structures of Rough Sets Induced by Equivalence Relations

Michiro Kondo* and Wieslaw A. Dudek**

Michiro Kondo^* and Wieslaw A. Dudek^**