JACIII Vol.10 No.5 pp. 621-624
doi: 10.20965/jaciii.2006.p0621


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

January 20, 2006
February 24, 2006
September 20, 2006
rough sets, topology

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:
Michiro Kondo and Wieslaw A. Dudek, “Topological Structures of Rough Sets Induced by Equivalence Relations,” J. Adv. Comput. Intell. Intell. Inform., Vol.10, No.5, pp. 621-624, 2006.
Data files:
  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.

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Last updated on Mar. 01, 2021