Authors: A.S. Salama; O.G. El-Barbary
Addresses: Mathematics Department, Faculty of Science, Tanta University, P.O. Box 20, Tanta, 31527, Egypt; Faculty of Science, Shaqra University, P.O. Box 18, Al-Dawadmi, 11911, Saudi Arabia ' Statistics and Computer Science Department, Faculty of Science, Tanta University, P.O. Box 20, Tanta, 31527, Egypt
Abstract: In this paper, we generalise Pawlak's approximation spaces to topological approximation spaces. These topological approximation spaces are generated using many topological notions such as regular open sets, semi-open sets, pre-open sets, γ-open sets, α-open sets and β-open sets and others. The basic definitions and properties of these topological approximation spaces are introduced and sufficiently illustrated. We put all topological generalisations in one generalisation called m-generalisation spaces.
Keywords: topological spaces; rough sets; rough approximations; information systems; data reduction; approximation spaces.
International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2013 Vol.3 No.1, pp.1 - 19
Received: 02 Apr 2012
Accepted: 24 Sep 2012
Published online: 22 May 2013 *