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Generalization of Pawlak's rough approximation spaces by using delta beta-open sets
Faculty
Science
Year:
2012
Type of Publication:
Article
Pages:
1094-1105
Authors:
Abu-Donia, H. M, Salama, A. S
DOI:
10.1016/j.ijar.2012.05.001
Journal:
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING ELSEVIER SCIENCE INC
Volume:
53
Research Area:
Computer Science
ISSN
ISI:000307803000011
Keywords :
Topological spaces, Rough sets, beta-Rough sets, beta-Open sets, delta beta-Open sets, Accuracy measure
Abstract:
The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of objects using an equivalence relation on the universe of his approximation space. This paper extends Pawlak's rough set theory to a topological model where the set approximations are defined using the topological notion delta beta-open sets. A number of important results using the topological notion delta beta-open set are obtained. We also, proved that some of the properties of Pawlak's rough set model are special instances of those of topological generalizations. Moreover, several important measures, related to the new model, such as accuracy measure and quality of approximation are presented. (C) 2012 Elsevier Inc. All rights reserved.
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