Rough Set Theory Based on Two Relations and Its Applications

Document Type : Original Article

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Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafr El-Sheikh University, Kafr El-Sheikh, Egypt.

Abstract

Abstract
Rough sets theory was introduced by Pawlak in the early 80's and has reached a level of high visibility and maturity. In recent year's we have witness diverse as well as widespread research in rough sets theory and its applications worldwide. In this paper, we introduce a new approximation space (biapproximation space) and define the lower and upper approximation based on two relations to take advantages of two relations in the same time. With this approximation and our definitions, we present two concepts to calculate the size of boundary region and discuss some of the basic properties of them. Examples are provided to illustrate the behavior of this new notion. Compared with Pawlak approximation space, our new approximation space is very efficient and settable when we have a lot of data for one case.

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