Affiliations: Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt | Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt | Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh, Egypt
Note: [] Corresponding author. A.M. Kozae, Department of Mathematics, Faculty of Science, Tanta university, Tanta 31527, Egypt. E-mail: [email protected]
Abstract: Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. In this paper we study covering-based rough fuzzy sets in which a fuzzy set can be approximated by the intersection of some elements in a covering of the universe of discourse. Some properties of the covering-based fuzzy lower and upper approximation operators are examined. We present the conditions under which two coverings generate the same covering-based fuzzy lower and upper approximation. We approximate fuzzy sets based on a binary relation and its properties are introduced. Finally, we establish the equivalency between rough fuzzy sets generated by a covering and rough fuzzy sets generated by a binary relation.
Keywords: Rough set, fuzzy set, data mining, covering, approximation
