Covering-based rough fuzzy sets and binary relation

  • Authors:
  • A. M. Kozae;S. A. El-Sheikh;R. Mareay

  • 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

  • Venue:
  • Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
  • Year:
  • 2014

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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.