Rough and rough fuzzy sets on two universes via covering approach

Article type: Research Article

Authors: Mareay, R.^*

Affiliations: Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt

Correspondence: [*] Corresponding author. R. Mareay, Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt. Tel.: +20473215174; Fax: +20473215175; E-mail: [email protected].

Abstract: Rough set theory is an important non-numeric method for dealing with uncertainty and data mining. In this paper, we study rough sets and rough fuzzy sets on two universes via covering models. We introduce a new definition for the lower and upper approximation by taking a covering of the second universe of discourse. Some properties of the new model are revealed. We believe that this model will be more realistic in the sense that rough sets (resp. rough fuzzy sets) are approximated by sets (resp. fuzzy sets) on the same universe. Moreover, some results, examples and counter examples are provided.

Keywords: Rough sets, covering, approximation space, strong covering, rough fuzzy sets

DOI: 10.3233/IFS-151837

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1139-1146, 2016