Affiliations: [a]
School of Sciences, Hebei University of Science and Technology, Shijiazhuang, China
| [b]
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
Correspondence:
[*]
Corresponding author. Wei Yao, School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China. E-mail: [email protected].
Abstract: Let L be a commutative unital quantale. For every L-fuzzy relation E on a nonempty set X, we define an upper rough approximation operator on LX, which is a fuzzy extension of the classical Pawlak upper rough approximation operator. We show that this operator has close relation with the subsethood operator on X. Conversely, by an L-fuzzy closure operator on X, we can easily get an L-fuzzy relation. We show that this relation can be characterized by more smooth ways. Without the help of the lower approximation operator, L-fuzzy rough sets can still be studied by means of constructive and axiomatic approaches, and L-fuzzy similarities and L-fuzzy closure operators are one-to-one corresponding. We also show that, the L-topology induced by the upper rough approximation operator is stratified and Alexandrov.
