Affiliations: [a]
College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China | [b]
Department of Applied Mathematics, Yuncheng University, Yuncheng, P.R. China
Correspondence:
[*]
Corresponding author. Qingguo Li, College of Mathematics and Econometrics, Hunan University, Changsha 410082, P.R. China. E-mail: liqingguoli@aliyun.com.
Abstract: Consider L = (L, ∗ , 1) be a complete residuated lattice. For an arbitrary function φ defined from the set of all singletons to that of all L-sets, Chen and Li introduced a type of L-fuzzy rough sets in 2007, called φ-fuzzy rough sets in this paper. The well-known R-fuzzy rough sets, where R is an L-fuzzy relation, can be regarded as a special φ-fuzzy rough sets. In this paper, we prove that φ-fuzzy rough sets can be represented by a family of R-fuzzy rough sets. Then we define some special φ of being serial, reflexive, symmetric, transitive and Euclidean, and discuss the corresponding φ-fuzzy rough sets, respectively. At last, we study the induced L-topology by φ when it is reflexive or reflexive and transitive.
