Affiliations: School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China. wuzhengjiang@hpu.edu.cn | School of Computer Science and Technology, Southwest Jiaotong University, Chengdu 610031, China. trli@swjtu.edu.cn | College of Mathematics, Southwest Jiaotong University, Chengdu 610031, China. qinkeyun@swjtu.edu.cn | Belgian Nuclear Research Centre (SCK•CEN), Boeretang 200, 2400 Mol, Belgium. druan@sckcen.be; da.ruan@ugent.be
Note: [] Address for correspondence: School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454001, China Also working: School of Computer Science and Technology, Henan Polytechnic Unviersity, Jiaozuo 454001, China
Note: [] Also working: Department of Applied Mathematics & Computer Science, Ghent University, 9000 Gent, Belgium
Abstract: Approximation operators play a vital role in rough set theory. Their three elements, namely, binary relation in the universe, basis algebra and properties, are fundamental in the study of approximation operators. In this paper, the interrelations among the three elements of approximation operators in L-fuzzy rough sets are discussed under the constructive approach, the axiomatic approach and the basis algebra choosing approach respectively. In the constructive approach, the properties of the approximation operators depend on the basis algebra and the binary relation. In the axiomatic approach, the induced binary relation is influenced by the axiom set and the basis algebra. In the basis algebra choosing approach, the basis algebra is constructed by properties of approximation operators and specific binary relations.
