The Single Axiomatization on CCRL-Fuzzy Rough Approximation Operators and Related Fuzzy Topology

Abstract

It is well known that lattice-valued rough sets are important branches of fuzzy rough sets. The axiomatic characterization and related topology are the main research directions of lattice-valued rough sets. For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on the basis of the L-fuzzy relation. In this article, we give a further study on Qiao’s LFLAO around the axiomatic characterization and induced L-topology. Firstly, we investigate and discuss three new LFLAO generated by ⊛-transitive, ⊛-Euclidean and ⊛-mediated L-fuzzy relations. Secondly, we utilize a single axiom to characterize the LFLAO generated by serial, symmetric, reflexive, ⊛-transitive and ⊛-mediate L-fuzzy relations and their compositions. Thirdly, we present a method to generate Alexandrov L-topology (ALTPO) from LFLAO and construct a bijection between ALTPO and ⊛-preorder (i.e., reflexive and ⊛-transitive L-fuzzy relation) on the same underlying set.