Variable Precision Rough Set Approximations in Concept Lattice

The notions of variable precision rough set and concept lattice are can be shared by a basic notion, which is the definability of a set of objects based on a set of properties. The two theories of rough set and concept lattice can be compared, combined and applied to each other based on definability. Based on introducing the definitions of variable precision rough set and concept lattice, this paper shows that any extension of a concept in concept lattice is an equivalence class of variable precision rough set. After that, we present a definition of lower and upper approximations in concept lattice and generate the lower and upper approximations concept of concept lattice. Afterwards, we discuss the properties of the new lower and upper approximations. Finally, an example is given to show the validity of the properties that the lower and upper approximation have.