Approximation operators on complete completely distributive lattices

Rough set, a tool for data mining, deals with the vagueness and granularity in information systems. In 2006, Chen et al. initiated the study of rough approximations on a complete completely distributive lattice (CCD lattice for short) and brought generalizations of rough sets into a unified framework. In this paper, we discuss the approximation operators on a CCD lattice. Based on the concept of neighborhood, three kinds of upper approximation operators and a kind of lower approximation operator are constructed. Basic properties of lower and upper approximation operators are examined. Furthermore, the relationships among these operators are analyzed.