Rough sets based on complete completely distributive lattice

In this paper, a pair of rough approximation operators on a complete completely distributive (CCD) lattice based on an ordinary binary relation is defined. This kind of rough sets can be seen as a unified framework for the study of rough sets based on ordinary binary relations, rough fuzzy sets and interval-valued rough fuzzy set. Moreover, depending on classes of binary relations, this paper defines several classes of rough sets on CCD lattices and investigates properties of these classes. Finally, two generalized rough set models on two CCD lattices are given at the end of this paper.