Concept granular computing systems and their approximation operators

In this paper, three kinds of adjoint extent-intent and intent-extent operators between two complete lattices are constructed. Three new types of concept granular computing systems are then formulated via a quadruple including two complete lattices and the corresponding adjoint operators. It is showed that all the concepts in any of the concept granular computing systems form a complete lattice. Furthermore, based on the four types of concept granular computing systems, we present four types of rough set approximation operators in a formal context which can characterize different aspect of knowledge. Some important properties of the proposed approximation operators are also proved.