Structure of Rough Approximations Based on Molecular Lattices

Generalization of rough set model is one important aspect of rough set theory study, and it is very helpful to consummate rough set theory. Developing rough set theory using algebra systems has been paid great attention, and some researchers had reported significant developments. But the base algebra systems, on which approximation operators are defined, are confined to special Boolean algebras, including set algebra and atomic Boolean lattice. This paper introduces molecular lattices as base algebra system. Based on molecules of a molecular lattice, a mapping called meta-mapping is defined. Consequently, the approximation operators, which are more general and abstract compared with approximation operators reported in some papers, are defined based on the frame of molecular lattices. The properties of the approximations are also studied.