A New Approach to Rough Set Based on Remote Neighborhood Systems

The notion of neighborhood systems is abstracted from the geometric notion of “near”, and it is primitive in the theory of topological spaces. Now, neighborhood systems have been applied in the study of rough set by many researches. The notion of remote neighborhood systems is initial in the theory of topological molecular lattice, and it is abstracted from the geometric notion of “remote”. Therefore, the notion of remote neighborhood systems can be considered as the dual notion of neighborhood systems. In this paper, we develop a theory of rough set based on remote neighborhood systems. Precisely, we construct a pair of lower and upper approximation operators and discuss their basic properties. Furthermore, we use a set of axioms to describe the lower and upper approximation operators constructed from remote neighborhood systems.