A topological approach to rough sets from a granular computing perspective.

There are mainly four kinds of rough set models: the binary relation model, the neighborhood operator/system model, the covering model and the subset system model. While in a broad sense, all of these models are related to topological structures. For this reason, this paper selects Alexandrov topology as the fundamental structure to construct approximation operators and to investigate rough sets from a granular computing perspective. By using the notions of open-hoods and closed-hoods, two zooming extension operators, two zooming intension operators, two zooming-in operators and four zooming-out operators are defined and the composition/decomposition problems are studied. These models can be considered as a common framework of the preordered relation model, the Alexandrov neighborhood operator model and the covering model of rough sets. [ABSTRACT FROM AUTHOR]