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This paper focuses on generalization of rough set model and rule induction. First a extension of rough set approximations is established on general granular structure, so that the rough set models on some special granular structures are meaningful. The new rough approximation operators are interpreted by topological terminology well. Conversely, by means of the new rough approximation operators, many special granular structures, such as, covering, knowledge space, topology space and Pawlak approximation space, are characterized. Furthermore, using new approximation operators, two types of decision rules can be induced.
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