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...

Introduction: Communicative approximations are equivalence relations. For considering Communicative approximation, new constructs are necessary including “rough points” and “rough intervals”. “Communication about quantities is defined on a shared conventional space, which constitutes a tessellation on the real number line”. The uncertainty which results from measurement error (±η) is defined on...

Let (U ;D) be a Gr-covering approximation space (U ; C) with covering lower approximation operator D and covering upper approximation operator D. For a subset X of U , this paper investigates the following three conditions: (1)X is a definable subset of (U ;D); (2) X is an inner definable subset of (U ;D); (3) X is an outer definable subset of (U ;D). It is proved that if one of the above three...