A novel roughness measure based on knowledge granulation

Roughness is an important uncertainty measure for a concept in an information system. By introducing a definition of α-knowledge granulation, a new uncertainty measure, called α-knowledge granulation based roughness (α-GKR), of a set is proposed in this paper. And then, MGKR, a special case of α-GKR measure, is deduced. It is generalized from the Pawlak´s roughness and has two significant properties. In the case that two concepts in an information system provide an identical Pawlak´s roughness, the new roughness measure for each concept depends on the corresponding partition or on the knowledge granulation of this partition. Moreover, the MGKR measure inherits the order relation from the Pawlak´s roughness. Theoretical and experimental results show that the new uncertainty measure is more precise than existing ones.