中文摘要：

粒结构是粒计算理论中信息粒及其相互关系的表现形式,为了描述不同形式的粒结构并对不同粒结构之间的差异性进行量化表示,可以借用知识距离的概念,但传统的知识距离是依赖粒结构本身形式构建的,它并不能用于刻画基于粒结构的粗糙近似之间的差异性.为解决这一问题,借助粗糙集模型,提出了粗糙上近似距离、粗糙下近似距离以及粗糙距离的概念,不仅分析了这些距离的内在关系,而且还揭示了所提出的距离与粗糙近似集之间的相关性.理论结果从度量差异性的层面丰富了粗糙集理论.

英文摘要：

Granular structure is an expression for information granulations and the corresponding relationships in the theory of Granular Computing. To describe different forms of granular structures and measure the differences between two granular structures,the concept of knowledge distance can be employed. Nevertheless,traditional knowledge distance is constructed based on the forms of granular structures; it cannot be used to characterize the difference between rough sets based on granular structures. To solve such problem,the concepts of rough lower approximate distance,rough upper approximate distance and rough distance are proposed by employing the basic model of rough set. Not only the relationships among these three distances are analyzed,but also the relationships between these distances and rough approximations are addressed. The theoretical results obtained enrich the rough set model from the viewpoint of measurement of difference.