Abstract: In recent years, the research on multi-granulation rough set has become one of hot research. Firstly, this paper defines support function and discusses the properties of support function. Secondly, this paper proposes the generalized multi-granulation rough set model by using support function, defines the upper and lower approximation operators? and discusses the properties of the approximation operators. What’s more, this paper studies the measure and properties of generalized multi-granulation rough set in ordered information system, as well as the relationship of generalized multi-granulation rough set approximation operators and multi-granulation rough set approximation operators in ordered information system. Finally, in order to better explain the practical application value of this model, an example on student admitting in college illustrates the feasibility and efficiency of this model.

Key words: ordered information system, multi-granulation, rough set, measure

摘要： 多粒度粗糙集已成为近年来研究的热点之一。定义了支撑函数，并讨论了支撑函数的性质；通过支撑函数建立了基于序信息系统的一般多粒度粗糙集模型，给出了上下近似算子的定义，并探讨了各近似算子的性质；还研究了序信息系统一般多粒度粗糙集的度量及性质，以及序信息系统的一般多粒度粗糙集近似算子和多粒度粗糙集近似算子之间的关系。最后，为了更好地解释该模型的实际应用价值，通过高校录取学生的实例验证了该模型的实用性和有效性。

关键词: 序信息系统, 多粒度, 粗糙集, 度量