Abstract: Attribute reductions based on generalized multi-granulation rough set are defined. Some basic properties are studied. Computation by matlab is carried out and an example is implemented. The contents include sharp consistence, soft inconsistence, granularly consistence, granularly inconsistence of a complete target information system. The reductions, granularly reductions, （lower/upper approximation） distribution consistent reductions, （lower/upper approximation） quality consistent reductions are defined and some theorems are approached. All reductions on the basis of generalized multi-granulation rough set are appropriate for optimistic and pessimistic multi-granulation rough sets. The results of the study can improve the multi-granularity rough set theory. It can also lay the foundation for theoretical research and applications.

Key words: multi-granulation rough set, generalized multi-granulation rough set, attribute reduction, Matlab computation

摘要： 定义了基于广义多粒度粗糙集的属性约简，研究了约简的一些基本性质，给出matlab计算的过程，并给出计算实例。定义了信息系统的严格协调、软不协调性、粒度协调、粒度不协调，定义了广义多粒度下约简、粒度约简、（下/上近似）分布协调约简、（下/上近似）质量协调约简，并给出部分结论。广义多粒度粗糙集的约简适用于乐观多粒度粗糙集和悲观多粒度粗糙集。研究结果可完善多粒度粗糙集理论，为理论研究和应用奠定基础。

关键词: 多粒度粗糙集, 广义多粒度粗糙集, 属性约简, Matlab计算