Abstract: In order to solve the problem that the domain partition of Zaike variable precision rough set can not overlap, an expansion was made on the domain of Zaike variable precision rough set based on multi-set, a multiple variable precision rough set model was put forward, and its corresponding definitions, theorems and properties were fully described, which included definitions of multiple domain and multiple variable precision approximate sets, proofs of their properties, and relations between multiple Zaike variable precision rough set and multiple variable precision rough set. These definitions, theorems and properties have not only differences but also relations between multiple variable precision rough set and Zaike variable precision rough set. Multiple variable precision rough set can fully describe overlap among knowledge particles, difference of significance among objects and polymorphism of objects, and can conveniently find associated knowledge from data saved in a relation database, having one-to-many and many-to-many dependency, and thought to have no relations.

Key words: knowledge discovery, rough set, multiple rough set, variable precision rough set, multi-set

摘要： 为了解决Zaike变精度粗糙集模型的论域划分不能重叠的问题，基于多重集合，对Zaike变精度粗糙集模型的论域进行了扩展，提出了基于多重集的多重变精度粗糙集模型，给出了该模型的完整定义、相关定理和重要性质，其中包括多重论域定义、多重变精度近似集的定义及其性质的证明、与Zaike变精度粗糙集的关系等。这些定义、定理和性质与Zaike变精度粗糙集既有区别又有联系。多重变精度粗糙集可充分反映知识颗粒间的重叠性，对象的重要度差别及其多态性，这样有利于用粗糙集理论从保存在关系数据库中的具有一对多、多对多依赖性的且认为不相关的数据中发现相关知识。

关键词: 知识发现, 粗糙集, 多重粗糙集, 变精度粗糙集, 多重集