Abstract: Based on multi-set，an expansion is made on the domain of Z.Pawlak rough sets，a multiple rough sets theory is put forward，its corresponding definitions，theorems and properties are fully described，which include the definitions of multiple domain，object and its states and significance，the object transferring method between multiple rough sets and Z.Pawlak rough sets，the definitions of multiple approximate sets and proofs of their properties，the definitions of multiple equivalence classes and their member relations and proofs of their properties，reduction of properties and decision analysis based on multiple rough sets，and so on.These definitions，theorems and properties have not only difference but also relation between multiple rough sets and Z.Pawlak rough sets.Multiple rough sets can fully describe overlap among knowledge particles，difference of significance among objects and polymorphism of objects，and can conveniently execute many kinds of operations among states of objects，these advantages can provide great convenience for mining knowledge lurking in a relation database.

Key words: knowledge discovery, rough sets, multiple rough sets, multi-set

摘要：

基于多重集合，对Z.Pawlak粗糙集的论域进行了扩展，提出了基于多重粗糙集理论，并给出了该理论相关内容的完整定义、定理和性质，其中包括多重论域定义、论域对象及其状态与重要度的定义与标识、多重粗糙集对象与Z.Pawlak粗糙集对象的相互转换方法、多重近似集的定义及其性质的证明、多重等价类及其成员关系的定义与性质的证明、多重粗糙集的属性约简与决策分析等内容。这些定义、定理和性质与Z.Pawlak粗糙集既有区别又有联系。多重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，可以很方便地实现对象状态间的各种运算，这些特性可为挖掘潜藏在关系数据结构中的知识提供方便。

关键词: 知识发现, 粗糙集, 多重粗糙集, 多重集