Abstract: Based on multi-set，an expansion is made on the domain of probabilistic rough set model in the sense of Z.Pawlak rough sets.Multiple probabilistic rough set models are put forward.Their corresponding definitions，theorems and properties are fully described，which include definitions of multiple domain，definitions of multiple probabilistic rough approximate sets and proofs of their important properties，definitions of approximation accuracy，definable sets and attribute reduction of multiple probabilistic rough sets，relations among rough approximation operators in multiple rough sets and relations between Z.Pawlak rough sets and multiple probabilistic rough sets.Multiple probabilistic rough sets 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 having incomplete or statistical properties.

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

摘要： 基于多重集合，对Z.Pawlak粗集意义下的概率粗糙集模型的论域进行了扩展，提出了基于多重集的概率粗糙集模型，即多重概率粗糙集模型，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、多重概率粗糙近似集的定义及其各种性质的证明、多重概率粗糙集的近似精度定义、可定义集与属性约简的定义、多重集意义下的粗糙近似算子之间的关系及其与Z.Pawlak意义下的粗糙近似算子之间的关系等。多重概率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、多对多依赖性的且具有不完全性或存在统计性的数据中挖掘知识。

关键词: 知识发现, 粗糙集, 多重粗糙集, 多重概率粗糙集, 概率粗糙集, 多重集