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

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