关键词: 知识发现, 粗糙集, 多重粗糙集, 多重集

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