Abstract: Rough sets theory is a recent approach for reasoning about data.It deals with the approximation of a subset of a universe by two definable subsets called lower and upper approximation.Since rough sets theory is proposed by Pawlak，various generalization of rough set lower and upper approximation is given.The paper studies the characteristic function representation of rough sets using two distinct but related universes.Unify characteristic function form of lower and upper approximation is given.The structure of rough sets is also investigated.

摘要： 粗集理论是处理不精确和不确定的数据的工具，自Pawlak 提出了粗集理论后，粗集模型得到拓广，人们提出了许多新的粗集模型，在用特征函数的方法表示上下近似的基础上研究两个论域上的粗集结构。统一了粗集的各种推广模型，使得特征函数的方法与通常的集合论的方法形成互补，对粗集结构的简化及推理有帮助，可以加深对粗集结构的认识。