摘要： 在不完备信息系统和模糊目标信息系统的基础上，将不完备近似空间和模糊目标信息系统有机地结合起来，提出了不完备模糊目标信息系统的概念；同时还给出了不完备模糊目标信息系统的粗糙集模型，该模型是完备模糊目标信息系统和经典目标信息系统粗糙集模型的推广。还给出了系统知识约简的一些相关概念及其辨识矩阵的知识约简方法。

关键词: 粗糙集；相容关系；不完备信息系统；模糊目标信息系统；知识约简

Abstract: This paper proposes the concept of incomplete and fuzzy objective information systems based on incomplete approximation space and fuzzy objective information system, and gives the rough set model of incomplete and fuzzy objective information systems by the tolerance relation. The model is not equivalent to the rough set model of incomplete information system or fuzzy objective information system in complete space, but is the generalization of the rough set model of fuzzy objective information system in complete space and of the rough set model of incomplete information system. The related concepts of knowledge reduction and the methods for discernibility matrix of knowledge reduction are presented,and the simple algorithm of the knowledge reduction is obtained.

Key words: Rough set; Tolerance relation; Incomplete information system; Fuzzy objective information system; Knowledge reduction