Abstract: The classical rough set theory is not useful for analyzing incomplete information system, and this problem is solved by tolerance relation, similarity relation, limited tolerance relation and completed tolerance relation to some extent. Limitations of these models were analyzed, and on the basis of the completed tolerance relation an extended rough set model based on improved complete tolerance relation was developed. The extended model not only retains the merits of the existing models, but also overcomes the limitations of the existing models to some extent. The result of case studies shows the effectiveness of the presented model.

Key words: Rough set, Incomplete information system, Tolerance relation, Similarity relation, Limited tolerance relation, Completed tolerance relation

摘要： 经典粗糙集理论不能直接处理不完备信息系统，而容差关系、相似关系限制容差关系和完备容差关系等扩充粗糙集模型在一定程度上解决了这个问题。分析了这些模型存在的局限性，并在完备容差关系的基础上，提出了基于改进的完备容差关系的扩充粗糙集模型，该模型既保留了已有模型的优点，又在一定程度上克服了它们的局限性。实例分析表明该模型对不完备信息系统的处理更符合实际情况。

关键词: 粗糙集, 不完备信息系统, 容差关系, 相似关系, 限制容差关系, 完备容差关系