Abstract
The traditional rough set (RS) theory is a powerful tool to deal with complete information system, and its performance to process incomplete information system is weak, especially, its effect of combining the incomplete information system with fuzzy objective information system is weaker. The paper improves the tolerance relation proposed by M.Kryszkiewcz to obtain the γ− tolerance relation and γ− tolerance classes, presents the concept of the incomplete and fuzzy objective information system (IFOIS in short), and gives its rough set model based on the γ− tolerance relation, i.e., the rough set model in incomplete and fuzzy objective information system. Finally, the concept of precision reduction is defined, and the corresponding algorithm is provided.
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