Abstract: The uncertainty of objects is considered in the incomplete information system. Based on the uncertainty of objects,the method in which lower and upper approximation are fuzzed,i. e.，the lower and upper approximation is a pair of fuzzy sets, was discussed in the incomplete information system. Onc hand, lower and upper approximations arc decided by the similarity relation;on the other hand,the objects with uncertainty due to“、”is existent Therefore, the uncertainty degree of an object and similarity degree among the objects were defined. Then the membership degree of the object belonging to lower and upper approximation was given by similarity degree. Formally,the process is considered as fuzzed of the lower and upper approximation sets. Finally, an example shows that membership degrees more visualy and reasonably describe that objects belong to the lower and upper approximation of the set.

Key words: Incomplete information system, Rough set, Fuzz set, Similarity relations, Similar degree, Membership degree