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To deal with attribute reduction in incomplete information systems, this paper proposed a direct method of attribute relative reduction based on rough set theory. This reduction algorithm gives the concept of tolerance relationship similar matrix via extending equivalence relationship of rough set theory, which is called tolerance relationship. It introduces the generalized decision function to solve the problem of inconsistency in the incomplete information system. This algorithm uses the tolerance relationship similar matrix to calculate the core attributes of incomplete information systems. It applies attribute significance, which this paper puts forward based on attribute frequency in the tolerance relationship similar matrix, as the heuristic knowledge. And it makes use of binsearch heuristic algorithm to calculate the candidate attribute expansion so that it can reduce the expansion times to speed up reduction. Experiment results show that the algorithm is simple and effective.

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