In an ordered decision information system, the consistent reduct, which is the minimal condition attribute subset keeping the set of consistent objects in the original information system invariant, is proposed. Then, it is proved that the consistent reduct is actually a L-reduct as well as a Q-reduct. Finally, the discernibility function of the consistent reduct is constructed, and used to compute the consistent reduct by using Boolean reasoning techniques. By discussing the consistent reduct, we get a new computing method which employs discernibility function for Q-redut.
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