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This paper focuses on fast algorithm for computing the assignment reduct in inconsistent incomplete decision systems. It is quite inconvenient to judge the assignment reduct directly according to its definition. We propose the judgment theorem for the assignment reduct in the inconsistent incomplete decision system, which greatly simplifies judging this type reduct. On such basis, we derive a novel attribute significance measure and construct the fast assignment reduction algorithm (F-ARA), intended for computing the assignment reduct in inconsistent incomplete decision systems. Finally, we make a comparison between F-ARA and the discernibility matrix-based method by experiments on 13 University of California at Irvine (UCI) datasets, and the experimental results prove that F-ARA is efficient and feasible. [ABSTRACT FROM AUTHOR]