Abstract: By now, the positivcbased attribute reduction is one of the most popular algorithms for attribute reduction.Some inconsistent objects may be present in the real world decision tables. And with the decrease of the number of attributes during the process of reduction, some new inconsistent objects may also occur in the decision tables. For a positivcbased attribute reduction algorithm, the inconsistent objects can not provide any useful information. I}herefore, dcleting those objects from the decision table will not change the results of positive regions, and the final result of reduction. Moreover, this operation may improve the efficiency of the algorithm obviously. However, most of the current positivcbased attribute reduction algorithms have not concerned this problem. I}hcy use all objects in the domain to calculate the positive regions and obtain the results of reduction. To solve this problem, we defined the notions of reconstructing consistent decision table and reconstructing consistent decision sulrtable. The aim for introducing the two notions is to delete the inconsistent objects in the original decision table and obtain a consistent decision table during the process of reduction. By virtue of the two notions, we proposed a novel positivcbased attribute reduction algorithm. I}he experimental results on real datasets demonstrate that our algorithm can obtain smaller reducts and higher classification accuracks than the traditional algorithms. And the time complexity of our algorithm is relatively low.

Key words: Rough sets, Positive region, Attribute reduction, Inconsistent decision table, Reconstruction consistent decision table