Attribute reduction algorithm for incomplete decision table based on attribute discernibility

Proposed in this paper is a novel attribute reduction algorithm based on the attribute discernibility to reduce the high computational complexity of the existing attribute reduction algorithms for incomplete decision tables. In the investigation, the external manifestation of condition attribute significance relative to the decision attribute in incomplete decision tables is analyzed, the attribute discernibility is defined, and the calculating method of dynamic update of attribute discernibility with the change of reduction subset is proposed. During the attribute reduction, the algorithm continuously deletes the objects belonging to the positive domain or the consistent blocks having no effect on the positive domain calculation. Thus, the data scale and the time consumption decreases, and the attribute reduction quickens. Theoretical analyses and simulation experiments demonstrate that the proposed attribute reduction algorithm for incomplete decision tables is effective and is superior to the existing algorithms in terms of time complexity.