Attribute reduction, also known as feature selection, is a vital application of rough set theory in areas such as machine learning and data mining. With several information systems constantly and dynamically changing in reality, the method of continuing the incremental attribute reduction for these dynamic information systems is the focus of this research. In an incomplete information system, the increasing form of attribute sets is an important form of dynamic change. In this paper, the definition of conditional entropy is first introduced in the incomplete information system, and for the circumstances of the dynamic change of the attribute sets, two types of incremental mechanisms of the matrix and non-matrix forms based on conditional entropy are subsequently proposed. In addition, on the basis of the two incremental mechanisms, the incremental attribute reduction algorithm is given when the attribute set increases dynamically. Finally, the experimental results of the UCI (University of California Irvine) datasets verify that the two proposed incremental algorithms exhibit a superior performance with regard to attribute reduction when compared with the non-incremental attribute reduction algorithm, which in turn is superior to other relative incremental algorithms.
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