Maximum decision entropy-based attribute reduction in decision-theoretic rough set model

Decision-theoretic rough set model, as a probabilistic generalization of the Pawlak rough set model, is an effective method for decision making from vague, uncertain or imprecise data. Attribute reduction is one of the most important problems in the decision-theoretic rough set model and several uncertainty measures for attribute reduction have been presented. However, the monotonicity of the uncertainty measures does not always hold. In this paper, a novel monotonic uncertainty measure is introduced for attribute reduction in the decision-theoretic rough set model. More specifically, based on the concepts of the maximum inclusion degree and maximum decision, a new uncertainty measure, named maximum decision entropy, is first proposed, and the definitions of the positive, boundary and negative region preservation reducts are then provided by using the proposed uncertainty measure. Theoretically, it is proved that the proposed uncertainty measure is monotonic when adding or deleting the condition attributes. Additionally, a heuristic attribute reduction algorithm based on the maximum decision entropy is developed, which maximizes the relevance of the reduct to the class attribute and also minimizes the redundancy of the condition attributes within the reduct. The experimental results on artificial as well as real data sets demonstrate the competitive performance of our proposal in comparison with the state-of-the-art algorithms.