Decision region distribution preservation reduction in decision-theoretic rough set model

In the Pawlak rough set model, the positive region, the boundary region and the non-negative region are monotonic with respect to the set inclusion of attributes. However, the monotonicity property of the decision regions (positive region, boundary region or non-negative region) with respect to the set inclusion of attributes does not hold in the decision-theoretic rough set model. Therefore, the decision regions may be changed after attribute reduction based on quantitative preservation or qualitative preservation of decision regions. This effect is observed partly because three decision regions are defined by introducing the probabilistic threshold values. In addition, heuristic reduction algorithms based on decision regions may find super reducts because of the non-monotonicity of decision regions. To address the above issues, this paper proposes solutions to the attribute reduction problem based on decision region preservation in the decision-theoretic rough set model. First, the (α,β)(α,β) positive region distribution preservation reduct, the (α,β)(α,β) boundary region distribution preservation reduct and the (α,β)(α,β) negative region distribution preservation reduct are introduced into the decision-theoretic rough set model. Second, three new monotonic measures are constructed by considering variants of the conditional information entropy, from which we can obtain the heuristic reduction algorithms. The results of the experimental analysis validate the monotonicity of new measures and verify the effectiveness of decision region distribution preservation reducts.