Cost-sensitive three-way class-specific attribute reduction.

The theory of rough sets provides a method to construct three types of classification rules, leading to three-way decisions. From such a point of view, we introduce the concept of cost-sensitive three-way class-specific attribute reducts. Based on the semantics of the three-way decisions, we introduce a monotonic result cost in decision-theoretic rough set model, called the result cost of three-way decisions. We provide a critical analysis of classification-based attribute reducts from result-cost-sensitive and test-cost-sensitive perspectives. On this basis, we propose class-specific cost-sensitive attribute reduction approaches. More specifically, we define a class-specific minimum cost reduct. The objective of attribute reduction is to minimize result cost and test cost with respect to a particular decision class. We design two algorithms for constructing a family of class-specific minimum cost reducts based on addition–deletion strategy and deletion strategy, respectively. The experimental results indicate that the result cost of three-way decisions is monotonic with respect to the set inclusion of attributes and the class-specific minimum cost reducts can make a better trade-off between misclassification cost and test cost with respect to a particular decision class.