Three-Way Approximate Criterion Reduction in Multi-Criteria Decision Analysis.

Attribute reduction is one of the major topics in rough set theory. The purpose of attribute reduction is to reduce the dimensionality of data. In multi-criteria decision analysis, criteria are treated as multiple and possibly conflicting points of views on decision alternatives. To reduce the complexity of multi-criteria decision analysis, we raise the problem of criterion reduction. In this paper, we propose the formal definition of criterion reduction and develop a heuristic method to deal with it. At first, we review the definitions of attribute reduction in rough set theory, generalized attribute reduction, and approximate attribute reduction. Then, we discuss the problem of criterion reduction in multi-criteria decision analysis. More specifically, we introduce three-way decision theory and define three-way approximate criterion reducts via a pair of thresholds. Finally, we adopt the point-wise loss function and propose heuristic algorithms to generate three-way approximate criterion reducts. A real-world data set of city rankings is used to validate the proposed method.