A robust approach to attribute reduction based on double fuzzy consistency measure

Attribute reduction with fuzzy rough sets is to obtain a compact and informative attribute subset from the original attribute set, in which the construction of the attribute evaluation function is a crucial issue. The existing evaluation functions are mainly based on the lower approximation, which ignore the discernment samples provided by the upper approximation or boundary information characterized by the two approximations. It is necessary to simultaneously mine the valuable information in upper and lower approximations from the absolute quantitative perspective and in the boundary from the relative quantitative perspective, which is helpful to comprehensively characterize the consistency and difference between attributes and decisions. In this paper, we first propose a double fuzzy consistency measure (DFCM) based on the two kinds of information described by fuzzy upper and lower approximations to evaluate the importance of attributes for learning tasks. By the mutual proximity of two approximations with the gradual increase of attributes, the measure DFCM is monotonically decreasing to attributes, which can be used to describe the consistency and difference between conditional and decision attributes. Meanwhile, attribute reduction model and algorithm based on the measure are developed. Finally, the detailed experimental comparisons indicate that the double fuzzy consistency measure based attribute reduction method can achieve effective and robust classification performance by grabbing fewer attributes with discernment information.