QFIG: A novel attribute reduction method using conditional entropy in quantified fuzzy approximation space

Abstract

At present, attribute reduction based on different attribute importance measures is one of the hot topics in granular computing. Conditional entropy is a common measure to evaluate the importance of attributes in classification tasks. This paper proposes a conditional entropy based on quantified fuzzy information granular and constructs a novel attribute reduction method. First, a quantified fuzzy similarity relation is explored to overcome the instability of the existing parameterized fuzzy relations. The quantified fuzzy information granular (QFIG) induced by the defined relation and their related properties are also discussed. Second, a new QFIG-based fuzzy rough set model and its properties are proposed. Meanwhile, a general framework of the proposed fuzzy rough approximation operators is established. Third, we construct a QFIG-based conditional entropy for evaluating the importance of attributes in decision information systems. At the same time, the corresponding attribute reduction algorithm is designed based on heuristic reduction strategy. Finally, the performance of the proposed algorithm is demonstrated by numerical comparison experiments on twelve public datasets. Experimental results not only confirm the effectiveness of the proposed algorithm but also show that the performance of the proposed algorithm is better than that of some existing attribute reduction algorithms.