A fuzzy α-similarity relation-based attribute reduction approach in incomplete interval-valued information systems

As generalizations of single-valued information systems, interval-valued information systems (IVISs) can better express the real data with uncertainty in some applications. Attribute reduction methods for complete IVISs or complete interval-valued decision systems (IVDSs) have been developed. However, there are few researches on attribute reduction for incomplete interval-valued information systems (IIVISs). The paper aims to investigate the attribute reduction issue in IIVISs. Firstly, the maximal and minimal distances, which characterize the difference between two interval values, are defined, and the maximal and minimal similarity degrees are given. Secondly, the fuzzy α-similarity relation is defined based on similarity between interval values, and the concept of α-equivalence relation is raised. Thirdly, entropy measures are investigated for IIVISs in view of α-equivalence relations. Fourthly, a new attribute reduction approach for IIVISs is proposed by using conditional entropy, and its corresponding algorithm is given. Finally, experiments to verify the effectiveness and feasibility of the newly proposed approach for attribute reduction in IIVISs are presented. These results will be helpful to perfect the uncertainty measurement model, and provide an approach for attribute reduction in IIVISs.