Uncertainty measurement for interval-valued information systems

Interval-valued information systems are generalized models of single-valued information systems. Accuracy and roughness are employed to depict the uncertainty of a set under an attribute subset in a Pawlak rough set model based on equivalence classes. Information-theoretic measures of uncertainty for rough sets have also been proposed. However, there are few studies on uncertainty measurements for interval-valued information systems. This paper addresses the uncertainty measurement problem in interval-valued information systems. The concept of the similarity degree, based on the possible degree, is introduced. Consequently, the similarity relation between two interval objects are constructed by a given similarity rate θ. Based on the similarity relation, θ-similarity classes are defined. Under this definition, θ-accuracy and θ-roughness are given for interval-valued information systems, which are generalizations of the concepts accuracy and roughness for the equivalence relation-based rough set model. Moreover, an alternative uncertainty measure, called the θ-rough degree, is proposed. Theoretical studies and numerical experiments show that the proposed measures are effective and suitable for interval-valued information systems.