Rough set theory and attribute reduction in interval-set information system

As an extension of traditional information systems, interval-set information systems have a strong expressive ability to describe uncertain information. Study of the rough set theory and the attribute reduction of interval-set information system are worth discussing. Here, the granularity structure of similar equivalence classes in an interval-set information system is mined, and an attribute reduction algorithm is constructed. The upper and lower approximation operators in the interval-set information system are defined. The accuracy and roughness are determined by these operators. At the same time, using rough sets, a concept of three branches of rough sets on the interval-set information system is constructed. The concepts of attribute dependency and attribute importance are induced by the positive number domain of the three branch domains, and they then lead to the attribute reduction algorithm. Experiments on the UCI datasets show that the uncertainty measure proposed in this paper is sensitive to the attributes and can effectively reduce redundant information of the interval-set information system.