Approaches to Knowledge Reduction in Interval-Valued Information Systems

Knowledge reduction is an important problem of rough set theory. The notion of a reduction plays an essential role in analyzing an information system. A reduction is a minimum subset of attributes that can provide the same descriptive or classification ability as the full set of available attributes. In other words, attributes in a reduction are jointly sufficient and individually necessary in an information system. Original knowledge reduction in Pawlak’s rough set theory is mainly based on single-valued information systems. However, there always exist interval numbers in a lot of information systems in reality. Thus, knowledge reduction in interval-valued information systems has been a hot issue in the related area in recent years. Although some research works for knowledge reduction in interval-valued information systems have been done, there are still critical problems, such as redundancy of classification results and low accuracy of rough approximation to be dealt with. Aiming at the existing problems, the authors introduce the α-maximal consistent class into interval-valued information systems to improve the accuracy of knowledge classification and rough approximation. A novel measurement for the similarity degree of different interval numbers is proposed in this paper. Furthermore, to simplify knowledge representation, the authors present the methods for constructing the discernibility matrix and attribute reduction in interval-valued information systems or decision systems. Finally, the latent knowledge can be discovered by knowledge reduction.