Attribute reducts of multi-granulation information system

In recent years, more and more methods and theories of multi-granulation information systems have been explored. However, there is very limited investigation on the attribute reducts of multi-granulation rough sets. Therefore, the main objective of this paper is to draw attention to the attribute reducts of multi-granulation information system. For any subset of information system, we usually characterize it by its upper and lower approximations. In order to calculate the upper and lower approximations faster, we must reduce the redundant information of the information system. According to the preceding analysis, we first introduce three types of attribute reduct, which are called arbitrary union reduct, neighborhood union reduct and neighborhood intersection reduct, respectively. Then many basic and important results of these reducts are deeply explored. In order to apply the theories of attribute reducts to deal with practical issues, we develop three algorithms so as to compute multi-granulation upper and lower approximations. Next, we further study the interrelationships among these attribute reducts. Finally, we present a multi-granulation information system with respect to thirty students’ exam scores and calculate the corresponding attribute reducts by using the algorithms listed in the paper.