Knowledge reductions in generalized approximation space over two universes based on evidence theory

Abstract

Knowledge reduction is one of the most important issues in rough set theory. According to various requirements and factors, information processing is based on two or more than two universes, other than single universe in many real-life cases. In this paper, we mainly investigate the knowledge reductions in generalized approximation space over two universes based on evidence theory. By defining the concepts of object belief and plausibility consistent sets over two universes, the object belief and plausibility consistent reductions are introduced in generalized approximation space over two universes. At the same time, the belief and plausibility significance reductions are also presented carefully in this space. Relationships among these proposed reductions are further studied, and it is proved that the object belief consistent reduction must be belief significance reduction and the object plausibility consistent reduction must be plausibility significance reduction.