An extension model of rough set in incomplete information system

The rough set theory, based on the original definition of complete information system, is not useful for analyzing the incomplete information system where some values of attributes are unknown. Therefore, it needs to extend the classical rough set model to deal with the incomplete information system. The present extensions mainly have the tolerance relation, the non-symmetric similarity relation, the valued tolerance relation, the limited tolerance relation as well as other improved models based on the above relations. In this paper, we study the non-symmetric relation and the limited tolerance relation. Also, we propose a new extension model of rough set based on the non-symmetric similarity relation and the limited tolerance relation. In addition, we give an example to illustrate the conceptual argument and explain the superiority of the new model. Finally, we provide some properties of the extension model we proposed.