Multigranulation with Different Grades Rough Set in Ordered Information System

The the graded rough set and multi-granulation rough set are two significant extended rough set models, both constructed on the the indiscernibility relations. The purpose of this paper is to study the good points of graded rough set in the multi-granulation environment which in different granule have different grades in ordered information system. Three new types multi-granulation with different grades rough set models are proposed, which include optimistic multi-granulation with different grades, pessimistic multi-granulation with different grades and the mean multi-granulation with different grades rough set. Then, their principal structure are studied, and their basic properties are obtained as well. Finally, we study a case about students' achievement estimate the performance of the proposed properties. In the viewpoint of granular computing, our study extension the classical rough set theory.