The Graded Multi-granulation Rough Set Based on Interval-valued Fuzzy Information System

Currently, the representative and extended rough set models are the graded rough set (GRS) and multi-granulation rough set (MGRS). And both of them have been applied in many fields. The main work of this paper is to combine the GRS with the MRS in the interval-valued fuzzy information system (IVFIS) and explore its mechanism. First, in the frame of IVFIS, we construct three new types of multi-granulation rough sets, i.e., graded optimistic MGRS, graded pessimistic MGRS and graded generalized MGRS, respectively. Then, their corresponding basic structure and some properties are studied as well. Finally, based on the above analysis, an illustrative example about class evaluation is introduced to further verify the validity of the model.