Multi-granulation rough set model in intuitionistic fuzzy-valued information system

In order to extend the theory of multi-granulation rough set (MGRS) to intuitionistic fuzzy-valued information system(IFIS),two different multi-granulation intuitionistic fuzzy-valued rough set models: optimistic multi-granulation intuitionistic fuzzy-valued rough set and pessimistic multi-granulation intuitionistic fuzzy-valued rough set based on multiple dominance relation are constructed in this paper. Not only the upper and the lower approximations are defined but also the properties of these two multi-granulation intuitionistic fuzzy-valued rough set models are discussed. Moreover, the differences and relationships between traditional intuitionistic fuzzy-valued rough set and the MGRS in IFIS are discussed.