A Study Of Multi-granulation Intuitionistic Fuzzy Rough Set Model Based On Two Universes

Rough set theory and intuitionistic fuzzy set theory have been put forward succes-sively by Pawlak of Poland and Atanassov of Bulgaria.They are specialized mathematics tools dealing with uncertainty and ambiguity.In fact,intuitionistic fuzzy set is an ex-tension of fuzzy set and it can describe fuzzy phenomenons better.Based on the two universes,this paper proposes multi-granulation intuitionistic fuzzy rough set model by combining these two theories with the theory of granular computing and investigates the properties.Through integrating the multi-granulation and intuitionistic fuzzy ideas into the rough sets over two different universes,this study develops optimistic multi-granulation rough intuitionistic fuzzy set and pessimistic multi-granulation rough intuitionistic fuzzy set over two different universes.Basic properties of two types of multi-granulation rough intuitionistic fuzzy sets model over two different universes are investigated.Moreover,the relationships between the rough intuitionistic fuzzy sets model and multi-granulation rough intuitionistic fuzzy sets model over two different universes are explored.In the intuitionistic fuzzy approximation space,two models are established:the multi-granulation rough set model and the multi-granulation intuitionistic fuzzy rough set model.Several important properties and theorems of the two models are further studied.Finally,the effectiveness of the model is illustrated by an example.Based on rough set theory and evidence theory,trust importance reduction and like-lihood importance reduction are presented in the approximation spaces over two different universes.These reductions are very important for knowledge acquisition and rule ex-traction.