In this paper, firstly we defined a new covering rough intuitionistic fuzzy set model in covering approximation space (U, C). Then, the properties of lower and upper approximation operators were discussed. Secondly, we extended covering rough intuitionistic fuzzy sets in rough sets from single-granulation to multi-granulation. From the view of granularity, we proposed three models, which are based on minimal description. Some properties of these models were proved and demonstrated with examples. These models were illustrated with examples.
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