Abstract: In the intuitionistic fuzzy information system, considering the relative and absolute double errors, the variable precision and degree "logic conjunction" rough set were studied. Based on intuitionistic fuzzy, the upper and lower approximate definitions of variable precision and degree "logic conjunction" optimistic multi granularity and pessimistic multi granularity rough set were proposed respectively. On this basis, a new binary matrix was defined to calculate the upper and lower approximate sets of multi granularity rough set, and some theories of computing upper and lower approximation by matrix sets were proposed. Finally, the correctness of the theories was verified by case analysis.