With respect to the uncertainty of intervalvalued intuitionistic fuzzy information, an approach to multiple attribute group decision making on the basis of continuous intervalvalued intuitionistic fuzzy Theil (CIVIFT) measure is investigated. Firstly, a CIVIFT measure based on the continuous intervalvalued intuitionistic fuzzy ordered weighted averaging (CIVIFOWA) operator is introduced, some desirable properties are discussed as well. Then, two programming models are constructed to derive the optimal weights of experts and attributes with the principle of minimum CIVIFT measure deviation. Moreover, similarity function and exact function are provided to rank the collective attribute values of alternatives. Finally, an example related to ERP software selection is provided to illustrate the feasibility and effectiveness of the proposed approach.