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Multiattribute group decision making (MAGDM) problems often involve both quantitative and qualitative attributes, where assessment values are expressed as imprecise data. This paper entertains interval-valued intuitionistic fuzzy sets (IVIFSs) to characterize fuzziness and uncertainty contained in imprecise decision data and processes such as subjective factors of linguistic terms and satisfaction degrees for decision-makers (DMs). Group consistency and inconsistency indices are defined based on pairwise comparison preference relations with respect to alternatives provided by the DMs. An auxiliary linear program is proposed for deriving the interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS) and weights. The distance of each alternative to the IVIFPIS is calculated to determine the ranking for all alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method.