An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

10 This article proposes a framework to handle multiattribute group decision making 11 problems with incomplete pairwise comparison preference over decision alternatives 12 where qualitative and quantitative attribute values are furnished as linguistic variables 13 and crisp numbers, respectively. Attribute assessments are then converted to interval14 valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in 15 the evaluation process. Group consistency and inconsistency indices are introduced for 16 incomplete pairwise comparison preference relations on alternatives provided by the 17 decision-makers (DMs). By minimizing the group inconsistency index under certain 18 constraints, an auxiliary linear programming model is developed to obtain unified 19 attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution 20 (IVIFPIS). Attribute weights are subsequently employed to calculate distances between 21 alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided 22 to demonstrate the applicability and effectiveness of this method. 23