Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives

• We define the new consistency and inconsistency indices.
• We construct novel interval programming models and discuss their special cases in detail.
• We have presented a comparative analysis between intuitionistic fuzzy LINMAP and the proposed method.

The aim of this study is to employ the main structure of LINMAP (LINear programming technique for Multidimensional Analysis of Preference) to propose an interval programming method for solving multi-attribute group decision making (MAGDM) problems in which the ratings of alternatives are taken as hesitant fuzzy elements (HFEs) and all pair-wise comparison judgments over alternatives are represented by interval numbers. The contribution of this study is fivefold: (1) we define the new consistency and inconsistency indices; (2) we construct an interval programming model to determine the hesitant fuzzy positive ideal solution and the optimal weights of attributes, and at the same time present a decision algorithm; (3) we discuss several special cases of the proposed model in detail; (4) we show that compared with intuitionistic fuzzy LINMAP method (Li et al., 2010), the proposed approach reveals more useful information including the interval preference information, and does not need to transform HFEs into intuitionistic fuzzy numbers but directly deals with MAGDM problems and thus obtains better final decision results; and (5) we demonstrate the applicability and implementation process of the proposed approach by using an energy project selection example.