Consensus improvement model in group decision making with hesitant fuzzy linguistic term sets or hesitant fuzzy linguistic preference relations

Hesitant fuzzy linguistic term sets (HFLTSs) and hesitant fuzzy linguistic preference relations (HFLPRs) are widely used where decision makers are permitted to provide qualitative preferences with several linguistic terms over two alternatives. There are several issues deserving further investigation in the existing consensus models of HFLTSs and HFLPRs: the extension process of HFLTSs which is always performed in distance measure and ag-gregation of HFLTSs distorts the original information, the modified HFLTSs does not belong to standardized HFLTSs, and most of the existing models don't discussed the number of optimal solutions. In order to solve the above problems, this paper introduces new distance and entropy measures for HFLTSs, by which information aggregation method and two consensus improvement models in group decision making (GDM) with HFLTSs and HFLPRs are proposed. The first model is a four-stage optimization model with four objectives, based on which an equivalent linear weighted optimization model is derived by assigning appropriate weights to four objectives with different priorities. According to either of these two models, the revised individual and collective opinions can be obtained. In addition, the prominent properties of the collective opinion obtained from optimization models are further investigated. As last, some examples are provided to demonstrate the applicability of the optimization models proposed, and the results demonstrate the models proposed can better deal with the abovementioned issues.