Local feedback mechanism based on consistency-derived for consensus building in group decision making with hesitant fuzzy linguistic preference relations

Considering that hesitant fuzzy linguistic preference relation (HFLPR) is an effective way to express decision makers' (DMs') hesitant qualitative preference information for a pair of alternatives or attributes, this paper pays attention to priority weights and consensus of HFLPRs in group decision making (GDM). First, a new similarity measure is presented to measure the similarity of hesitant fuzzy linguistic term sets (HFLTSs), then a consensus improving process with local feedback mechanism is developed to improve the consensus level of HFLPRs until they satisfy a predefined consensus threshold. The new consensus improving process not only provides some specific adjustment scales for DMs, but also maintains the consistency of HFLPRs. After that, a mixed 0-1 programming model is put forward to derive the priority weights of HFLPR. Finally, an example of an investment project selection details the application of the proposed methods and comparative analysis demonstrates the practicability of the proposed methods.