Group decision-making with hesitant fuzzy linguistic preference relations in view of worst and average indexes

\nTo address the multi-criteria group decision-making (MCGDM) problems with hesitant fuzzy linguistic preference relations (HFLPRs), this study introduces a group decision-making (GDM) method in view of worst additive consistency index (WACI) and average additive consistency index (AACI) simultaneously. First, several optimization models are constructed for deriving the WACI and AACI. The main characteristic of the constructed models is that it takes into accounted the personalized individual semantics (PISs). Based on this, the concept of acceptable additive consistent HFLPRs is developed. Second, to improve the consistency of HFLPRs, several optimization models are constructed. Two predefined thresholds for the WACI and AACI are considered in the proposed models. It requires the consistency levels of all the linguistic preference relations (LPRs) associated with an HFLPR meets the threshold of WACI, and the average consistency level of all LPRs reaches the threshold of AACI. Third, an algorithm is designed for deriving priority weights from acceptable consistent HFLPRs. Finally, the presented models are validated for 3D visualization management system selection problem and extensive comparative analyses.\n