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

To address the situation where Multi-criteria decision-making (MCDM) problems with hesitant fuzzy linguistic preference relations (HFLPRs), this study introduces a group decision-making method in view of worst and average indexes simultaneously. First, several optimization models for deriving the worst and average additive consistency indexes of HFLPRs are proposed. The main characteristic of the constructed optimization models is that the personalized individual semantics (PISs) model is taken into accounted. And then the concept of acceptable additive consistent HFLPRs is developed, which takes into accounted the worst consistency index (WCI) and average consistency index (ACI). Second, several optimization models are constructed for improving the consistency of HFLPRs. The main characteristic of the constructed optimization models is that two predefined thresholds for the WCI and ACI are considered. It requires the consistency level of all the linguistic preference relations (LPRs) derived from original HFLPR meet the threshold of WCI, and the average consistency level of all LPRs reaches the threshold of ACI. Third, an algorithm is designed for deriving priority weights from acceptable consistent HFLPRs. Finally, the presented models are validated using a numerical example and extensive comparative analyses.