A Novel Group Decision-Making Method with Adjustment Willingness in a Distributed Hesitant Fuzzy Linguistic Environment

This research aims to construct a group decision-making (GDM) method that considers decision makers’ (DMs’) willingness to adjust in a distributed hesitant fuzzy linguistic (DHFL) environment. First, to address the practical scenario where DMs may express preferences using multiple linguistic values with explicit preference strengths, this paper extends the distributed hesitant fuzzy linguistic preference relation (DHFLPR) and supplements missing probabilities. Second, we integrate multiplicative consistency and consensus within a DHFL environment to construct two preference optimization models, whose objective functions are to minimize the overall adjustment based on DMs’ willingness to adjust, thus making the decision more consistent with actual environments. Finally, the viability and effectiveness of the new method are validated by numerical examples. The results show that our new method allows individual preferences to quickly meet the consistency requirement while maximally preserving their original preferences. Additionally, the DHFLPRs maintain the fuzziness and hesitancy in the new preferences, and effectively address the issue of unequal importance among distinct linguistic preference values.