Controlling the worst consistency index for hesitant fuzzy linguistic preference relations in consensus optimization models

Consistency and consensus using hesitant fuzzy linguistic preference relations (HFLPRs) are two closely related issues for group decision making. However, there are still some gaps that need to be addressed: the normalization methods applied in previous research change the initial information, most approaches modify every element of the original HFLPRs, and the consistency level is uncontrolled in the consensus reaching process. In this paper, two optimization methods are proposed: one that improves the worst consistency index (WCI) and the other that assists groups achieve a predefined consensus level: in which the revised preferences all belong to the original linguistic term set, which makes the revised preferences easier for decision makers (DMs) to interpret and accept. By using the worst consistency level, all possible LPRs in the given HFLPRs are analyzed. After the WCI is controlled, it is then possible to use any part of the preference information from the modified HFLPRs to satisfy the consistency level. Finally, the presented models are validated using numerical examples and extensive comparative analyses.