Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems.

An interval-valued hesitant fuzzy linguistic set (IVHFLS) can serve as an extension of both a linguistic term set and an interval-valued hesitant fuzzy set. This new set combines quantitative evaluation with qualitative evaluation; these can describe the real preferences of decision-makers and reflect their uncertainty, hesitancy, and inconsistency. This work focuses on multi-criteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of interval-valued hesitant fuzzy linguistic numbers (IVHFLNs). The new approach to solving these problems is based on the prioritized aggregation operators of IVHFLNs. Having reviewed the relevant literature, we provide interval-valued hesitant fuzzy linguistic operations and apply some linguistic scale functions, which have been improved on the basis of psychological theory and prospect theory. Ultimately, two kinds of prioritized aggregation operators of IVHFLNs are developed, which extend to a grouping prioritized situation and are applied to MCDM problems. Finally, an example is provided to illustrate and verify the proposed approach in two separate situations, which are then compared to other representative methods.