Novel Distance Measures of Multigranular Unbalanced Hesitant Fuzzy Linguistic Term Sets Based on Semantics Intervals

In the field of qualitative decision making with hesitant fuzzy linguistic term sets (HFLTSs), distance measure (DM) is a significant concept that reflects the degree of difference between HFLTSs. Various DMs among HFLTSs have been proposed, which enhance the applicability of HFLTSs in multicriteria decision making (MCDM) under qualitative hesitation information. However, existing strategies not only have their own pros and cons but also fail to measure linguistic assessments from multiple linguistic term sets with different distributions (i.e., multigranular unbalanced linguistic information). In this article, we first propose a new strict DM between two hesitant fuzzy linguistic elements (HFLEs) based on the Wasserstein distance of their semantics intervals. Then, two novel kinds of DMs (Euclidean and Chebyshev forms) for HFLTSs are proposed and their strictness is proved. Weighted and ordered weighted versions of HFLTSs based on Euclidean form are derived. Afterward, illustrative examples, simulations, and related analyses are given to demonstrate the rationality of the proposals. Finally, two cases are applied to verify the efficiency and practicality of the novel measures in real life.