Multi-criteria decision-making approaches based on distance measures for linguistic hesitant fuzzy sets

Linguistic hesitant fuzzy sets (LHFSs), which can be used to both represent decision-makers' qualitative preferences and reflect their hesitancy and inconsistency, have attracted much attention due to their flexibility and efficiency. In this paper, some distance-based approaches for resolving multi-criteria decision-making (MCDM) problems with linguistic hesitant fuzzy information are introduced. To begin, a new order relationship between LHFSs, based on the defined LHFSs, is presented. Then, distance measures for LHFSs are proposed, which include the generalised, Hamming, and Euclidean distance measures. Additionally, some approaches for handling MCDM problems with linguistic hesitant fuzzy information are proposed, which are based on the TOPSIS, VIKOR, and TODIM methods, as well as the proposed distance measures. Finally, an illustrative example is provided to show the feasibility and usability of the methods, which are then compared with the existing method.