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The hesitant fuzzy linguistic term set (HFLTS) has gained great success as it can be used to represent several linguistic terms or comparative linguistic expressions together with some context-free grammars. This new approach has enabled the analysis and computing of linguistic expressions with uncertainties and opened the door for the possibility to develop more comprehensive and powerful decision theories and methods based on linguistic knowledge. Lots of new approaches and proposals for decision-making problems have been proposed to overcome the limitations of previous linguistic decision-making approaches. Now and in the future, decision-making methodologies and algorithms with hesitant fuzzy linguistic models would be a quite promising research line representing a high-quality breakthrough in this topic. To facilitate the study on HFLTS theory, this paper makes a state-of-the-art survey …