۱- Introduction

۲- Hesitant Fuzzy Linguistic Term Set: Motivation, Definitions, Operations, Comparisons and Measures

۳- Extensions of the HFLTS

۴- Multiple Criteria Decision Making with HFLTSs

۵- Hesitant Fuzzy Linguistic Preference Relation Theory

۶- Applications of the HFLTSs

۷- Challenges and Future Research Directions Over HFLTSs

۸- Concluding Remarks

References

Abstract

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 on HFLTSs based on the 134 selected papers from Web of Sciences published from January 2012 to October 2017. We justify the motivation, definitions, operations, comparison methods and measures of HFLTSs. We also summarize the different extensions of HFLTSs. The studies on multiple criteria decision making (MCDM) with HFLTSs in terms of aggregation operators and MCDM methods are clearly reviewed. We also conduce some overviews on decision making with hesitant fuzzy linguistic preference relations. The applications, research challenges and future directions are also given.

Introduction

Even though it has been investigated for several decades, the decision-making process still faces many challenges as it may involve multiple alternatives (sometimes may be with huge amount), multiple objectives/criteria (sometimes may be conflicting) and multiple experts (sometimes may be out of mutual agreement). Even though scholars have proposed different methodologies for different circumstances of decision-making analyses, the most fundamental yet essential step is to represent information appropriately and objectively, especially in those ill-structured decisionmaking problems involving uncertainty, vagueness and incomplete information that cannot be identified by probabilistic models [4]. To formally formulate the uncertainty of linguistic descriptors in decision making, Zadeh [137] proposed the fuzzy linguistic model, which uses the linguistic variables, whose values are not numbers but words or sentences in a natural or artificial language, to represent the qualitative opinions of a person. In spite of being less precise than a number, the linguistic variables enhance the feasibility, flexibility and reliability of decision models and provide many useful applications in different fields [57]. The progress of analyzing linguistic variables has led to an active research area today named computing with words (CWW) [66]: CWW is a methodology for reasoning,