Hesitant Fuzzy Linguistic Term Soft Sets and Their Applications in Decision Making

The hesitant fuzzy linguistic term set (HFLTS) and its extensions have been intensively investigated as a useful tool for the qualitative information problems in recent years. In the present paper, the concept of hesitant fuzzy linguistic term soft sets (HFLTSSs), a combination of HFLTSs and soft sets, are developed. First of all, relationships between any two HFLTSSs are provided, including inclusion, equivalence, and complementation. Then, several basic set operations for HFLTSSs are studied, such as AND, OR, union, and intersection. Meanwhile, corresponding properties of these operations are also discussed. In view of decision-making (DM) problem, we propose two algorithms for HFLTSSs, using the level soft sets and the hesitant fuzzy linguistic weighted distance (HFLWD) operator. Finally, a numerical third-party evaluation-related example in green development is used to present the utility and effectiveness of our algorithms. We also make comparisons between proposed method and some existing ones to confirm its feasibility and rationality. The main contribution of this paper possesses three points: (1) Enriching soft set theory by proposing the HFLTSSs, a soft set that can reflect the evaluation on objects more reasonably. (2) Redefining the HFLWD operator based on a novel distance of any two hesitant fuzzy linguistic term elements (HFLTEs), which can make the operations among HFLTEs much easier. (3) Applying the level soft set and new distance operator to develop two algorithms for decision-making problem with the information of HFLTSs.