A Novel Comparative Linguistic Distance Measure Based on Hesitant Fuzzy Linguistic Term Sets and Its Application in Group Decision-Making

The linguistic approaches are required in order to assess qualitative aspects of many real problems. In most of these problems, decision makers only adopt single and very simple terms which would not reflect exactly what the experts mean for many intricate applications. Frequently, the assessments of decision making problems involve comparative linguistic expressions. Accordingly, we propose a novel distance measure between hesitant fuzzy linguistic term sets (HFLTSs) to solve fuzzy group decision making (FGDM) problems. Firstly we define the characteristic functions to describe the HFLTSs transformed from comparative linguistic expressions. Then we construct a weighted HFLTSs graph containing all notes in the HFLTSs. Distances in the graph of individual assessments are defined by measures considering diversity and specificity of HFLTS’s granularity. We put forward a new approach to achieve aggregation results for group decision making to realize the minimal distances with individual assessments. Finally, numerical examples are illustrated.