Distance Measures for Hesitant Fuzzy Linguistic Sets and Their Applications in Multiple Criteria Decision Making

Hesitant fuzzy linguistic term sets (HFLTSs) provide a linguistic and computational basis to increase the flexibility and richness of linguistic elicitation based on the fuzzy linguistic approach. Based on the traditional Hamming distance, Euclidean distance and generalized distance, some new class of distance measures for hesitant fuzzy linguistic numbers which include the hesitance degree of hesitant fuzzy element are provided and some linguistic scale functions are applied. We also define the continuous distance measure between two collections of HFLTSs. Furthermore, the proposed distance measures based on TOPSIS method for hesitant fuzzy linguistic multiple criteria decision making are developed, which calculate the distances between the alternatives and the positive ideal solution, the negative ideal solution, respectively. Then, the relative closeness degree to the ideal solution is calculated to rank all the alternatives. The main characteristics of the proposed distance measures are that it not only considers the hesitance of the hesitant fuzzy elements but also deals with linguistic transformation problem under different semantic situations, which efficiently avoid information loss and distortion. Finally, an example is provided to illustrate the feasibility and effectiveness of the developed method, which are then compared to the existing methods.