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Novel Distance and Similarity Measures on Hesitant Fuzzy Linguistic Term Sets and Their Application in Clustering Analysis

The existing distance and similarity measures of hesitant fuzzy linguistic term sets (HFLTSs) only cover the difference of linguistic terms but have no consideration of the difference between the numbers of linguistic terms. Thus, the concept of hesitance degree of HFLTSs is introduced to describe the hesitant degree among several linguistic terms in each HFLTS during the decision-makers’ evaluating process. Considering the hesitance degree of HFLTSs, several novel distance and similarity measures of HFLTSs are developed, and their properties are discussed. Afterward, a novel hesitant fuzzy linguistic-based on the novel similarity measures and the Boole matrix is developed to classify the objects with hesitant fuzzy linguistic information and a numerical example of the automobile recommendation is given to illustrate the performance of our developed clustering method. The results indicate that our developed clustering method can fully express the original evaluation information and has less computational effects on clustering results than the previous method.