Novel Distance Measure for Hesitant Fuzzy Sets and Its Application to K-Means Clustering

Distance measures have recently been studied in-depth within the context of hesitant fuzzy sets. The authors analyze existing research on the distance measures of hesitant fuzzy sets and identify several limitations. This paper proposes a new distance measure for hesitant fuzzy sets to overcome these shortcomings. First, a new hesitance degree with better accuracy and applicability is defined. Then, a new method for measuring the distance between hesitant fuzzy sets is proposed by considering the hesitance degree. On this basis, an improved hesitant fuzzy K-means clustering algorithm is introduced to classify hesitant fuzzy sets. Finally, an example is given to illustrate the specific implementation process of the clustering method, and a comparative study on the example is conducted.