New distance and similarity measures for hesitant fuzzy sets and their application in hierarchical clustering

The hesitant fuzzy sets (HFSs) are an extension of the classical fuzzy sets. The membership degree of each element in a hesitant fuzzy set can be a set of possible values in the interval [0,1]. On the other hand, distance and similarity measures are important tools in several applications such as pattern recognition, clustering, medical diagnosis, etc. Hence, numerous studies have focused on investigating distance and similarity measures for HFSs. In this paper, some improved distance and similarity measures are introduced for the HFSs, considering the variation range as a hesitance degree for these sets. Comparing the proposed measures to some available distance and similarity measures indicated the better results of the proposed measures. Finally, the application of the proposed measures was investigated in the clustering.