Inclusion measure and its use in measuring similarity and distance measure between hesitant fuzzy sets

In this paper, we propose a variety of inclusion measures for hesitant fuzzy sets (HFSs), based on which the corresponding similarity and distance measures can be obtained. First, we investigate the hybrid monotonic inclusion measures between two hesitant fuzzy elements (HFEs) and present their properties. Second, the hybrid monotonic inclusion measure between two HFSs are proposed. Furthermore, similarity measures and distance are postulated by inclusion measures. Last, numerical examples are provided to illustrate the inclusion measures, similarity measures and distance.