Novel similarity measure between hesitant fuzzy set and their applications in pattern recognition and clustering analysis

The extension of classical fuzzy sets are hesitant fuzzy sets (HFSs), in which each element has a possible value from [0,1]. Similarity and distance measures are useful implements for solving medical, clustering and pattern-recognition problems. Most of the researchers have suggested their ideas for HFSs using distance measures and extract the similarity measure from distance measure but most of them are getting inadequate results. Therefore, we proposed a new similarity measure to resolve these problems and also satisfied the properties of proposed measure for HFSs. Additionally, numerous examples are taken in consideration using HFS and compared the performance of existing measures with proposed measure for different cases. Furthermore, we have applied proposed measure for pattern recognition problems using three different examples and also calculate performance index (i.e., Degree of Confidence) to explore the behavior of different measures. Finally, we suggested MST based clustering algorithm using HF-environment and contrast the performance of proposed measure with existing ones. All these comparison illustrate that proposed measure is getting efficient and reasonable results and it also verified that proposed measure is not restricted to particular domain, it can be effectively applied for diverse field of application.