Correlation coefficients of dual type-2 hesitant fuzzy sets and their applications in clustering analysis

Recently, many researchers have studied some types of sets which are extension of fuzzy sets widely. Some of them are interval-valued fuzzy set, intuitionistic fuzzy sets, type-2 fuzzy sets, type-n fuzzy sets, hesitant fuzzy sets (HFSs), dual fuzzy sets, and neutrosophic sets. In solving decision-making problems, these sets have more advantages than classical sets. In this paper, we introduce a new concept called dual type-2 hesitant fuzzy sets (DT2HFSs) by combining concepts of the dual HFS and the type-2 fuzzy set. Then we give correlation coefficient formulas and weighted correlation coefficient formulas between two DT2HFSs and obtain some results related to the proposed correlation coefficient formulas. On the basis of the proposed correlation coefficient formulas, we develop the clustering method under DT2HF environment. Finally, we present an application of the proposed method for a problem to illustrate the process and validate the proposed method.