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.

中文翻译：

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对偶二类犹豫模糊集的相关系数及其在聚类分析中的应用

近年来，许多研究人员广泛研究了一些类型的集合，这些集合是模糊集的扩展。其中一些是区间值模糊集、直觉模糊集、2 型模糊集、n 型模糊集、犹豫模糊集 (HFS)、对偶模糊集和中智集。在解决决策问题时，这些集合比经典集合更有优势。在本文中，我们通过结合对偶 HFS 和 2 型模糊集的概念，引入了一个新概念，称为对偶 2 型犹豫模糊集（DT2HFSs）。然后我们给出了两个DT2HFS之间的相关系数公式和加权相关系数公式，并获得了与所提出的相关系数公式相关的一些结果。在提出的相关系数公式的基础上，我们开发了DT2HF环境下的聚类方法。最后，