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In many branches of modern information science and decision science, decision-making and cluster analysis in hesitant fuzzy environment has always been an important research field at home and abroad. Decision problem is using a certain way to sort or select a group of alternatives under known decision information. Under the complex information of the objective world, human’s description and evaluation of things are often difficult to be accurate, with a certain fuzziness, and the fuzzy set theory represents the similarity of objects and imprecisely defined attributes (Zadeh, 1996). After Zadeh introduced the fuzzy set theory, it attracted extensive attention from academia, industry, and government. Fuzzy set theory has become more popular in the process of auxiliary decision-making (Bezdek, 1993); various extension models of fuzzy set are developed successively, such as intuitionistic fuzzy set (Xu, 2009), interval fuzzy set (Moore & Lodwick, 2003), complex fuzzy set (Ramot et al., 2003), cubic fuzzy set (Jun et al., 2017), and type 2 fuzzy set (Dubois, 1980). Correspondingly, lots of the extensions of these aforementioned distance measures and similarity and dissimilarity measures have been developed for measuring the distances between these extensions of fuzzy sets, such as IFSs (Li & Wan, 2017; Zhu & Li, 2016; Li & Cheng, 2002; Li, 2004), interval-valued IFSs (Wei et al., 2019; Wei et al., 2021) and type 2 fuzzy set (Yang & Lin, 2009), etc. Because of the difference in personal cognitive levels, there are often different views on the same problem, and sometimes it is difficult to reach an agreement, decision-makers often show hesitation and indecision when making decisions. Therefore, Torra and Narukawa (2009) proposed hesitant fuzzy sets. The membership degree of a hesitant fuzzy set is a set composed of some potential values, which can take into account the different preferences of decision makers and obtain more reasonable and comprehensive decision results. Since the advent of hesitant fuzzy sets, it has received extensive attention and achieved rich research results. For example, Zhang and Xu (2015) proposed a hesitant fuzzy power average operator considering that attributes may be interrelated in real decision-making problems. Xu and Zhang (2013) introduced a hesitant fuzzy TOPSIS method based on the maximum deviation principle and applied it to multi-attribute decision-making problems. Liao and Xu (2013) proposed hesitant fuzzy VIKOR multi-attribute decision-making method considering the psychological preferences of decision makers. Tan et al. (2015) proposed a series of hesitant fuzzy Hamacher operators. Ai et al. (2014) developed some related hesitant fuzzy aggregation operators to aggregate hesitant fuzzy information, Rodriguez et al. (2011) applied them to develop a new technology to solve hesitant fuzzy multi-criteria decision-making problems. Meng and An (2017) discussed multiple attribute decision-making under a linguistic hesitant environment. The above results show that a hesitant fuzzy set is an important tool for solving decision problems.