**5. Conclusions**

Hesitant fuzzy information aggregation is one of key issues in the hesitant fuzzy MADM, an important field of research in decision science in an uncertain environment as well as HFS theory. Based on Hamacher operations of HFEs, in this paper, we have developed a family of hesitant fuzzy Hamacher power-aggregation operators, including the HFHWPA, HFHPWG, GHFHPWA, GHFHPWG, HFHPOWA, HFHPOWG, GHFHPOWA, and GHFHPOWG operators. Some basic properties of the proposed aggregation operators, such as boundedness and monotonicity, and the relationships between them have been investigated and discussed. We compared the proposed aggregation operators with the hesitant fuzzy aggregation operators developed by Yu et al. [18] and Zhang [15] and represented their corresponding relations. These proposed hesitant fuzzy Hamacher power-aggregation operators are integrated treatment of operators proposed by Yu et al. [18] and Zhang [15], and provide a complement to the existing work on HFSs. An approach of the hesitant fuzzy MADM based on the HFHPWA and HFHPWG operators has been developed and an example of money investment selection has been provided to describe the hesitant fuzzy MADM process. Some advantages of our proposed approach are shown by comparison with those previously proposed by Xia and Xu [10], Zhu et al. [13] and Tan et al. [17].

In future work, we will present a series of hesitant fuzzy power-aggregation operators using Frank *t*-norm and *t*-conorm and apply them to develop approaches for multiple-attribute group

decision-making. Furthermore, we will discuss the extension of power-aggregation operators to probabilistic hesitant fuzzy environment.

**Author Contributions:** J.H.P. drafted the initial manuscript and conceived the MADM framework. M.J.S. provided the relevant literature review and illustrated example. M.J.S. and K.H.K. revised the manuscript and analyzed the data.

**Funding:** This work was supported by a Research Grant of Pukyong National University (2019).

**Conflicts of Interest:** The authors declare no conflict of interest.
