**6. Conclusions**

Dual hesitant Pythagorean fuzzy numbers have applied the advantages of DHFSs and PFSs. They can flexibly denote decision-making information as well as e ffectively characterize the reliability of information. Thus, it is meaningful to study MADM problems with DHPFNs. In this paper, based on the generalized Heronian mean operator and generalized geometric Heronian mean operator, we developed some dual hesitant Pythagorean fuzzy Heronian mean aggregation operators: dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator. The significant merits of these defined operators are investigated. Moreover, we have adopted DHPFGWHM and DHPFGGWHM operators to build a decision-making model for MADM problems. In the end, we utilize a concrete instance for suppliers selection in supply chain managemen<sup>t</sup> to demonstrate our defined model and to testify its accuracy and scientific ability. However, our developed methods can only deal with MADMs with dual hesitant Pythagorean fuzzy information, and it is clear that these operators cannot handle more complicated decision making problems, such as when the sum square of the membership and non-membership is more than 1. In the future, we shall continue studying MADM problems with the application and extension of the developed operators to other domains [67,68] and proposed more suitable methods [69–75].

**Author Contributions:** M.T., J.W., J.L., G.W., C.W. and Y.W. conceived and worked together to achieve this work, M.T. and J.W. compiled the computing program by Excel and analyzed the data, J.W. and G.W. wrote the paper. Finally, all the authors have read and approved the final manuscript.

**Funding:** This work was supported by the University Students' Innovation and Entrepreneurship Training Program Project of Sichuan Normal University under Grant No. 201810636122 and the National Natural Science Foundation of China under Grant No. 71571128.

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