**6. Conclusions**

Ventilation systems selection is an essential decision for a mining project. However, the influence characteristics of a ventilation system are complex and of strong fuzziness or uncertainty. Since preference relations play a significant role in the decision making process, HLPRs were proposed to deal with mine ventilation systems selection problems. HLPRs can be regarded as extensions of LPRs. They provide not only the priority intensity of alternatives, but also the possible membership degrees of this priority intensity. The likelihood-based index was defined to test the consistency of experts and the improving model was constructed to modify consistency level of HLPRs. Preference information in HFPRs is in the form of HFLNs. For the accuracy of HFLNs' computation, new operational laws and the comparison method were presented after reviewing the relevant literature. Furthermore, the decision making framework based on HLPRs was built to select a proper ventilation system for mines. Finally, an illustration and some comparisons with other methods were drawn to highlight the applicability and advantages of the developed approach. In the future, more engineering applications with this proposed method could be researched or more decision making methods can be developed to address complex decision making problems in mines.

**Author Contributions:** W.L., G.Z. and S.L. conceived and worked together to achieve this work, W.L. wrote the paper, and G.Z. made contribution to the case study.

**Funding:** This work was supported by National Natural Science Foundation of China (51774321).

**Acknowledgments:** We sincerely thank the anonymous reviewers for their helpful and constructive suggestions and the editors for their careful and patient work.

**Conflicts of Interest:** The authors declare that there is no conflict of interests regarding the publication of this paper.
