# Assessing the Performance of Green Mines via a Hesitant Fuzzy ORESTE–QUALIFLEX Method

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Hesitant Fuzzy Sets

#### 3.2. Hesitant Fuzzy ORESTE–QUALIFLEX Method

## 4. Case Study

#### 4.1. Engineering Background Description

#### 4.2. Assessment Criteria System of Green Mines

#### 4.3. Performance Assessment of Green Mines

_{ik}of each alternative was obtained, as shown in Table 8.

## 5. Discussions

#### 5.1. Sensitivity Analysis

_{1}, respectively. As the aim of this case was to choose the best option, the evaluation results of adopting our approach was relatively stable.

#### 5.2. Comparison Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Ali, S.H.; Giurco, D.; Arndt, N.; Nickless, E.; Brown, G.; Demetriades, A.; Durrheim, R.; Enriquez, M.A.; Kinnaird, J.; Littleboy, A.; et al. Mineral supply for sustainable development requires resource governance. Nature
**2017**, 543, 367–372. [Google Scholar] [CrossRef] [PubMed] - Luo, S.Z.; Liang, W.Z.; Xing, L.N. Selection of mine development scheme based on similarity measure under fuzzy environment. Neural Comput. Appl.
**2019**, 1–12. [Google Scholar] [CrossRef] - Sun, S.Y.; Sun, H.; Zhang, D.S.; Zhang, J.F.; Cai, Z.Y.; Qin, G.H.; Song, Y.M. Response of soil microbes to vegetation restoration in coal mining subsidence areas at Huaibei coal mine China. Int. J. Environ. Res. Public Health
**2019**, 16, 1757. [Google Scholar] [CrossRef] [PubMed] - Liang, W.Z.; Zhao, G.Y.; Wu, H.; Dai, B. Risk assessment of rockburst via an extended MABAC method under fuzzy environment. Tunn. Undergr. Space Tech.
**2019**, 83, 533–544. [Google Scholar] [CrossRef] - Timofeev, I.; Kosheleva, N.; Kasimov, N. Contamination of soils by potentially toxic elements in the impact zone of tungsten—Molybdenum ore mine in the Baikal region: A survey and risk assessment. Sci. Total. Environ.
**2018**, 642, 63–76. [Google Scholar] [CrossRef] [PubMed] - Shang, D.L.; Yin, G.Z.; Li, X.S.; Li, Y.J.; Jiang, C.B.; Kang, X.T.; Liu, C.; Zhang, C. Analysis for green mine (phosphate) performance of China: An evaluation index system. Resour. Policy
**2015**, 46, 71–84. [Google Scholar] [CrossRef] - Wang, W.S.; Zou, J.L. Efficiency evaluation and optimization of green mining construction in coal enterprises based on DEA. China Coal
**2013**, 39, 119–121. [Google Scholar] - Xu, J.Q.; Yu, G.; He, D.Y. Multi-expert evaluation method of Green Mine: A case study on Xinwen mining group’s Huafeng mine. Resour. Ind.
**2016**, 18, 61–68. [Google Scholar] - Hu, J.H.; Xiao, K.L.; Chen, X.H.; Liu, Y.M. Interval type-2 hesitant fuzzy set and its application in multi-criteria decision making. Comput. Ind. Eng.
**2015**, 87, 91–103. [Google Scholar] [CrossRef] - Luo, S.Z.; Zhang, H.Y.; Wang, J.Q.; Li, L. Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. J. Oper. Res. Soc.
**2019**, 1–17. [Google Scholar] [CrossRef] - Torra, V. Hesitant fuzzy sets. Int. J. Intell. Syst.
**2010**, 25, 529–539. [Google Scholar] [CrossRef] - Alcantud, J.C.R.; Torra, V. Decomposition theorems and extension principles for hesitant fuzzy sets. Inform. Fusion
**2018**, 41, 48–56. [Google Scholar] [CrossRef] - Torra, V.; Narukawa, Y. On hesitant fuzzy sets and decision. In Proceedings of the 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 20–24 August 2009; pp. 1378–1382. [Google Scholar]
- Rodríguez, R.M.; Martínez, L.; Torra, V.; Xu, Z.S.; Herrera, F. Hesitant fuzzy sets: state of the art and future directions. Int. J. Intell. Syst.
**2014**, 29, 495–524. [Google Scholar] [CrossRef] - Xu, Y.; Liu, L.Z.; Zhang, X.Y. Multilattices on typical hesitant fuzzy sets. Inform. Sci.
**2019**, 491, 63–73. [Google Scholar] [CrossRef] - Deveci, M.; Özcan, E.; John, R.; Öner, S.C. Interval type-2 hesitant fuzzy set method for improving the service quality of domestic airlines in Turkey. J. Air Trans. Manag.
**2018**, 69, 83–98. [Google Scholar] [CrossRef] - Iordache, M.; Schitea, D.; Deveci, M.; Akyurt, İ.Z.; Iordache, I. An integrated ARAS and interval type-2 hesitant fuzzy sets method for underground site selection: Seasonal hydrogen storage in salt caverns. J. Petrol. Sci. Eng.
**2019**, 175, 1088–1098. [Google Scholar] [CrossRef] - Iiang, W.Z.; Zhao, G.Y.; Wang, X.; Zhao, J.; Ma, C.D. Assessing the rockburst risk for deep shafts via distance-based multi-criteria decision making approaches with hesitant fuzzy information. Eng. Geol.
**2019**, 105211. [Google Scholar] [CrossRef] - Xu, Z.S.; Zhang, X.L. Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl. Based Syst.
**2013**, 52, 53–64. [Google Scholar] [CrossRef] - Zeng, S.; Baležentis, A.; Su, W. The multi-criteria hesitant fuzzy group decision making with MULTIMOORA method. Econ. Comput. Econ. Cybern.
**2013**, 47, 171–184. [Google Scholar] - Zhang, N.; Wei, G.W. Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Appl. Math. Model.
**2013**, 37, 4938–4947. [Google Scholar] [CrossRef] - Zhang, X.L.; Xu, Z.S. The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl. Based Syst.
**2014**, 61, 48–58. [Google Scholar] [CrossRef] - Zhang, X.L.; Xu, Z.S. Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives. Comput. Ind. Eng.
**2014**, 75, 217–229. [Google Scholar] [CrossRef] - Chen, N.; Xu, Z.S.; Xia, M.M. The ELECTRE I multi-criteria decision-making method based on hesitant fuzzy sets. Int. J. Inf. Tech. Decis.
**2015**, 14, 621–657. [Google Scholar] [CrossRef] - Chen, N.; Xu, Z.S. Hesitant fuzzy ELECTRE II approach: A new way to handle multi-criteria decision making problems. Inform. Sci.
**2015**, 292, 175–197. [Google Scholar] [CrossRef] - Zhang, X.L.; Xu, Z.S. Hesitant fuzzy qualiflex approach with a signed distance-based comparison method for multiple criteria decision analysis. Expert Syst. Appl.
**2015**, 42, 873–884. [Google Scholar] [CrossRef] - Mahmoudi, A.; Sadi-Nezhad, S.; Makui, A.; Vakili, M.R. An extension on PROMETHEE based on the typical hesitant fuzzy sets to solve multi-attribute decision-making problem. Kybernetes
**2016**, 45, 1213–1231. [Google Scholar] [CrossRef] - Acar, C.; Beskese, A.; Temur, G.T. Sustainability analysis of different hydrogen production options using hesitant fuzzy AHP. Int. J. Hydrogen Energy
**2018**, 43, 18059–18076. [Google Scholar] [CrossRef] - Kutlu Gündoğdu, F.; Kahraman, C.; Civan, H.N. A novel hesitant fuzzy EDAS method and its application to hospital selection. J. Intell. Fuzzy Syst.
**2018**, 35, 6353–6365. [Google Scholar] [CrossRef] - Galo, N.R.; Calache, L.D.D.R.; Carpinetti, L.C.R. A group decision approach for supplier categorization based on hesitant fuzzy and ELECTRI TRI. Int. J. Prod. Econ.
**2018**, 202, 182–196. [Google Scholar] [CrossRef] - Peng, J.J.; Wang, J.Q.; Yang, W.E. A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems. Int. J. Syst. Sci.
**2017**, 48, 425–435. [Google Scholar] [CrossRef] - Dong, J.Y.; Chen, Y.; Wan, S.P. A cosine similarity based QUALIFLEX approach with hesitant fuzzy linguistic term sets for financial performance evaluation. Appl. Soft Comput.
**2018**, 69, 316–329. [Google Scholar] [CrossRef] - Tian, Z.P.; Wang, J.; Wang, J.Q.; Zhang, H.Y. Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis. Negotiat.
**2017**, 26, 597–627. [Google Scholar] [CrossRef] - Ji, P.; Zhang, H.Y.; Wang, J.Q. Fuzzy decision-making framework for treatment selection based on the combined QUALIFLEX–TODIM method. Int. J. Syst. Sci.
**2017**, 48, 3072–3086. [Google Scholar] [CrossRef] - Liang, W.Z.; Zhao, G.Y.; Hong, C.S. Performance assessment of circular economy for phosphorus chemical firms based on VIKOR-QUALIFLEX method. J. Clean. Prod.
**2018**, 196, 1365–1378. [Google Scholar] [CrossRef] [Green Version] - Zhang, C.; Wu, X.L.; Wu, D.; Liao, H.C.; Luo, L.; Herrera-Viedma, E. An intuitionistic multiplicative ORESTE method for patients’ prioritization of hospitalization. Int. J. Environ. Res. Public Health
**2018**, 15, 777. [Google Scholar] [CrossRef] [PubMed] - Roubens, M. Preference relations an actions and criteria in multicriteria decision making. Eur. J. Oper. Res.
**1982**, 10, 51–55. [Google Scholar] [CrossRef] - Yerlikaya, M.A.; Arikan, F. Constructing the performance effectiveness order of SME supports programmes via Promethee and Oreste techniques. J. Fac. Eng. Archit. Gaz.
**2016**, 31, 1007–1016. [Google Scholar] - Kaya, T. Monitoring brand performance based on household panel indicators using a fuzzy rank-based ORESTE methodology. J. Mult. Valued Log. Soft
**2018**, 31, 443–467. [Google Scholar] - Wu, X.L.; Liao, H.C. An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making. Inform. Fusion
**2018**, 43, 13–26. [Google Scholar] [CrossRef] - Tian, Z.P.; Nie, R.X.; Wang, J.Q.; Zhang, H.Y. Signed distance-based ORESTE for multicriteria group decision-making with multigranular unbalanced hesitant fuzzy linguistic information. Expert Syst.
**2019**, 36, e12350. [Google Scholar] [CrossRef] - Li, J.; Luo, L.; Wu, X.L.; Liao, C.C.; Liao, H.C.; Shen, W.W. Prioritizing the elective surgery patient admission in a Chinese public tertiary hospital using the hesitant fuzzy linguistic ORESTE method. Appl. Soft Comput.
**2019**, 78, 407–419. [Google Scholar] [CrossRef] - Liang, W.Z.; Luo, S.Z.; Zhao, G.Y. Evaluation of cleaner production for gold mines employing a hybrid multi-criteria decision making approach. Sustainability
**2019**, 11, 146. [Google Scholar] [CrossRef] - Delgado, A.; Romero, I. Environmental conflict analysis using an integrated grey clustering and entropy-weight method: A case study of a mining project in Peru. Environ. Model. Softw.
**2016**, 77, 108–121. [Google Scholar] [CrossRef] - Kokangül, A.; Polat, U.; Dağsuyu, C. A new approximation for risk assessment using the AHP and Fine Kinney methodologies. Saf. Sci.
**2017**, 91, 24–32. [Google Scholar] - Wang, Y.M. Using the method of maximizing deviations to make decision for multi-indicies. J. Syst. Eng. Electron.
**1997**, 8, 21–26. [Google Scholar] - Mardani, A.; Nilashi, M.; Zakuan, N.; Loganathan, N.; Soheilirad, S.; Saman, M.Z.M.; Ibrahim, O. A systematic review and meta-analysis of SWARA and WASPAS methods: Theory and applications with recent fuzzy developments. Appl. Soft Comput.
**2017**, 57, 265–292. [Google Scholar] [CrossRef] - Luo, S.Z.; Liang, W.Z. Optimization of roadway support schemes with likelihood–based MABAC method. Appl. Soft Comput.
**2019**, 80, 80–92. [Google Scholar] [CrossRef] - Xia, M.M.; Xu, Z.S. Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason.
**2011**, 52, 395–407. [Google Scholar] [CrossRef] [Green Version] - Xu, Z.S.; Xia, M.M. On distance and correlation measures of hesitant fuzzy information. Int. J. Intell. Syst.
**2011**, 26, 410–425. [Google Scholar] [CrossRef] - Zhou, Z.X.; Dou, Y.J.; Liao, T.J.; Tan, Y.J. A preference model for supplier selection based on hesitant fuzzy sets. Sustainability
**2018**, 10, 659. [Google Scholar] [CrossRef] - Farhadinia, B. A series of score functions for hesitant fuzzy sets. Inform. Sci.
**2014**, 277, 102–110. [Google Scholar] [CrossRef] - Liang, W.Z.; Zhao, G.Y.; Wu, H.; Chen, Y. Assessing the risk degree of goafs by employing hybrid TODIM method under uncertainty. Bull. Eng. Geol. Environ.
**2018**, 78, 3767–3782. [Google Scholar] [CrossRef] - Ministry of Natural Resources of the People’s Republic of China (MNRPRC). Announcement of the Nine Industry Standards such as Green Mine Construction Specification of Non-Metallic Minerals Industry Released by Ministry of Natural Resources of the People’s Republic of China. 2018. Available online: http://gi.mlr.gov.cn/201806/t20180628_1962186.html. (accessed on 5 July 2019).

**Figure 1.**Structure of the presented hesitant fuzzy Organísation, rangement et synthèse de données relationnelles (ORESTE)–qualitative flexible (QUALIFLEX) method.

Author (Year) | MCDM Methods | Case Study |
---|---|---|

Xu and Zhang (2013) [19] | Technique for order performance by similarity to ideal solution (TOPSIS) | Energy policy selection |

Zeng et al. (2013) [20] | Multiobjective optimization by ratio analysis plus the full multiplicative from (MULTIMOORA) | Manager selection |

Zhang and Wei (2013) [21] | Visekriterijumsko kompromisno rangiranje (VIKOR) | Project selection |

Zhang and Xu (2014) [22] | Traditional acronym in Portuguese of interactive and multicriteria decision-making (TODIM) | Evaluation of the service quality among domestic airlines |

Zhang and Xu (2014) [23] | Linear programming technique for multidimensional analysis of preference (LINMAP) | Energy project selection |

Chen et al. (2015) [24] | Elimination and choice translating reality (ELECTRE) I | Project selection |

Chen and Xu (2015) [25] | ELECTRE II | Third-party reverse logistics provider selection |

Zhang and Xu (2015) [26] | QUALIFLEX | Green supplier selection |

Mahmoudi et al. (2016) [27] | Preference ranking organization method for enrichment evaluation (PROMETHEE) | Ranking of overseas outstanding teachers |

Acar et al. (2018) [28] | Analytic hierarchy process (AHP) | Sustainability evaluation of hydrogen production options |

Kutlu Gündoğdu et al. (2018) [29] | Evaluation based on distance from average solution (EDAS) | Hospital selection |

Galo et al. (2018) [30] | ELECTRE TRI | Supplier categorization |

Evaluation Criteria | Descriptions |
---|---|

Mining area environment ${B}_{1}$ | This refers to the environment of the mining area and mainly includes appearance of the mining area, layout of function, and greening of the mining area. |

Resource development approaches ${B}_{2}$ | This refers to the superiority of development approaches and mainly includes mining technology, environmental monitoring, and environmental restoration. |

Comprehensive utilization of resources ${B}_{3}$ | This refers to the comprehensive utilization of resources and mainly includes the utilization of solid waste, wastewater, and associated resources. |

Energy conservation and emission reduction ${B}_{4}$ | This refers to the saving of energy and emission of various pollutants and mainly includes energy conservation, discharge of solid waste, wastewater, exhaust gas, and dust. |

Technological innovation ${B}_{5}$ | This refers to the level of technical innovation and mainly includes innovation ability, automation performance, and digital mine. |

Management level ${B}_{6}$ | This refers to the management level of enterprise and mainly includes the culture, management, and credit of enterprise, social stability, and responsibility. |

${\mathit{B}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{B}}_{3}$ | ${\mathit{B}}_{4}$ | ${\mathit{B}}_{5}$ | ${\mathit{B}}_{6}$ | |
---|---|---|---|---|---|---|

${A}_{1}$ | {0.5,0.7,0.6,0.6} | {0.8,0.7,0.7,0.7} | {0.9,0.8,0.9,0.7} | {0.7,0.6,0.6,0.7} | {0.6,0.7,0.6,0.5} | {0.6,0.5,0.5,0.7} |

${A}_{2}$ | {0.9,0.7,0.9,0.8} | {0.7,0.7,0.6,0.6} | {0.6,0.7,0.8,0.6} | {0.7,0.6,0.5,0.5} | {0.5,0.6,0.6,0.5} | {0.7,0.8,0.8,0.7} |

${A}_{3}$ | {0.7,0.8,0.7,0.8} | {0.9,0.7,0.8,0.7} | {0.6,0.8,0.8,0.7} | {0.9,0.8,0.9,0.7} | {0.8,0.7,0.6,0.7} | {0.8,0.8,0.7,0.8} |

${A}_{4}$ | {0.7,0.6,0.6,0.5} | {0.7,0.5,0.6,0.6} | {0.5,0.6,0.5,0.7} | {0.8,0.7,0.8,0.9} | {0.7,0.9,0.7,0.7} | {0.6,0.7,0.7,0.8} |

${\mathit{B}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{B}}_{3}$ | ${\mathit{B}}_{4}$ | ${\mathit{B}}_{5}$ | ${\mathit{B}}_{6}$ | |
---|---|---|---|---|---|---|

${S}_{1}$ | 0.6 | 0.8 | 0.8 | 0.7 | 0.8 | 0.7 |

${S}_{2}$ | 0.8 | 0.7 | 0.7 | 0.8 | 0.9 | 0.8 |

${S}_{3}$ | 0.7 | 0.8 | 0.9 | 0.7 | 0.9 | 0.8 |

${S}_{4}$ | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.9 |

${e}_{j}$ | {0.6,0.8,0.7,0.8} | {0.8,0.7,0.8,0.8} | {0.8,0.7,0.9,0.8} | {0.7,0.8,0.7,0.8} | {0.8,0.9,0.9,0.8} | {0.7,0.8,0.8,0.9} |

$F({e}_{j})$ | 0.7200 | 0.7737 | 0.7969 | 0.7483 | 0.8485 | 0.7969 |

${w}_{j}^{S}$ | 0.1537 | 0.1652 | 0.1701 | 0.1597 | 0.1811 | 0.1701 |

${\mathit{B}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{B}}_{3}$ | ${\mathit{B}}_{4}$ | ${\mathit{B}}_{5}$ | ${\mathit{B}}_{6}$ | |
---|---|---|---|---|---|---|

A_{1} | 0.2158 | 0.2643 | 0.2952 | 0.2286 | 0.2305 | 0.2042 |

A_{2} | 0.2973 | 0.2367 | 0.2410 | 0.2008 | 0.2119 | 0.2684 |

A_{3} | 0.2711 | 0.2814 | 0.2590 | 0.2895 | 0.2694 | 0.2776 |

A_{4} | 0.2158 | 0.2176 | 0.2047 | 0.2811 | 0.2883 | 0.2498 |

${\mathit{D}}_{\mathit{i}\mathit{j}}$ | ${\mathit{B}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{B}}_{3}$ | ${\mathit{B}}_{4}$ | ${\mathit{B}}_{5}$ | ${\mathit{B}}_{6}$ |
---|---|---|---|---|---|---|

${A}_{1}$ | 0.0000 | 0.6517 | 1.0000 | 0.3245 | 0.3090 | 0.0000 |

${A}_{2}$ | 1.0000 | 0.3483 | 0.3874 | 0.0000 | 0.0000 | 0.7829 |

${A}_{3}$ | 0.6461 | 1.0000 | 0.6126 | 1.0000 | 0.6910 | 1.0000 |

${A}_{4}$ | 0.0000 | 0.0000 | 0.0000 | 0.8209 | 1.0000 | 0.6044 |

${\mathit{E}}_{\mathit{i}\mathit{j}}$ | ${\mathit{B}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{B}}_{3}$ | ${\mathit{B}}_{4}$ | ${\mathit{B}}_{5}$ | ${\mathit{B}}_{6}$ |
---|---|---|---|---|---|---|

${A}_{1}$ | 0.1192 | 0.4728 | 0.7177 | 0.2615 | 0.2503 | 0.1118 |

${A}_{2}$ | 0.7171 | 0.2681 | 0.3002 | 0.1254 | 0.1221 | 0.5647 |

${A}_{3}$ | 0.4722 | 0.7150 | 0.4502 | 0.7181 | 0.5036 | 0.7159 |

${A}_{4}$ | 0.1192 | 0.1058 | 0.1228 | 0.5938 | 0.7176 | 0.4417 |

$\u2206{G}_{ik}$ | ${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ${\mathit{A}}_{4}$ |
---|---|---|---|---|

A_{1} | 0.0000 | −0.0274 | −0.2736 | −0.0279 |

${A}_{2}$ | 0.0274 | 0.0000 | −0.2462 | −0.0005 |

${A}_{3}$ | 0.2736 | 0.2462 | 0.0000 | 0.2457 |

${A}_{4}$ | 0.0279 | 0.0005 | −0.2457 | 0.0000 |

${\u2206}_{1}$ | ${\u2206}_{2}$ | ${\u2206}_{3}$ | ${\u2206}_{4}$ | ${\u2206}_{5}$ | ${\u2206}_{6}$ | ${\u2206}_{7}$ | ${\u2206}_{8}$ |

−0.3301 | −0.8214 | 0.1624 | 0.1635 | −0.8203 | −0.3279 | −0.2753 | −0.7666 |

${\u2206}_{9}$ | ∆_{10} | ${\u2206}_{11}$ | ${\u2206}_{12}$ | ${\u2206}_{13}$ | ${\u2206}_{14}$ | ${\u2206}_{15}$ | ${\u2206}_{16}$ |

0.2720 | 0.3279 | −0.7108 | −0.1635 | 0.7097 | 0.7381 | 0.7644 | 0.8203 |

${\u2206}_{17}$ | ${\u2206}_{18}$ | ${\u2206}_{19}$ | ${\u2206}_{20}$ | ${\u2206}_{21}$ | ${\u2206}_{22}$ | ${\u2206}_{23}$ | ∆_{24} |

0.7666 | 0.8214 | −0.7644 | −0.2720 | −0.7097 | −0.1624 | 0.2753 | 0.3301 |

$\mathit{\beta}$ | Rank | $\mathit{\beta}$ | Rank |
---|---|---|---|

0 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | 0.6 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.1 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | 0.7 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.2 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | 0.8 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.3 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | 0.9 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.4 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | 1 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.5 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

$\mathit{\delta}$ | Rank | $\mathit{\delta}$ | Rank |
---|---|---|---|

0 | ${A}_{3}\succ {A}_{2}\succ {A}_{4}\succ {A}_{1}$ | 0.6 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.1 | ${A}_{3}\succ {A}_{2}\succ {A}_{4}\succ {A}_{1}$ | 0.7 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.2 | ${A}_{3}\succ {A}_{2}\succ {A}_{4}\succ {A}_{1}$ | 0.8 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.3 | ${A}_{3}\succ {A}_{2}\succ {A}_{4}\succ {A}_{1}$ | 0.9 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

0.4 | ${A}_{3}\succ {A}_{2}\succ {A}_{4}\succ {A}_{1}$ | 1 | -- |

0.5 | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

${\Theta}_{1}$ | ${\Theta}_{2}$ | ${\Theta}_{3}$ | ${\Theta}_{4}$ | ${\Theta}_{5}$ | ${\Theta}_{6}$ | ${\Theta}_{7}$ | ${\Theta}_{8}$ |

−0.1281 | −0.2959 | 0.0521 | 0.0646 | −0.2834 | −0.1032 | −0.1153 | −0.2830 |

${\Theta}_{9}$ | ${\Theta}_{10}$ | ${\Theta}_{11}$ | Θ_{12} | ${\Theta}_{13}$ | ${\Theta}_{14}$ | ${\Theta}_{15}$ | ${\Theta}_{16}$ |

0.0778 | 0.1032 | −0.2577 | −0.0646 | 0.2452 | 0.2641 | 0.2581 | 0.2834 |

${\Theta}_{17}$ | ${\Theta}_{18}$ | ${\Theta}_{19}$ | ${\Theta}_{20}$ | ${\Theta}_{21}$ | Θ_{22} | ${\Theta}_{23}$ | ${\Theta}_{24}$ |

0.2830 | 0.2959 | −0.2581 | −0.0778 | −0.2452 | −0.0521 | 0.1153 | 0.1281 |

${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ${\mathit{A}}_{4}$ | |
---|---|---|---|---|

${A}_{1}$ | - | R | R | R |

${A}_{2}$ | P | - | R | I |

${A}_{3}$ | P | P | - | P |

A_{4} | P | I | R | - |

Approach | Rank | The Best Alternative | The Worst Alternative |
---|---|---|---|

TOPSIS [19] | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | ${A}_{3}$ | ${A}_{1}$ |

TODIM [22] | ${A}_{3}\succ {A}_{1}\succ {A}_{2}\succ {A}_{4}$ | ${A}_{3}$ | ${A}_{4}$ |

VIKOR [21] | ${A}_{3}\succ {A}_{4}\succ {A}_{1}\succ {A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

QUALIFLEX [26] | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | ${A}_{3}$ | ${A}_{1}$ |

ORESTE | ${A}_{3}\succ \{{A}_{2},{A}_{4}\}\succ {A}_{1}$ | ${A}_{3}$ | ${A}_{1}$ |

The proposed approach | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ | ${A}_{3}$ | ${A}_{1}$ |

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**MDPI and ACS Style**

Liang, W.; Dai, B.; Zhao, G.; Wu, H.
Assessing the Performance of Green Mines via a Hesitant Fuzzy ORESTE–QUALIFLEX Method. *Mathematics* **2019**, *7*, 788.
https://doi.org/10.3390/math7090788

**AMA Style**

Liang W, Dai B, Zhao G, Wu H.
Assessing the Performance of Green Mines via a Hesitant Fuzzy ORESTE–QUALIFLEX Method. *Mathematics*. 2019; 7(9):788.
https://doi.org/10.3390/math7090788

**Chicago/Turabian Style**

Liang, Weizhang, Bing Dai, Guoyan Zhao, and Hao Wu.
2019. "Assessing the Performance of Green Mines via a Hesitant Fuzzy ORESTE–QUALIFLEX Method" *Mathematics* 7, no. 9: 788.
https://doi.org/10.3390/math7090788