# Evaluation of Cleaner Production for Gold Mines Employing a Hybrid Multi-Criteria Decision Making Approach

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Evaluation Criteria of Cleaner Production for Gold Mines

#### 2.2. Probabilistic Linguistic Term Sets

## 3. Hybrid Multi-Criteria Decision Making Approach

#### 3.1. Phase I: Collect Hybrid Evaluation Information

#### 3.2. Phase II: Calculate the Criteria Weights based on PLTSs

#### 3.3. Phase III: Determine the Ranking Order Based on Extended TODIM

## 4. Case Study

## 5. Discussions

#### 5.1. Sensitivity Analysis

#### 5.2. Comparison Analysis

#### 5.3. Managerial Implication

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgement

## Conflicts of Interest

## References

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**Figure 2.**Structure of the proposed hybrid multi-criteria decision making (MCDM) approach. PLTS—probabilistic linguistic term set; TODIM—Tomada de Decisão Interativa Multicritério.

DMs | Education | Positional Titles | Employment Position | Working Years |
---|---|---|---|---|

${D}_{1}$ | M.S. | Senior Engineer | Mine manager | 21 |

${D}_{2}$ | M.S. | Senior Engineer | Deputy mine manager | 18 |

${D}_{3}$ | M.S. | Senior Engineer | Engineering technologist | 19 |

${D}_{4}$ | Ph.D. | Engineer | Deputy mine manager | 23 |

${D}_{5}$ | Ph.D. | Engineer | Engineering technologist | 22 |

${D}_{6}$ | Ph.D. | Engineer | Senior adviser | 30 |

${D}_{7}$ | Ph.D. | Senior Engineer | Mine manager | 25 |

${D}_{8}$ | Ph.D. | Senior Engineer | Mine manager | 33 |

${D}_{9}$ | Ph.D. | Senior Engineer | Deputy mine manager | 29 |

${D}_{10}$ | Ph.D. | Senior Engineer | Senior adviser | 35 |

${A}_{1}$ | ${A}_{2}$ | ${A}_{3}$ | ${A}_{4}$ | |

${B}_{1}$ | $\left\{{p}_{0}(0.2),{p}_{1}(0.4),{p}_{2}(0.4)\right\}$ | $\left\{{p}_{1}(0.4),{p}_{2}(0.4),{p}_{3}(0.2)\right\}$ | $\left\{{p}_{1}(0.4),{p}_{2}(0.6)\right\}$ | $\left\{{p}_{-1}(0.1),{p}_{1}(0.6),{p}_{2}(0.3)\right\}$ |

${B}_{2}$ | $\left\{{p}_{1}(0.7),{p}_{2}(0.3)\right\}$ | $\left\{{p}_{0}(0.2),{p}_{1}(0.6),{p}_{2}(0.2)\right\}$ | $\left\{{p}_{-1}(0.1),{p}_{1}(0.5),{p}_{2}(0.4)\right\}$ | $\left\{{p}_{1}(0.5),{p}_{2}(0.5)\right\}$ |

${B}_{3}$ (m^{3}/t) | 0.37 | 0.42 | 0.29 | 0.31 |

${B}_{4}$ (kgce/t) | 3.31 | 4.54 | 3.94 | 5.65 |

${B}_{5}$ (%) | 76 | 69 | 73 | 65 |

${B}_{6}$ (%) | 71 | 58 | 84 | 67 |

${B}_{7}$ (%) | 28 | 21 | 36 | 27 |

${B}_{8}$ (%) | 100 | 91 | 100 | 96 |

${B}_{9}$ (%) | 92 | 85 | 94 | 100 |

${B}_{10}$ (%) | 73 | 93 | 90 | 80 |

${B}_{11}$ (%) | 86 | 92 | 77 | 82 |

${B}_{12}$ (%) | 74 | 89 | 86 | 93 |

${B}_{13}$ (%) | 21 | 19 | 12 | 18 |

${B}_{14}$ (%) | 13 | 19 | 17 | 15 |

${B}_{15}$ | $\left\{{p}_{1}(0.3),{p}_{2}(0.3),{p}_{3}(0.4)\right\}$ | $\left\{{p}_{1}(0.6),{p}_{2}(0.4)\right\}$ | $\left\{{p}_{0}(0.4),{p}_{1}(0.3),{p}_{2}(0.3)\right\}$ | $\left\{{p}_{2}(0.7),{p}_{3}(0.3)\right\}$ |

${B}_{16}$ | $\left\{{p}_{1}(0.3),{p}_{2}(0.7)\right\}$ | $\left\{{p}_{1}(0.6),{p}_{2}(0.3),{p}_{3}(0.1)\right\}$ | $\left\{{p}_{0}(0.1),{p}_{2}(0.9)\right\}$ | $\left\{{p}_{-1}(0.1),{p}_{2}(0.6),{p}_{3}(0.3)\right\}$ |

${A}_{1}$ | ${A}_{2}$ | ${A}_{3}$ | ${A}_{4}$ | |

${B}_{1}$ | $\left\{{p}_{0}(0.2),{p}_{1}(0.4),{p}_{2}(0.4)\right\}$ | $\left\{{p}_{1}(0.4),{p}_{2}(0.4),{p}_{3}(0.2)\right\}$ | $\left\{{p}_{1}(0.4),{p}_{2}(0.6),{p}_{1}(0)\right\}$ | $\left\{{p}_{-1}(0.1),{p}_{1}(0.6),{p}_{2}(0.3)\right\}$ |

${B}_{2}$ | $\left\{{p}_{1}(0.7),{p}_{2}(0.3),{p}_{1}(0)\right\}$ | $\left\{{p}_{0}(0.2),{p}_{1}(0.6),{p}_{2}(0.2)\right\}$ | $\left\{{p}_{-1}(0.1),{p}_{1}(0.5),{p}_{2}(0.4)\right\}$ | $\left\{{p}_{1}(0.5),{p}_{2}(0.5),{p}_{1}(0)\right\}$ |

${B}_{3}$ (m^{3}/t) | 0.3846 | 0.0000 | 1.0000 | 0.8462 |

${B}_{4}$ (kgce/t) | 1.0000 | 0.4744 | 0.7308 | 0.0000 |

${B}_{5}$ (%) | 1.0000 | 0.3636 | 0.7273 | 0.0000 |

${B}_{6}$ (%) | 0.5000 | 0.0000 | 1.0000 | 0.3462 |

${B}_{7}$ (%) | 0.4667 | 0.0000 | 1.0000 | 0.4000 |

${B}_{8}$ (%) | 1.0000 | 0.0000 | 1.0000 | 0.5556 |

${B}_{9}$ (%) | 0.4667 | 0.0000 | 0.6000 | 1.0000 |

${B}_{10}$ (%) | 0.0000 | 1.0000 | 0.8500 | 0.3500 |

${B}_{11}$ (%) | 0.6000 | 1.0000 | 0.0000 | 0.3333 |

${B}_{12}$ (%) | 0.0000 | 0.7895 | 0.6316 | 1.0000 |

${B}_{13}$ (%) | 0.0000 | 0.6667 | 1.0000 | 0.7778 |

${B}_{14}$ (%) | 1.0000 | 0.0000 | 0.3333 | 0.6667 |

${B}_{15}$ | $\left\{{p}_{1}(0.3),{p}_{2}(0.3),{p}_{3}(0.4)\right\}$ | $\left\{{p}_{1}(0.6),{p}_{2}(0.4),{p}_{1}(0)\right\}$ | $\left\{{p}_{0}(0.4),{p}_{1}(0.3),{p}_{2}(0.3)\right\}$ | $\left\{{p}_{2}(0.7),{p}_{3}(0.3),{p}_{2}(0)\right\}$ |

${B}_{16}$ | $\left\{{p}_{1}(0.3),{p}_{2}(0.7),{p}_{1}(0)\right\}$ | $\left\{{p}_{1}(0.6),{p}_{2}(0.3),{p}_{3}(0.1)\right\}$ | $\left\{{p}_{0}(0.1),{p}_{2}(0.9),{p}_{0}(0)\right\}$ | $\left\{{p}_{-1}(0.1),{p}_{2}(0.6),{p}_{3}(0.3)\right\}$ |

${D}_{1}$ | ${D}_{2}$ | ${D}_{3}$ | ${D}_{4}$ | ${D}_{5}$ | $L(s)$ | $\eta {(L(s))}_{f}$ | ${w}_{f}$ | |

${B}_{1}$ | Very high | High | High | High | Very high | $\left\{{p}_{2}(0.6),{p}_{3}(0.4)\right\}$ | ${p}_{2.4}$ | 0.0774 |

${B}_{2}$ | High | High | Very high | Very high | Very high | $\left\{{p}_{2}(0.4),{p}_{3}(0.6)\right\}$ | ${p}_{2.6}$ | 0.0839 |

${B}_{3}$ | Medium | Slightly high | High | Medium | Slightly high | $\left\{{p}_{0}(0.4),{p}_{1}(0.4),{p}_{2}(0.2)\right\}$ | ${p}_{0.8}$ | 0.0258 |

${B}_{4}$ | High | Medium | Slightly high | High | Very high | $\left\{{p}_{0}(0.2),{p}_{1}(0.2),{p}_{2}(0.4),{p}_{3}(0.2)\right\}$ | ${p}_{1.6}$ | 0.0516 |

${B}_{5}$ | High | Very high | Very high | High | Slightly high | $\left\{{p}_{1}(0.2),{p}_{2}(0.4),{p}_{3}(0.4)\right\}$ | ${p}_{2.2}$ | 0.0710 |

${B}_{6}$ | Slightly high | Medium | High | Slightly high | Medium | $\left\{{p}_{0}(0.4),{p}_{1}(0.4),{p}_{2}(0.2)\right\}$ | ${p}_{0.8}$ | 0.0258 |

${B}_{7}$ | Very high | High | Slightly high | High | Slightly high | $\left\{{p}_{1}(0.4),{p}_{2}(0.4),{p}_{3}(0.2)\right\}$ | ${p}_{1.8}$ | 0.0581 |

${B}_{8}$ | High | Very high | High | Very high | high | $\left\{{p}_{2}(0.6),{p}_{3}(0.4)\right\}$ | ${p}_{2.4}$ | 0.0774 |

${B}_{9}$ | Very high | Very high | high | High | High | $\left\{{p}_{2}(0.6),{p}_{3}(0.4)\right\}$ | ${p}_{2.4}$ | 0.0774 |

${B}_{10}$ | Very high | High | Very high | High | Slightly high | $\left\{{p}_{1}(0.2),{p}_{2}(0.4),{p}_{3}(0.4)\right\}$ | ${p}_{2.2}$ | 0.0710 |

${B}_{11}$ | Very high | Very high | High | High | High | $\left\{{p}_{2}(0.6),{p}_{3}(0.4)\right\}$ | ${p}_{2.4}$ | 0.0774 |

${B}_{12}$ | High | High | High | High | Very high | $\left\{{p}_{2}(0.8),{p}_{3}(0.2)\right\}$ | ${p}_{2.2}$ | 0.0710 |

${B}_{13}$ | Very high | Very high | Slightly high | High | High | $\left\{{p}_{1}(0.2),{p}_{2}(0.4),{p}_{3}(0.4)\right\}$ | ${p}_{2.2}$ | 0.0710 |

${B}_{14}$ | High | High | Slightly high | Slightly high | Slightly high | $\left\{{p}_{1}(0.6),{p}_{2}(0.4)\right\}$ | ${p}_{1.4}$ | 0.0452 |

${B}_{15}$ | Slightly high | Slightly high | Slightly high | Slightly high | High | $\left\{{p}_{1}(0.8),{p}_{2}(0.2)\right\}$ | ${p}_{1.2}$ | 0.0387 |

${B}_{16}$ | High | High | Very high | Very high | High | $\left\{{p}_{2}(0.6),{p}_{3}(0.4)\right\}$ | ${p}_{2.4}$ | 0.0774 |

${A}_{1}$ | ${A}_{2}$ | ${A}_{3}$ | ${A}_{4}$ | |

${A}_{1}$ | 0 | –11.7793 | –22.1894 | –14.9051 |

${A}_{2}$ | –26.9445 | 0 | –29.9559 | –25.5474 |

${A}_{3}$ | –12.7369 | –7.41886 | 0 | −9.90802 |

${A}_{4}$ | −20.3134 | −12.4199 | −26.099 | 0 |

$\mathit{\theta}$ | Ranking Results | The Optimal Alternative | The Worst Alternative |
---|---|---|---|

$\theta =0.2$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =0.4$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =0.6$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =0.8$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =1.0$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =2.0$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =4.0$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =6.0$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

$\theta =8.0$ | ${A}_{3}>{A}_{1}>{A}_{4}>{A}_{2}$ | ${A}_{3}$ | ${A}_{2}$ |

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**MDPI and ACS Style**

Liang, W.; Luo, S.; Zhao, G.
Evaluation of Cleaner Production for Gold Mines Employing a Hybrid Multi-Criteria Decision Making Approach. *Sustainability* **2019**, *11*, 146.
https://doi.org/10.3390/su11010146

**AMA Style**

Liang W, Luo S, Zhao G.
Evaluation of Cleaner Production for Gold Mines Employing a Hybrid Multi-Criteria Decision Making Approach. *Sustainability*. 2019; 11(1):146.
https://doi.org/10.3390/su11010146

**Chicago/Turabian Style**

Liang, Weizhang, Suizhi Luo, and Guoyan Zhao.
2019. "Evaluation of Cleaner Production for Gold Mines Employing a Hybrid Multi-Criteria Decision Making Approach" *Sustainability* 11, no. 1: 146.
https://doi.org/10.3390/su11010146