# A GIS-Based Probabilistic Spatial Multicriteria Roof Water Inrush Risk Evaluation Method Considering Decision Makers’ Risk-Coping Attitude

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}. The mining area is located in the northwest inland, belongs to the temperate semi-arid continental climate and has an average annual precipitation of 435.7 mm and a mean annual evaporation of 1774.1 mm.

^{−2}coal seam is the main coal seam in the mining area, with a thickness of 3.40–4.20 m, a buried depth of 13.45–160.92 m, and a mining elevation of 1120–1080 m.

_{3y}), Middle Jurassic Yan’an Formation (J

_{2y}), Zhiluo Formation (J

_{2z}), Upper Neogene Xintong Baode Formation (N

_{2}

^{b}), Quaternary Middle Pleistocene Lishi Formation (Q

_{2}1), Upper Pleistocene Salawusu Formation (Q

_{3}

^{s}), and Holocene Aeolian Sand (Q

_{4}

^{eol}). The stratigraphic profile is shown in Figure 2.

^{−2}coal and weathered bedrock aquifer is 2.84–80.1 m, with an average of 47.5 m. After 4

^{−2}coal mining, the average height of the water flowing fractured zone is 51.72 m. The height of the water flowing fractured zone is greater than the distance between coal seam and aquifer, which can easily connect to the aquifer and affect coal mining.

## 3. Probabilistic Spatial Multicriteria Analysis Method

#### 3.1. Monte Carlo Analytical Hierarchy Process (MAHP)

- (1)
- Experts are required to use an accurate numerical value to describe the relative importance between criteria, but it is often difficult to give a precise numerical description.
- (2)
- The unbalanced criterion judgment scale is used to quantify the relative importance of the criteria.
- (3)
- When the relative importance of multiple criteria is very close, it is impossible to determine which criterion is the most important.
- (4)
- The various possibilities of the relative importance of each element criterion in the pairwise judgment matrix are not fully examined.

_{ij}represents the pairwise comparison between the decision criteria.

_{ij}as a continuous random variable and use the Beta-PERT probability distribution to describe the continuous random variable. The Beta-PERT probability distribution has a small amount of data and can better fit the uniform distribution and normal distribution, so it is very suitable for describing expert scoring in the decision making process [60,61,65,66].

_{min}, x

_{max}, x

_{mode}, x

_{mean}are the minimum value, maximum value, most probable value, and average value, respectively. The default value $\lambda $ is 4.

_{norm}of the judgment matrix A. The element ${\stackrel{\u2014}{a}}_{ij}$ of A

_{norm}is calculated as:

_{norm}:

#### 3.2. Ordered Weighted Averaging (OWA)

_{i}

_{1}> z

_{i}

_{2}> … > z

_{in}is the queue reordered by size after normalizing the evaluation criteria attribute value a

_{ij}; u

_{j}is the weight of the criteria; v

_{j}is the order weight, which has nothing to do with a

_{ij}but is only related to the sorting position of the criteria, v

_{1}is assigned to z

_{i}

_{1}, v

_{2}is assigned to z

_{i}

_{2}, and so on, v

_{n}is assigned to z

_{in}.

_{1}, w

_{2}, …, w

_{n}(0 < w

_{j}< 1, $\sum {w}_{j}$), which represents the relative importance between the evaluation criteria; and the order weight, v

_{1}, v

_{2}, …, v

_{n}(0 < v

_{j}< 1, $\sum {v}_{j}$), which represents the decision maker’s attitude to the roof water inrush risk [70,71].

_{j}is the order weight of the evaluation criteria. The higher the value of a, the more optimistic the decision maker is about the roof water inrush risk. When 0.5 ≥ a ≥ 0, it means that decision makers are unwilling to accept high-risk solutions and tend to accept less risky solutions; when a = 0.5, it indicates that decision makers are neither willing to accept high-risk schemes nor willing to accept low-risk schemes; when 1 ≥ a ≥ 0.5, it indicates that decision makers prefer to risk it and tend to accept more risky options [69,70,71,72].

_{j}= 1, other weights are 0, when $\phi $ = 1, the order weight v = [n

^{−1}, n

^{−1}, …, n

^{−1}].

## 4. Results and Discussion

#### 4.1. Determining Evaluation Criteria of Roof Water Inrush

#### 4.2. Standardization of Evaluation Criteria

#### 4.3. Evaluation Criteria Weight

#### 4.3.1. Criteria Weight

#### 4.3.2. Order Weight

#### 4.4. Influence of Risk Attitudes on Roof Water Inrush Risk Evaluation Results

#### 4.5. Verification and Comparison of Evaluation Results under Different Risk Attitudes

## 5. Conclusions

- (1)
- In this paper, the Monte Carlo analytical hierarchy process (MAHP) was used to calculate the evaluation criteria weight, which eliminates randomness and uncertainty in the process of determining the evaluation indicators in the traditional analytical hierarchy process. This gives the relative importance of the evaluation criteria in descending order: water abundance of the aquifer, coal seam thickness, aquifuge thickness, aquifer thickness, aquifer permeability, overburden failure height, and mining depth.
- (2)
- In this paper, the risk-coping attitude of decision makers was considered during the risk evaluation of roof water inrush. The OWA operator quantifies the impact of the risk attitude of decision makers on the water inrush risk evaluation. This paper assumed that the risk-coping attitude of decision makers to deal with roof water inrush has five situations: pessimistic, moderately pessimistic, neutral, moderately optimistic, and optimistic. The corresponding a values were 0.1, 0.3, 0.5, 0.7, and 0.9, respectively.
- (3)
- As decision makers become more optimistic about their risk-coping attitudes, the area of high-risk areas for roof water inrush within mining becomes significantly larger. The roof water inrush risk assessment results strongly depend on the risk-coping attitude of decision makers. A slight change in the decision makers’ risk-coping attitude can have a significant impact on the final risk assessment results..
- (4)
- Using the method proposed in this paper, the roof water inrush risk assessment results can be made more objective and accurate, thereby reducing or eliminating the risks associated with subjective decision making.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Flowchart for calculating the weights of the evaluation criteria by the Monte Carlo analytical hierarchy process.

**Figure 7.**The dimensionless thematic map for the evaluation criteria: (

**a**) T1; (

**b**) T2; (

**c**) T3; (

**d**) T4; (

**e**) T5; (

**f**) T6; (

**g**) T7.

**Figure 10.**The evaluation result map of the roof water inrush risk under different risk attitudes: (

**a**) a = 0.1; (

**b**) a = 0.5; (

**c**) a = 0.7; (

**d**) a = 0.9; (

**e**) a = 0.9.

**Figure 11.**Verification diagram of the roof water inrush risk evaluation results under different risk-coping attitudes: (

**a**) a = 0.1; (

**b**) a = 0.5; (

**c**) a = 0.7; (

**d**) a = 0.9.

Criteria | Mean | Min | Max | Standardization | Confidence Interval |
---|---|---|---|---|---|

Water abundance of the aquifer | 0.2678 | 0.1974 | 0.3301 | 0.02498 | (0.2647–0.2708) |

Aquifer permeability | 0.0911 | 0.0633 | 0.1288 | 0.01233 | (0.0895–0.0925) |

Aquifer thickness | 0.1463 | 0.1044 | 0.1985 | 0.0209 | (0.1437–0.1488) |

Mining depth | 0.0497 | 0.0370 | 0.0761 | 0.0070 | (0.0488–0.0505) |

Coal seam thickness | 0.1965 | 0.1401 | 0.2613 | 0.0220 | (0.1938–0.1992) |

Overburden failure height | 0.0665 | 0.0484 | 0.0875 | 0.0074 | (0.0656–0.0674) |

Aquifuge thickness | 0.1819 | 0.1395 | 0.2398 | 0.01979 | (0.1795–0.1843) |

a | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 |
---|---|---|---|---|---|

Order weight v_{1} | 0.002 | 0.0438 | 0.1428 | 0.3096 | 0.6226 |

Order weight v_{2} | 0.0052 | 0.0607 | 0.1428 | 0.2236 | 0.2367 |

Order weight v_{3} | 0.0136 | 0.0841 | 0.1428 | 0.1614 | 0.09 |

Order weight v_{4} | 0.0353 | 0.1165 | 0.1429 | 0.1166 | 0.0342 |

Order weight v_{5} | 0.0918 | 0.1614 | 0.1429 | 0.0842 | 0.0130 |

Order weight v_{6} | 0.2391 | 0.2236 | 0.1429 | 0.0608 | 0.0049 |

Order weight v_{7} | 0.6224 | 0.3097 | 0.1429 | 0.0439 | 0.0019 |

**Table 3.**The number of pixels of the roof water inrush risk areas in Figure 10.

Risk Attitude | a | Number of Pixels |
---|---|---|

Pessimistic | 0.1 | 13,774,955 |

Moderately pessimistic | 0.3 | 15,245,159 |

Neutral | 0.5 | 19,685,325 |

Moderately optimistic | 0.7 | 43,416,472 |

Optimistic | 0.9 | 50,369,478 |

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**MDPI and ACS Style**

Wang, D.; Gao, C.; Liu, K.; Gong, J.; Fang, Y.; Xiong, S.
A GIS-Based Probabilistic Spatial Multicriteria Roof Water Inrush Risk Evaluation Method Considering Decision Makers’ Risk-Coping Attitude. *Water* **2023**, *15*, 254.
https://doi.org/10.3390/w15020254

**AMA Style**

Wang D, Gao C, Liu K, Gong J, Fang Y, Xiong S.
A GIS-Based Probabilistic Spatial Multicriteria Roof Water Inrush Risk Evaluation Method Considering Decision Makers’ Risk-Coping Attitude. *Water*. 2023; 15(2):254.
https://doi.org/10.3390/w15020254

**Chicago/Turabian Style**

Wang, Dangliang, Chengyue Gao, Kerui Liu, Junling Gong, Yafei Fang, and Shijie Xiong.
2023. "A GIS-Based Probabilistic Spatial Multicriteria Roof Water Inrush Risk Evaluation Method Considering Decision Makers’ Risk-Coping Attitude" *Water* 15, no. 2: 254.
https://doi.org/10.3390/w15020254