# Research on Extension Evaluation Method of Mudslide Hazard Based on Analytic Hierarchy Process–Criteria Importance through Intercriteria Correlation Combination Assignment of Game Theory Ideas

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

#### 2.1. Overview of the Evaluation Area

#### 2.2. Determination of Debris Flow Hazard Evaluation Index

_{1}).

_{2}).

_{3}).

_{4}).

_{5}).

_{6}).

_{7}).

_{8}).

#### 2.3. Data Sources

## 3. Methods

#### 3.1. Extensional Matter Element Model

_{ot}is the classical domain element of debris flow hazard, N

_{ot}is the evaluation level of debris flow hazard, c

_{i}is the corresponding evaluation index of debris flow hazard level, and V

_{ot}is the range of quantity values taken by c

_{i}, that is <a

_{oti},b

_{oti}> (i = 1, 2, 3, …, 8).

_{p}is the nodal domain object element, N

_{P}is the whole debris flow hazard evaluation level, V

_{pi}is the quantitative range of evaluation factors, and the quantitative range of classical domain and nodal domain evaluation factors are related as follows: <a

_{ot},b

_{ot}>⊂<a

_{pi},b

_{pi}> (i = 1, 2, 3, …, 8).

_{j}is the object element to be evaluated, that is, the object element of a single debris flow; N

_{j}is the debris flow hazard level to be evaluated, and v

_{i}is the relevant quantity value of the debris flow hazard level.

_{i}is the weight coefficient of each evaluation index and $\rho \left({v}_{i},{v}_{Pj}\right)$ is the distance of the evaluation index.

#### 3.2. Weighting Factor

_{ij}> 0, b

_{ij}= 1/b

_{ji}, b

_{ij}= 1(i = j), and (i, j = 1, 2, 3, …, 8). By normalizing the judgment matrix to find the eigenvector and then finding the maximum latent root λ

_{max}, a consistency test is performed to check the reasonableness of the judgment matrix [56,57].

_{ij}is calculated using the Pearson correlation coefficient, and x

_{i}and y

_{i}are evaluation indicators, respectively.

_{k}deviations.

#### 3.3. Evaluation Index Level and Grading

## 4. Results

#### 4.1. Topological Model

#### 4.2. Weighting Coefficient

#### 4.3. Matter-Element Model to Be Evaluated

## 5. Discussion

#### 5.1. Evaluation Results

^{4}, the relative height difference is 150 m, the volume of loose material reserves is approximately 3.5 × 10

^{4}m

^{3}, the average slope of both sides of the gully valley is 30°, the debris siltation in the gully is obvious, the circulation area is slightly blocked, and the rainfall in the study area from 2016 to 2021 is large. From this, it is inferred that the hazard class of mudslide #1 is medium hazardous(Figure 4). It is concluded that the extension evaluation method can be used to assess the risk posed by debris flows and that the evaluation’s findings are accurate and logical.

#### 5.2. Evaluation Method Optimization

#### 5.3. Application of Evaluation Methods

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Statistics of evaluation indicators. (

**a**) Melton ratio; (

**b**) basin elongation; (

**c**) basin height difference rate; (

**d**) slope gradient; (

**e**) loose material reserves; (

**f**) NDVI vegetation index; (

**g**) average annual precipitation; and (

**h**) distance from structure.

**Figure 4.**Features of 1# debris flow development. (

**a**) three-dimensional image map of the debris flow; (

**b**) debris flow site survey photos; (

**c**) terrain height difference of debris flow; and (

**d**) average annual precipitation.

Order n | RI | Order n | RI |
---|---|---|---|

1 | 0 | 6 | 1.26 |

2 | 0 | 7 | 1.36 |

3 | 0.58 | 8 | 1.41 |

4 | 0.89 | 9 | 1.46 |

5 | 1.12 | 10 | 1.49 |

Evaluation Indicators | Low Risk | Medium Risk | High Risk | Extremely High Risk |
---|---|---|---|---|

Melton ratio (c_{1}) | 0~0.10 | 0.10~0.30 | 0.30~0.50 | 0.50~1.20 |

Basin elongation (c_{2}) | 0.60~40.00 | 0.30~0.60 | 0.10~0.30 | 0~0.10 |

Basin height difference rate (c_{3}) | 0~0.10 | 0.10~0.20 | 0.20~0.30 | 0.30~5.0 |

Slope gradient (°) (c_{4}) | 0~15 | 15~30 | 30~40 | 40~90 |

Loose material reserves (10^{4} m^{3}) (c_{5}) | 0~1.0 | 1.0~5.0 | 5.0~10.0 | 10.0~150 |

NDVI vegetation index (c_{6}) | 0.75~1.00 | 0.6~0.75 | 0.4~0.6 | 0~0.4 |

Average annual precipitation (mm) (c_{7}) | 0~450 | 450~550 | 550~620 | 620~800 |

Distance from structure (10^{3} m) (c_{8}) | 5~25 | 2.5~5 | 1.0~2.5 | 0~1.0 |

Evaluating Indicator | Low Risk | Medium Risk | High Risk | Very High Risk |
---|---|---|---|---|

Melton ratio (c_{1}) | 0~0.0833 | 0.0833~0.25 | 0.25~0.4167 | 0.4167~1 |

Basin elongation (c_{2}) | 0.015~1 | 0.0075~0.015 | 0.0075~0.0025 | 0.0025~0 |

Basin height difference rate (c_{3}) | 0~0.02 | 0.02~0.04 | 0.04~0.06 | 0.06~1 |

Slope gradient (c_{4}) | 0~0.1667 | 0.1667~0.3333 | 0.3333~0.4444 | 0.4444~1 |

Loose material reserves (c_{5}) | 0~0.0067 | 0.0067~0.0333 | 0.0333~0.0667 | 0.0667~1 |

NDVI vegetation index (c_{6}) | 0.75~1 | 0.6~0.75 | 0.4~0.6 | 0~0.4 |

Average annual precipitation (c_{7}) | 0~0.5625 | 0.5625~0.6875 | 0.6875~0.775 | 0.775~1 |

Distance from structure (c_{8}) | 0.2~1 | 0.1~0.2 | 0.04~0.1 | 0~0.04 |

Evaluation Indicators | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | c_{7} | c_{8} |
---|---|---|---|---|---|---|---|---|

Weights | 0.1015 | 0.0677 | 0.2030 | 0.0761 | 0.1585 | 0.0507 | 0.3044 | 0.0381 |

Evaluation Indicators | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | c_{7} | c_{8} |
---|---|---|---|---|---|---|---|---|

Variability of indicators | 0.170 | 0.087 | 0.068 | 0.107 | 0.065 | 0.203 | 0.196 | 0.152 |

Conflicting indicators | 6.379 | 7.295 | 6.826 | 6.963 | 6.827 | 8.188 | 6.975 | 7.018 |

Amount of information | 1.086 | 0.633 | 0.466 | 0.742 | 0.445 | 1.665 | 1.364 | 1.067 |

Weighting factor | 0.1454 | 0.0848 | 0.0623 | 0.0993 | 0.0596 | 0.223 | 0.1827 | 0.1429 |

Evaluation Indicators | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | c_{7} | c_{8} |
---|---|---|---|---|---|---|---|---|

Analytic hierarchy process | 0.1015 | 0.0677 | 0.2030 | 0.0761 | 0.1585 | 0.0507 | 0.3044 | 0.0381 |

CRITIC method | 0.1454 | 0.0848 | 0.0623 | 0.0993 | 0.0596 | 0.2230 | 0.1827 | 0.1429 |

The optimal combination weighting factor | ${w}_{1}^{*}$ = 0.6509, ${w}_{2}^{*}$ = 0.3491 | |||||||

Portfolio weights | 0.1168 | 0.0737 | 0.1539 | 0.0842 | 0.1240 | 0.1108 | 0.2619 | 0.0747 |

Number | Low Risk | Medium Risk | High Risk | Extremely High Risk |
---|---|---|---|---|

1# | −0.2524 | −0.2076 | −0.2398 | −0.2708 |

2# | −0.3152 | −0.0071 | −0.1815 | −0.2710 |

3# | −0.3330 | −0.2220 | −0.1679 | −0.2461 |

4# | −0.3713 | −0.2645 | −0.1726 | −0.1247 |

Number | Extension Evaluation | Information Quantity Evaluation | Related Technique Standard | Field Check |
---|---|---|---|---|

1# | Medium risk | Low risk | Medium risk | Medium risk |

2# | Medium risk | Medium risk | Medium risk | Medium risk |

3# | high risk | high risk | high risk | high risk |

4# | Extremely high risk | Extremely high risk | Extremely high risk | Extremely high risk |

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Li, H.; Bai, X.; Zhai, X.; Zhao, J.; Zhu, X.; Li, C.; Liu, K.; Wang, Q.
Research on Extension Evaluation Method of Mudslide Hazard Based on Analytic Hierarchy Process–Criteria Importance through Intercriteria Correlation Combination Assignment of Game Theory Ideas. *Water* **2023**, *15*, 2961.
https://doi.org/10.3390/w15162961

**AMA Style**

Li H, Bai X, Zhai X, Zhao J, Zhu X, Li C, Liu K, Wang Q.
Research on Extension Evaluation Method of Mudslide Hazard Based on Analytic Hierarchy Process–Criteria Importance through Intercriteria Correlation Combination Assignment of Game Theory Ideas. *Water*. 2023; 15(16):2961.
https://doi.org/10.3390/w15162961

**Chicago/Turabian Style**

Li, Hui, Xueshan Bai, Xing Zhai, Jianqing Zhao, Xiaolong Zhu, Chenxi Li, Kehui Liu, and Qizhi Wang.
2023. "Research on Extension Evaluation Method of Mudslide Hazard Based on Analytic Hierarchy Process–Criteria Importance through Intercriteria Correlation Combination Assignment of Game Theory Ideas" *Water* 15, no. 16: 2961.
https://doi.org/10.3390/w15162961