# Evaluation Model and Application of the Implementation Effectiveness of the River Chief System (RCS)—Taking Henan Province as an Example

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. CRITIC, AHP, and Game Theory for Weighting Method

#### 2.2. River Chief System and Set Pair Analysis Methodology

## 3. Determination of Indicator Weights

#### 3.1. AHP for Determining Subjective Weight of Indicators

- (1)
- According to the selected set of indicators, construct the corresponding hierarchical structure. Using the RCS as the evaluation object, establish a three-level hierarchy, including the goal level, criterion level, and indicator level. The goal level represents the effectiveness of implementing the RCS, and the criterion level consists of six aspects: organizational management effectiveness, water resource protection effectiveness, water environment governance effectiveness, water pollution prevention and control effectiveness, water ecological restoration effectiveness, and water area shoreline management effectiveness. The goal level provides a detailed description and explanation of the criterion level.
- (2)
- Construct the judgment matrix. To reduce errors caused by subjective judgments during the evaluation process, a 1–5 scale method is used. By consulting expert opinions, scores are given to each indicator based on their importance to the effectiveness of implementing the RCS, and the judgment matrix is constructed.
- (3)
- Calculation of eigenvectors, eigenvalues, and weights. Using the maximum eigenvalue method, calculate the maximum eigenvalue and the corresponding normalized eigenvector for the judgment matrix.
- (4)
- Consistency test. If the consistency test is passed, it indicates that the judgment matrix is reasonable and has an explanatory value.

#### 3.2. Improved CRITIC Method for Determining Objective Weights of Indicators

- (1)
- For measuring the conflicts among indicators, the traditional CRITIC method typically uses the Pearson correlation coefficient. However, the Pearson coefficient may not accurately represent the correlation when data do not follow a normal distribution, or the sample size is less than 30 [54]. Therefore, this study replaces the Pearson coefficient with the Spearman correlation coefficient.
- (2)
- The correlation coefficient can be positive or negative, but in this study, absolute values of the correlation coefficients are used to avoid unnecessary biases during the calculation.
- (3)
- The traditional CRITIC method uses the standard deviation to measure the relative importance of indicators. However, in practical applications, it has been found that using the standard deviation is not sufficient. Instead, using the average deviation can provide better reliability and reduce errors caused by non-normality and skewness in these data. Therefore, this study replaces the standard deviation with the average deviation to measure the relative importance of indicators.

#### 3.3. Game Theory-Based Weight Optimization

## 4. Model for Evaluating the Effectiveness of River Chief System

## 5. Application Case

#### 5.1. Study Area Overview

#### 5.2. System of Indicators

#### 5.3. Data Sources and Indicator Values

#### 5.4. Evaluation Grading Criteria

#### 5.5. Evaluation Results of River Chief System in Henan Province

#### 5.5.1. Weighting Results of Evaluation Indicators

#### 5.5.2. Comprehensive Evaluation Result and Analysis

#### 5.5.3. Analysis of Single Indicator Evaluation Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Table 1.**Evaluation Index System for Assessing the Implementation Effectiveness of the RCS in Henan Province.

Goal Layer | Criterion Layer | Indicator Layer |
---|---|---|

Effectiveness | organizational and managerial effectiveness (S1) | Establishment and Operation of Working Mechanism (C1) |

River Inspection Task Implementation (C2) | ||

Regulatory Digitization (C3) | ||

Enforcement Oversight (C4) | ||

Problem Rectification Status (C5) | ||

Public Satisfaction Level (C6) | ||

water resource protection effectiveness (S2) | Underground Water Resources Total Volume (C7) | |

Efficient Utilization Coefficient of Irrigation Water in Farmland (C8) | ||

Recycling Rate of Industrial Water (C9) | ||

Rural Tap Water Coverage Rate (C10) | ||

water environment governance effectiveness (S3) | Compliance Rate of Centralized Drinking Water Source Water Quality (C11) | |

Compliance Rate of Surface Water Environmental Quality (C12) | ||

Percentage of Surface Water in Class V Poor Quality (C13) | ||

water pollution control effectiveness (S4) | Comprehensive Utilization Rate of Livestock and Poultry Manure in Animal Farming (C14) | |

Harmless Treatment Rate of Sludge (C15) | ||

Fertilizer Application Intensity (C16) | ||

Pesticide Application Intensity (C17) | ||

Urban Wastewater Centralized Treatment Rate (C18) | ||

Rural Domestic Wastewater Treatment Rate (C19) | ||

Rate of Harmless Treatment of Household Waste (C20) | ||

water ecological restoration effectiveness (S5) | Rate of Soil and Water Conservation (C21) | |

Rate of wetland conservation (C22) | ||

Construction Status of Wetland Parks (C23) | ||

water area shoreline management effectiveness (S6) | Rate of Compliance with Levee Standards (C24) | |

Rate of Rectification of Four Disorderly Issues (C25) | ||

Elimination Rate of Black and Odorous Water Bodies in Built-up Areas (C26) |

**Table 2.**Values of Indicators for Evaluating the Implementation Effectiveness of the RCS in Henan Province.

Indicators | Year 2018 | Year 2019 | Year 2020 | Year 2021 |
---|---|---|---|---|

C1 (Score) | 85 | 90 | 90 | 90 |

C2 (Score) | 100 | 100 | 100 | 100 |

C3 (Score) | 80 | 85 | 90 | 90 |

C4 (Score) | 80 | 85 | 90 | 90 |

C5 (Score) | 88 | 90 | 95 | 96 |

C6 (Score) | 83 | 85 | 88 | 88 |

C7 (1 × 10^{8} m^{3}) | 188 | 119.1 | 185.8 | 257 |

C8 | 0.614 | 0.615 | 0.617 | 0.62 |

C9 (%) | 94.83 | 95.93 | 96.61 | 90.07 |

C10 (%) | 87 | 91 | 91 | 91 |

C11 (%) | 96.80 | 100 | 100 | 100 |

C12 (%) | 60.40 | 64 | 73.70 | 79.90 |

C13 (%) | 3.50 | 0 | 0 | 0 |

C14 (%) | 75 | 77.20 | 79.50% | 82 |

C15 (%) | 93.75 | 94.64 | 79.20 | 99.37 |

C16 (kg/hm^{2}) | 1310 | 1251 | 1186 | 1143 |

C17 (kg/hm^{2}) | 21.48 | 20.12 | 18.74 | 17.83 |

C18 (%) | 97.30 | 97.72 | 98.30 | 99.21 |

C19 (%) | 20.00 | 24.70 | 30 | 33.40 |

C20 (%) | 99.71 | 99.65 | 99.94 | 100 |

C21 (%) | 87.05 | 87.27 | 87.36 | 87.27 |

C22 (%) | 47.80 | 47.80 | 52.19 | 56.58 |

C23 (Score) | 88 | 91 | 95 | 90 |

C24 (%) | 66.56 | 66.86 | 67.5 | 68.36 |

C25 (%) | 20.21 | 99.20 | 100 | 100 |

C26 (%) | 92.00 | 100.00 | 100.00 | 100.00 |

**Table 3.**Grading Criteria for Indicators Used to Evaluate the Implementation Effectiveness of the RCS in Henan Province.

Indicators | Classification Levels and Standards | |||
---|---|---|---|---|

Level I | Level II | Level III | Level IV | |

C1 (Score) | [85, 100] | [75, 85] | [60, 75] | [0, 60] |

C2 (Score) | [95, 100] | [80, 95] | [60, 80] | [0, 60] |

C3 (Score) | [85, 100] | [60, 85] | [40, 60] | [0, 40] |

C4 (Score) | [85, 100] | [75, 85] | [60, 75] | [0, 60] |

C5 (Score) | [85, 100] | [75, 85] | [60, 75] | [0, 60] |

C6 (Score) | [80, 100] | [70, 80] | [60, 70] | [0, 60] |

C7 (1 × 10^{8} m^{3}) | [180, +∞) | [120, 180] | [100, 120] | [0, 100] |

C8 | [0.6, 1] | [0.5, 0.6] | [0.4, 0.5] | [0, 0.4] |

C9 (%) | [91, 100] | [81, 91] | [71, 81] | [0, 71] |

C10 (%) | [85, 100] | [75, 85] | [60, 75] | [0, 60] |

C11 (%) | [97.7, 100] | [75, 97.7] | [60, 75] | [0, 60] |

C12 (%) | [80, 100] | [70, 80] | [56.4, 70] | [0, 56.4] |

C13 (%) | [0, 9.6] | [9.6, 20] | [20, 50] | [50, 100] |

C14 (%) | [80, 100] | [70, 80] | [60, 70] | [0, 60] |

C15 (%) | [90, 100] | [80, 90] | [60, 80] | [0, 60] |

C16 (kg/hm^{2}) | [0, 225] | [225, 240] | [240, 250] | (−∞, 250] |

C17 (kg/hm^{2}) | [0, 10] | [10, 20] | [20, 25] | (−∞, 25] |

C18 (%) | [95, 100] | [75, 95] | [50, 75] | [0, 50] |

C19 (%) | [75, 100] | [50, 75] | [25, 50] | [0, 25] |

C20 (%) | [85, 100] | [75, 85] | [60, 75] | [0, 60] |

C21 (%) | [80, 100] | [70, 80] | [60, 70] | [0, 60] |

C22 (%) | [70, 100] | [50, 70] | [40, 50] | [0, 40] |

C23 (Score) | [85, 100] | [75, 85] | [60, 75] | [0, 60] |

C24 (%) | [70, 100] | [60, 70] | [40, 60] | [0, 40] |

C25 (%) | [90, 100] | [70, 90] | [50, 70] | [0, 50] |

C26 (%) | [90, 100] | [80, 90] | [70, 80] | [0, 70] |

**Table 4.**Weights of Indicators for Evaluating the Implementation Effectiveness of the RCS in Henan Province.

Indicators | AHP | CRITIC | Game Theory |
---|---|---|---|

C1 | 0.0248 | 0.0398 | 0.0318 |

C2 | 0.0097 | 0.0286 | 0.0184 |

C3 | 0.0059 | 0.0286 | 0.0164 |

C4 | 0.0059 | 0.0286 | 0.0164 |

C5 | 0.0157 | 0.0293 | 0.0220 |

C6 | 0.0381 | 0.0305 | 0.0346 |

C7 | 0.0245 | 0.0617 | 0.0417 |

C8 | 0.0454 | 0.0241 | 0.0355 |

C9 | 0.0847 | 0.0907 | 0.0875 |

C10 | 0.0454 | 0.0398 | 0.0428 |

C11 | 0.1094 | 0.0398 | 0.0772 |

C12 | 0.0379 | 0.0270 | 0.0329 |

C13 | 0.0526 | 0.0398 | 0.0467 |

C14 | 0.0083 | 0.0240 | 0.0156 |

C15 | 0.0152 | 0.0836 | 0.0469 |

C16 | 0.0163 | 0.0251 | 0.0206 |

C17 | 0.0163 | 0.0249 | 0.0203 |

C18 | 0.0546 | 0.0235 | 0.0402 |

C19 | 0.0546 | 0.0252 | 0.0410 |

C20 | 0.0346 | 0.0660 | 0.0491 |

C21 | 0.0163 | 0.0381 | 0.0264 |

C22 | 0.0297 | 0.0375 | 0.0333 |

C23 | 0.0540 | 0.0511 | 0.0526 |

C24 | 0.0286 | 0.0245 | 0.0267 |

C25 | 0.0857 | 0.0285 | 0.0592 |

C26 | 0.0857 | 0.0398 | 0.0645 |

Time Period | Components of Connection Numbers | Connection Numbers | Ranking Results | Evaluation Results | ||||

Level I | Level II | Level III | Level IV | |||||

Set Pair Analysis Model | 2018 | 0.4525 | 0.3539 | 0.1041 | 0.0895 | 0.4454 | 4 | Level II |

2019 | 0.5289 | 0.2931 | 0.1213 | 0.0567 | 0.5289 | 3 | Level I | |

2020 | 0.5524 | 0.2934 | 0.1170 | 0.0372 | 0.5734 | 2 | Level I | |

2021 | 0.6035 | 0.2948 | 0.0694 | 0.0324 | 0.6455 | 1 | Level I | |

Time Period | Positive Ideal Solution Distance(D+) | Negative Ideal Solution Distance(D−) | Composite Scores | Ranking Results | Evaluation Results | |||

Entropy-based Weighted TOPSIS | 2018 | 0.4809 | 0.7483 | 0.6088 | 4 | Level II | ||

2019 | 0.4245 | 0.8257 | 0.6604 | 3 | Level II | |||

2020 | 0.3365 | 0.8699 | 0.721 | 2 | Level II | |||

2021 | 0.2944 | 0.888 | 0.751 | 1 | Level II |

**Table 6.**Evaluation Results of Single Indicator for the Implementation Effectiveness of the RCS in Henan Province, 2018–2019.

Indicators | Year 2018 | Year 2019 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Level I | Level II | Level III | Level IV | Evaluation Result | Level I | Level II | Level III | Level IV | Evaluation Result | |

C1 | 1 | 1 | −1 | −1 | Level I | 1 | 0.3333 | −1 | −1 | Level I |

C2 | 1 | −1 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

C3 | 0.6 | 1 | −0.6 | −1 | Level II | 1 | 1 | −1 | −1 | Level I |

C4 | 0 | 1 | 0 | −1 | Level II | 1 | 1 | −1 | −1 | Level I |

C5 | 1 | 0.6 | −1 | −1 | Level I | 1 | 0.3333 | −1 | −1 | Level I |

C6 | 1 | 0.7 | −1 | −1 | Level I | 1 | 0.5 | −1 | −1 | Level I |

C7 | 1 | 0.8667 | −1 | −1 | Level I | −1 | 0.91 | 1 | −0.91 | Level III |

C8 | 1 | 0.93 | −1 | −1 | Level I | 1 | 0.925 | −1 | −1 | Level I |

C9 | 1 | 0.1489 | −1 | −1 | Level I | 1 | −0.0956 | −1 | −1 | Level I |

C10 | 1 | 0.7333 | −1 | −1 | Level I | 1 | 0.2 | −1 | −1 | Level I |

C11 | 0.9207 | 1 | −0.9207 | −1 | Level II | 1 | −1 | −1 | −1 | Level I |

C12 | 1 | −0.4118 | −1 | 0.4118 | Level I | −1 | 0.1176 | 1 | −0.1176 | Level III |

C13 | 1 | −0.2708 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

C14 | 0 | 1 | 0 | −1 | Level II | 0.44 | 1 | −0.44 | −1 | Level II |

C15 | 1 | 0.25 | −1 | −1 | Level I | 1 | 0.072 | −1 | −1 | Level I |

C16 | −1 | −1 | −0.2114 | 1 | Level IV | −1 | −1 | −0.144 | 1 | Level IV |

C17 | −1 | 0.408 | 1 | −0.408 | Level III | −1 | 0.952 | 1 | −0.952 | Level III |

C18 | 1 | 0.08 | −1 | −1 | Level I | 1 | 0.12 | −1 | −1 | Level I |

C19 | −1 | −1 | 0.6 | 1 | Level IV | −1 | −1 | 0.624 | 1 | Level IV |

C20 | 1 | −0.9613 | −1 | −1 | Level I | 1 | −0.9533 | −1 | −1 | Level I |

C21 | 1 | 0.295 | −1 | −1 | Level I | 1 | 0.273 | −1 | −1 | Level I |

C22 | −1 | 0.56 | 1 | −0.56 | Level III | −1 | 0.56 | 1 | −0.56 | Level III |

C23 | 1 | 0.6 | −1 | −1 | Level I | 1 | 0.2 | −1 | −1 | Level I |

C24 | 0.312 | 1 | −0.312 | −1 | Level II | 0.372 | 1 | −0.372 | −1 | Level II |

C25 | −1 | −1 | −0.1916 | 1 | Level IV | 1 | −0.84 | −1 | −1 | Level I |

C26 | 1 | 0.6 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

**Table 7.**Evaluation Results of Single Indicator for the Implementation Effectiveness of the RCS in Henan Province, 2020–2021.

Indicators | Year 2020 | Year 2021 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Level I | Level II | Level III | Level IV | Evaluation Result | Level I | Level II | Level III | Level IV | Evaluation Result | |

C1 | 1 | 0.3333 | −1 | −1 | Level I | 1 | 0.3333 | −1 | −1 | Level I |

C2 | 1 | −1 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

C3 | 1 | 0.3333 | −1 | −1 | Level I | 1 | 0.3333 | −1 | −1 | Level I |

C4 | 1 | 0.3333 | −1 | −1 | Level I | 1 | 0.3333 | −1 | −1 | Level I |

C5 | 1 | −0.3333 | −1 | −1 | Level I | 1 | −0.4667 | −1 | −1 | Level I |

C6 | 1 | 0.2 | −1 | −1 | Level I | 1 | 0.2 | −1 | −1 | Level I |

C7 | 1 | 0.9033 | −1 | −1 | Level I | 1 | −0.2833 | −1 | −1 | Level I |

C8 | 1 | 0.915 | −1 | −1 | Level I | 1 | 0.9 | −1 | −1 | Level I |

C9 | 1 | −0.2467 | −1 | −1 | Level I | 0.814 | 1 | −0.814 | −1 | Level II |

C10 | 1 | 0.2 | −1 | −1 | Level I | 1 | 0.2 | −1 | −1 | Level I |

C11 | 1 | −1 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

C12 | −0.26 | 1 | 0.26 | −1 | Level II | 0.98 | 1 | −0.98 | −1 | Level II |

C13 | 1 | −1 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

C14 | 0.9 | 1 | −0.9 | −1 | Level II | 1 | 0.8 | −1 | −1 | Level I |

C15 | −1 | 0.92 | 1 | −0.92 | Level III | 1 | −0.874 | −1 | −1 | Level I |

C16 | −1 | −1 | −0.0697 | 1 | Level IV | −1 | −1 | −0.0206 | 1 | Level IV |

C17 | −0.748 | 1 | 0.748 | −1 | Level II | −0.566 | 1 | 0.566 | −1 | Level II |

C18 | 1 | −0.32 | −1 | −1 | Level I | 1 | −0.684 | −1 | −1 | Level I |

C19 | −1 | −0.6 | 1 | 0.6 | Level III | −1 | −0.328 | 1 | 0.328 | Level III |

C20 | 1 | −0.992 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

C21 | 1 | 0.264 | −1 | −1 | Level I | 1 | 0.273 | −1 | −1 | Level I |

C22 | −0.781 | 1 | 0.781 | −1 | Level II | −0.342 | 1 | 0.342 | −1 | Level II |

C23 | 1 | −0.333 | −1 | −1 | Level I | 1 | 0.3333 | −1 | −1 | Level I |

C24 | 0.5 | 1 | −0.5 | −1 | Level II | 0.672 | 1 | −0.672 | −1 | Level II |

C25 | 1 | −1 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

C26 | 1 | −1 | −1 | −1 | Level I | 1 | −1 | −1 | −1 | Level I |

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## Share and Cite

**MDPI and ACS Style**

Liu, J.; Chen, X.; Su, L.; Li, Y.; Xu, Y.; Qi, L.
Evaluation Model and Application of the Implementation Effectiveness of the River Chief System (RCS)—Taking Henan Province as an Example. *Systems* **2023**, *11*, 481.
https://doi.org/10.3390/systems11090481

**AMA Style**

Liu J, Chen X, Su L, Li Y, Xu Y, Qi L.
Evaluation Model and Application of the Implementation Effectiveness of the River Chief System (RCS)—Taking Henan Province as an Example. *Systems*. 2023; 11(9):481.
https://doi.org/10.3390/systems11090481

**Chicago/Turabian Style**

Liu, Jianting, Xuanyu Chen, Limin Su, Yanbin Li, Yanxue Xu, and Lei Qi.
2023. "Evaluation Model and Application of the Implementation Effectiveness of the River Chief System (RCS)—Taking Henan Province as an Example" *Systems* 11, no. 9: 481.
https://doi.org/10.3390/systems11090481