# Sustainability Analysis of the Water Environment Carrying Capacity of Harbin City Based on an Optimized Set Pair Analysis Posture-Deviation Coefficient Method Evaluation Model

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{3}, with a national per-capita level of 55%. Harbin City’s per-capita water resource possession is only 230 m

^{3}, and the city’s water area has been recovering year by year. Up until now, there have been four municipal nature reserves, with an area of 57,000 hectares. The forest coverage rate reaches 45.88%, ranking third among sub-provincial cities in China. The total area of the wetlands is 300,200 hectares, accounting for 5.8% of the city’s total land area, including eight national-level wetlands and four provincial-level wetlands. The proportion of ecological demonstration areas has reached 80%, and the city’s per-capita park green space has reached 10.1 square meters. By the end of 2020, the water area of Harbin City only accounted for 0.08% of the total land area. Over the past 10 years, 100% of the city’s centralized drinking water has met standards. The city’s 25 surface water national examination sections meet the standard rate of 88%, including an excellent rate of 72%. The centralized urban sewage treatment rate reached 88%, an increase of 2.5 percentage points, and the water quality of the main Songhua River steadily rose to the national three-class standard. The municipal domestic waste treatment rate reached 75.09%, an increase of 0.3 percentage points. The industrial solid waste disposal utilization rate reached 100%. At present, Harbin City has become an aging society; the mobile population has become the main driving force of population growth in Harbin City. From the perspective of economic structure, the proportion of tertiary industry has reached over 50% and is expected to expand further in the future. From the perspective of water allocation, the structure of water consumption is extremely uncoordinated with the structure of the economy. With the future expansion of industry, there will be a tendency for this to continue to worsen.

#### 2.2. Data Sources

#### 2.3. Methods

#### 2.3.1. Relationship between System Methods

#### 2.3.2. Calculating Optimization Index Weights

_{ij}is the standard sample value. x*

_{ij}is the dimensionless standard sample value.

^{*}

_{ij}} is projected in the direction of vector c to obtain the one-dimensional projection value Z

_{i}. To explore the correlation between the evaluation level and the bearing capacity evaluation index, the projection index function is constructed so that the absolute value of the correlation coefficient |R| between the projection value Z

_{i}and the experience level y

_{i}is as large as possible.

_{j}is the corresponding weight of the element in the criterion layer B. c

_{j}is the corresponding weight of the element in the scheme layer P. ω

_{j}is the combination weight.

_{j}is obtained, and the weight of indicator j is taken as c

_{2j}. Based on the mathematical properties of the projection values and the requirements of the weight solution of this paper, the constraints of the projection indicator function are set.

#### 2.3.3. Calculating Evaluation Linkage

_{1j}to s

_{3j}are the critical values of the evaluation criteria from Levels 1 to 3, respectively. s

_{0j}is another, more distant critical value in the evaluation criteria interval; i = 1, 2,…, j = 1, 2,…, n. For positive indicators, it is sufficient to reverse the interval number on the right side of Equations (8)–(10).

_{j}is the weight of the jth evaluation index.

#### 2.3.4. Calculating Set-to-Potential Eigenvalues

#### 2.3.5. Determination of Rank by the Partial Coefficient Method

^{+}a reflects the rate of evolution of level b to level a, i.e., the support of component b to Level 1. Component c plays an absolute antagonistic role to Level 1, and the support rate is recorded as 0. The number of ternary evaluation links is noted as vector U = (a, b, c), its first-order support rate matrix for each level, and the first-order support degree vector S′ for the levels.

_{1}′, S

_{2}′, S

_{3}′)

_{1}′, S

_{2}′, and S

_{2}′ are compared and the rank is determined according to the principle of maximum support. Second-order biased positive correlations ∂

^{2+}a indicate the evolution rate of the opposite component to the positive component and reflect the support of the opposite component to “Rank 1” in the evaluation process. In contrast, the second-order negative correlation ∂

^{−}c indicates the evolution rate of the positive component to the negative component and reflects the support of the same component to “Rank 3” in the evaluation process. Based on this, Equation (16) is extended to obtain the second-order support matrix for rank determination and the second-order support vector S″ for each rank. The magnitudes of S

_{1}″, S

_{2}″, and S

_{3}″ are compared, and the rank is determined again according to the principle of maximum support.

_{1}″, S

_{2}″, S

_{3}″)

#### 2.3.6. Comparative Test of Applicability by the Confidence Criterion Judging Method

_{1}, C

_{2},…, C

_{k}) be an ordered partition class (i.e., the set of evaluation levels) of the rubric space F, If C

_{1}> C

_{2}> … > C

_{k}(i.e., “good > good > fair > poor > poor”).

## 3. Results and Discussion

#### 3.1. Load Factor Values and Evaluation Index Weights

_{6}and C

_{7}; C

_{1}and C

_{10}; and C

_{14}, C

_{15}, C

_{16}, and C

_{18}having the same weight values, which indicates that the AHP weights are relatively rough in reflecting the complex situations of multi-objective, multi-level, and multi-criteria real systems. Xu et al. used the AHP method and entropy weighting method to calculate the weights of each indicator, ignoring the importance of the indicators themselves, and sometimes the determined indicator weights can be far from the expected results [50]. The PP-AHP method can further optimize the index weights, and the PP-AHP weight-solving method closely combines the AHP experts’ empirical weighting with the objective weighting of the PP method. This is not only close to the actual situation but also avoids excessive human intervention. According to the PP-AHP weighting results, the five indicators with the greatest impact on the carrying capacity of the water environment in Harbin are C

_{7}, C

_{15}, C

_{18}, C

_{17}, and C

_{14}. The corresponding weight for the water quantity indicator system is 0.157; the corresponding weight for the water consumption indicator system is 0.297; and the corresponding weight for the water quality indicator system is 0.55. The quality impact indicator system represents the largest proportion of the evaluation of the carrying capacity of the water environment in Harbin from 2006 to 2020 and is the subsystem with the largest impact on the carrying capacity of the water environment in Harbin.

#### 3.2. Eigenvalue and Evaluation Result Level

#### 3.3. Support and Judgment Level

_{14}, C

_{15}, C

_{17}, and C

_{18}, which have a larger weight in water quality impact indicators, have been significantly improved.

#### 3.4. Confidence Method for the Comparison Test Optimization Model

#### 3.5. Sustainability Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Duan, C.; Liu, C.; Chen, X.; Liu, W.; Zheng, H. Discussion on the Concept and Research Methods of Regional Water Resources Carrying Capacity. Acta Geogr. Sin.
**2010**, 65, 82–90. [Google Scholar] - Wang, S.; Zou, L.X.; Li, H.B.; Zheng, K.K.; Wang, Y.; Zheng, G.C.; Li, J. Full-scale membrane bioreactor process WWTPs in East Taihu basin: Wastewater characteristics, energy consumption and sustainability. Sci. Total Environ.
**2020**, 723, 137983. [Google Scholar] [CrossRef] - Yang, Q.C.; Wang, H.; Mu, H.K.; Luo, J.N.; Bao, X.H.; Bian, J.M.; Martin, J.D. Risk assessment of water resources and environmental carrying capacity in Yinchuan city. Hum. Ecol. Risk Assess.
**2019**, 25, 120–131. [Google Scholar] [CrossRef] - Zhu, L.J.; Li, X.C.; Bai, Y.R.; Yi, T.L.; Yao, L.Q. Evaluation of water resources carrying capacity and its obstruction factor Analysis: A case study of hubei province, China. Water
**2019**, 11, 2573. [Google Scholar] [CrossRef] - Bian, D.H.; Yang, X.H.; Wu, F.F.; Babuna, P.; Luo, Y.K.; Wang, B.; Chen, Y.J. A three-stage hybrid model investigating regional evaluation, pattern analysis and obstruction factor analysis for water resource spatial equilibrium in China. J. Clean. Prod.
**2022**, 331, 129940. [Google Scholar] [CrossRef] - Chi, M.B.; Zhang, D.S.; Fan, G.W.; Zhang, W.; Liu, H.L. Prediction of water resource carrying capacity by the analytic hierarchy process-fuzzy discrimination method in a mining area. Ecol. Indic.
**2019**, 96, 647–655. [Google Scholar] [CrossRef] - Wang, W.; Zeng, W. Optimizing the Regional Industrial Structure Based on the Environmental Carrying Capacity: An Inexact fuzzy Multi-Objective Programming Model. Sustainability
**2013**, 5, 5391. [Google Scholar] [CrossRef] - Chen, H.S. The Establishment and Application of Environment Sustainability Evaluation Indicators for Ecotourism Environments. Sustainability
**2015**, 7, 727. [Google Scholar] [CrossRef] - Wang, W.; Sun, Y.; Wu, J. Environmental Warning System Based on the DPSIR Model: A Practical and Concise Method for Environmental Assessment. Sustainability
**2018**, 10, 1728. [Google Scholar] [CrossRef] - Wang, H.R.; Gong, S.X.; Deng, C.Y.; Yang, B.; Zuo, P. Research on water resources carrying capacity based on five-element connection number. J. Northwest Univ.
**2019**, 49, 211–218. [Google Scholar] - Ye, F.; Jin, J.L.; Fang, G.H. Evaluation of water resources carrying capacity of Hefei City based on set pair analysis connection number. J. Water Resour. Eng.
**2020**, 31, 85–90. [Google Scholar] - Liu, Y.H.; Li, Y.B.; Liang, X.Y.; Ran, C.H. Study on water resource carrying capacity evaluation and change in China. Resour. Environ. Yangtze Basin
**2019**, 28, 1080–1091. [Google Scholar] - Davies, E.G.R.; Simonovic, S.P. Global water resources modeling with an integrated model of the social–economic–environmental system. Adv. Water Resour.
**2011**, 34, 684–700. [Google Scholar] [CrossRef] - Paredes-Arquiola, J.; Andreu-Alvarez, J.; Martin-Monerris, M.; Solera, A. Water quantity and quality models applied to the Jucar River basin, Spain. Water Resour. Manag.
**2010**, 24, 2759–2779. [Google Scholar] [CrossRef] - Langsdale, S.; Beall, A.; Carmichael, J.; Cohen, S.; Forster, C. An exploration of water resources futures under climate change using system dynamics modeling. Integr. Assess.
**2007**, 7, 51–79. [Google Scholar] - Almendinger, J.E.; Ulrich, J.S. Use of SWAT to Estimate Spatial Scaling of Phosphorus Export Coefficients and Load Reductions Due to Agricultural BMPS. J. Am. Water Resour. Assoc.
**2017**, 53, 547–561. [Google Scholar] [CrossRef] - Dai, M.; Wang, L.; Wei, X. Spatial differentiation of water resources carrying capacity in Guangxi based on entropy weight fuzzy comprehensive evaluation model. Soil Water Conserv. Res.
**2016**, 23, 193–199. [Google Scholar] - Gao, J. The evaluation of water resources carrying capacity in Hohhot based on fuzzy analysis method. Inner Mong. Water Conserv.
**2020**, 4, 13–15. [Google Scholar] - Guo, Y.; Wang, R.; Tong, Z.J.; Liu, X.P.; Zhang, J.Q. Dynamic evaluation and regionalization of maize drought vulnerability in the midwest of Jilin Province. Sustainability
**2019**, 11, 4234. [Google Scholar] [CrossRef] - Jago-on, K.A.B.; Kaneko, S.; Fujikura, R.; Fujiwara, A.; Imai, T.; Matsumoto, T.; Zhang, J.Y.; Tanikawa, H.; Tanaka, K.; Lee, B.; et al. Urbanization and subsurface environmental issues: An attempt at DPSIR model application in Asian cities. Sci. Total Environ.
**2009**, 407, 3089–3104. [Google Scholar] [CrossRef] [PubMed] - Wang, Z.; Zhou, J.Q.; Loaiciga, H.; Guo, H.C.; Hong, S. A DPSIR model for ecological security assessment through indicator screening: A case study at Dianchi Lake in China. PLoS ONE
**2015**, 10, e0131732. [Google Scholar] [CrossRef] - Beltaos, S. Threshold between mechanical and thermal breakup of river ice cover. Cold Reg. Sci. Technol.
**2003**, 37, 1–13. [Google Scholar] [CrossRef] - Yang, H.M.; Zhao, K.Q. The calculation and application of partial connection numbers. CAAI Trans. Intell. Syst.
**2019**, 14, 865–876. [Google Scholar] - Wang, T.Y.; Du, C.; Nie, T.Z.; Sun, Z.Y.; Zhu, S.J.; Feng, C.X.; Dai, C.L.; Chu, L.L.; Liu, Y.; Liang, Q.Z. Spatiotemporal Analysis of Maize Water Requirement in the Heilongjiang Province of China during 1960–2015. Water
**2020**, 12, 2472. [Google Scholar] [CrossRef] - Zhang, J.; Zhang, C.L.; Shi, W.L.; Fu, Y.C. Quantitative evaluation and optimized utilization of water resources-water environment carrying capacity based on naturebased solutions. J. Hydrol.
**2019**, 568, 96–107. [Google Scholar] [CrossRef] - Zhu, Y.H.; Drake, S.; Lü, H.S.; Xia, J. Analysis of Temporal and Spatial Differences in Eco-environmental Carrying Capacity Related to Water in the Haihe River Basins, China. Water Resour. Manag.
**2010**, 24, 1089–1105. [Google Scholar] [CrossRef] - Miao, H.C.; Li, D.L.; Zuo, Q.T.; Yu, L.; Fei, X.X.; Hao, L.G. A scenario-based optimization model for planning sustainable water-resources process management under uncertainty. Processes
**2019**, 7, 312. [Google Scholar] [CrossRef] - Beltaos, S. Hydro-climatic impacts on the ice cover of the lower Peace River. Hydrol. Process.
**2008**, 22, 3252–3263. [Google Scholar] [CrossRef] - Song, X.M.; Kong, F.Z.; Zhan, C.S. Assessment of Water Resources Carrying Capacity in Tianjin City of China. Water Resour. Manag.
**2011**, 25, 857–873. [Google Scholar] [CrossRef] - Klavins, M.; Briede, A.; Rodinov, V. Long term changes in ice and discharge regime of rivers in the Baltic region in relation to climatic variability. Clim. Chang.
**2009**, 95, 485–498. [Google Scholar] [CrossRef] - Sagin, J.; Van Der Sanden, J.J.; Evans, E.; McKay, H.; Das, A.; Lindenschmidt, K.-E. Monitoring the freeze-up and ice cover progression of the Slave River. Can. J. Civ. Eng.
**2015**, 42, 609–621. [Google Scholar] - Yang, J.F.; Lei, K.; Khu, S.; Meng, W. Assessment of Water Resources Carrying Capacity for Sustainable Development Based on A System Dynamics Model: A Case Study of Tieling City, China. Water Resour. Manag.
**2014**, 29, 885–899. [Google Scholar] [CrossRef] - Zhang, Q.; Liu, B.; Zhang, W.G.; Jin, G.; Li, Z.H. Assessing the Regional Spatio-temporal Pattern of Water Stress: A Case Study in Zhangye City of China. Phys. Chem. Earth
**2015**, 1, 2–9. [Google Scholar] [CrossRef] - Li, Z.L.; Shao, Q.X.; Xu, Z.X.; Cai, X.T. Analysis of Parameter Uncertainty in Semi-distributed Hydrological Models Using Bootstrap Method: A Case Study of Swat Model Applied to Yingluoxia Watershed in Northwest China. J. Hydrol.
**2010**, 385, 76–83. [Google Scholar] [CrossRef] - Yang, J.F.; Lei, K.; Khu, S.; Meng, W.; Qiao, F. Assessment of water environmental carrying capacity for sustainable development using a coupled system dynamics approach applied to the Tieling of the Liao River Basin, China. Environ. Earth Sci.
**2015**, 73, 5173–5183. [Google Scholar] [CrossRef] - Park, H.; Yoshikawa, Y.; Oshima, K.; Kim, Y.; Ngo-Duc, T.; Kimball, J.S.; Yang, D. Quantification of Warming Climate-Induced Changes in Terrestrial Arctic River Ice Thickness and Phenology. J. Clim.
**2016**, 29, 1733–1754. [Google Scholar] [CrossRef] - Zhang, Z.; Lu, W.X.; Zhao, Y.; Song, W.B. Development tendency analysis and evaluation of the water ecological carrying capacity in the Siping area of Jilin Province in China based on system dynamics and analytic hierarchy process. Ecol. Modell.
**2014**, 275, 9–21. [Google Scholar] [CrossRef] - Wang, Q.; Li, S.Q.; Li, R.R. Evaluating water resource sustainability in Beijing, China: Combining PSR model and matter-element extension method. J. Clean. Prod.
**2019**, 206, 171–179. [Google Scholar] [CrossRef] - Zhang, S.H.; Xiang, M.S.; Yang, J.S.; Fan, W.W.; Yi, Y.J. Distributed hierarchical evaluation and carrying capacity models for water resources based on optimal water cycle theory. Ecol. Indic.
**2019**, 101, 432–443. [Google Scholar] [CrossRef] - Gu, H.M.; Jia, L.; Jiang, X.H.; Xu, J.X.; Dong, G.T. Evaluation of water resources bearing capacity based on entropy-weight and matter-element assessment methods in midstream of Heihe River. J. Irrig. Drain Eng.
**2016**, 35, 87–92. [Google Scholar] - Mashaly, A.F.; Fernald, A.G. Identifying Capabilities and Potentials of System Dynamics in Hydrology and Water Resources as a Promising Modeling Approach for Water Management. Water
**2020**, 12, 1432. [Google Scholar] [CrossRef] - Barati, A.A.; Azadi, H.; Scheffran, J. A system dynamics model of smart groundwater governance. Agric. Water Manag.
**2019**, 221, 502–518. [Google Scholar] [CrossRef] - Vieira, E.D.; Sandoval-Solis, S. Water resources sustainability index for a water-stressed basin in Brazil. J. Hydrol. Reg. Stud.
**2018**, 19, 97–109. [Google Scholar] [CrossRef] - Zhao, Z.Y.; Li, W.C.; Wang, X.; Cui, T.T.; Cheng, Z.H.; Wang, S. Study on Water Resources Carrying Capacity in Ningxia Based on Principal Component Analysis and Factor Analysis. J. Hydrol.
**2017**, 37, 64–72. [Google Scholar] - Panno, A.; Carrus, G.; Lafortezza, R.; Mariani, L.; Sanesi, G. Nature-based solutions to promote human resilience and wellbeing in cities during increasingly hot summers. Environ. Res.
**2017**, 159, 249–256. [Google Scholar] [CrossRef] [PubMed] - Morris, R.L.; Konlechner, T.M.; Ghisalberti, M.; Swearer, S.E. From grey to green: Efficacy of eco-engineering solutions for nature-based coastal defence. Glob. Chang. Biol.
**2018**, 24, 1827–1842. [Google Scholar] [CrossRef] [PubMed] - Lorenz, S.; Pusch, M.T. Estimating the recreational carrying capacity of a lowland river section. Water Sci. Technol.
**2012**, 66, 2033–2039. [Google Scholar] [CrossRef] - Lin, L.; Liu, Y.; Chen, J.N.; Zhang, T.Z.; Zeng, S.Y. Comparative analysis of environmental carrying capacity of the Bohai Sea Rim area in China. J. Environ. Monit.
**2011**, 13, 3178–3184. [Google Scholar] [CrossRef] [PubMed] - Zhang, H.; Bian, J.M.; Wan, H.L. Hydrochemical appraisal of groundwater quality and pollution source analysis of oil field area: A case study in Daqing City, China. Environ. Sci. Pollut. Res.
**2021**, 28, 18667–18685. [Google Scholar] [CrossRef] [PubMed] - Xu, S.B.; Xu, D.S.; Liu, L.L. Construction of Regional Informatization Ecological Environment Based on the Entropy Weight Modified AHP Hierarchy Model. Sustain. Comput. Inform. Syst.
**2019**, 18, 2210–5379. [Google Scholar] [CrossRef] - Dai, D.; Sun, M.D.; Xu, X.Q.; Lei, K. Assessment of the water resource carrying capacity based on the ecological footprint: A case study in zhangjiakou city, North China. Environ. Sci. Pollut. Res.
**2019**, 26, 11000–11011. [Google Scholar] [CrossRef] [PubMed] - Huang, L.; Zhou, M.; Lv, J.; Chen, K. Trends in global research in forest carbon sequestration: A bibliometric analysis. J. Clean. Prod.
**2020**, 252, 119908. [Google Scholar] [CrossRef] - Li, Z.; Jin, J.L.; Cui, Y.; Zhou, R.X.; Ning, S.W.; Zhou, Y.L.; Zhou, L.G. Evaluation method of regional water resources carrying capacity based on semipartial connection number and dynamic subtraction set pair potential. J. Lake Sci.
**2022**, 34, 1656–1669. [Google Scholar] - Jin, J.L.; Chen, P.F.; Chen, M.L.; Li, J.Q.; Xu, X.Y.; Chang, T. Bibliometric analysis of research progress on water resources carrying capacity based on knowledge map. Water Resour. Prot.
**2019**, 35, 14. [Google Scholar] - Li, C.; Li, H.J.; Feng, S.D.; Liu, X.Y.; Guo, S. A study on the spatiotemporal characteristics and change trend of the atmospheric environmental carrying capacity in the Jing-Jin-Ji region, China. J. Clean. Prod.
**2019**, 211, 27–35. [Google Scholar] [CrossRef] - Meng, C.; Wang, X.; Li, Y. An optimization model for water management based on water resources and environmental carrying capacities: A case study of the yinma river basin, northeast China. Water
**2018**, 10, 565. [Google Scholar] [CrossRef] - Secinaro, S.; Brescia, V.; Calandra, D.; Biancone, P. Employing bibliometric analysis to identify suitable business models for electric cars. J. Clean. Prod.
**2020**, 264, 121503. [Google Scholar] [CrossRef] - Yang, Y.F.; Wang, H.R.; Zhou, J.W.; Yan, J.W. Evaluation Model of Water Resources Carrying Capacity Based on Set Pair Potential and Partial Connection Number. Adv. Eng. Sci.
**2021**, 53, 99–105. [Google Scholar]

**Figure 2.**Factors affecting the water environment carrying capacity of Harbin City: (

**a**) is a numerical plot of water quality indicators, (

**b**) is a numerical plot of water consumption indicators, and (

**c**) is a numerical plot of water quality impact indicators.

**Figure 6.**A comparison of the AHP method, PP-AHP method, and confidence level judging method; (

**a**–

**c**) are radar plots of the results of the confidence level judging method, compared with the results of the two weighting methods, when the confidence levels are taken to be λ = 0.5, λ = 0.6 and λ = 0.7.

Evaluation Indicators | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} |

Loadable | ≥100 | ≥600 | ≥200 | ≥40 | ≤45,000 | ≤800 | ≤50 | ≤8000 | ≤1000 | ≥50 |

Criticality | [70, 100) | [300, 600) | [100, 200) | [20, 40) | (45,000, 60,000] | (800, 1000] | (50, 80] | (8000, 20,000] | (1000, 1400] | [20, 50) |

Overloading | <70 | <300 | <100 | <20 | >60,000 | >1000 | >80 | >20,000 | >1400 | <20 |

Evaluation Indicators | C_{11} | C_{12} | C_{13} | C_{14} | C_{15} | C_{16} | C_{17} | C_{18} | C_{19} | C_{20} |

Loadable | ≤66 | ≤10,000 | ≤5000 | ≥80 | ≥90 | ≥80 | ≥80 | ≥95 | ≥40 | ≥80 |

Criticality | (66, 248] | (10,000, 40,000] | (5000, 7500] | [60, 80) | [70, 90) | [50, 90) | [50, 80) | [90, 95) | [25, 40) | [50, 80) |

Overloading | >248 | >40,000 | >7500 | <60 | <70 | <50 | <50 | <90 | <25 | <50 |

Posture | SE | Grade |
---|---|---|

Same posture | [1.0, 1.4] | Positive Level 1 |

Favoring the same dynamics | (1.4, 1.8] | Bias positive Level 2 |

Parity posture | (1.8, 2.2] | Positive Level 2 |

Favoring the opposite dynamics | (2.2, 2.6] | Bias negative Level 2 |

Opposite posture | (2.6, 3.0] | Positive Level 3 |

Evaluation Indicators | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} |

AHP weights | 0.07 | 0.073 | 0.06 | 0.083 | 0.093 | 0.063 | 0.063 | 0.03 | 0.037 | 0.07 |

PP-AHP weights | 0.026 | 0.026 | 0.024 | 0.026 | 0.055 | 0.02 | 0.103 | 0.04 | 0.049 | 0.017 |

Evaluation Indicators | C_{11} | C_{12} | C_{13} | C_{14} | C_{15} | C_{16} | C_{17} | C_{18} | C_{19} | C_{20} |

AHP weights | 0.017 | 0.03 | 0.02 | 0.057 | 0.057 | 0.057 | 0.037 | 0.057 | 0.03 | 0.02 |

PP-AHP weights | 0.049 | 0.019 | 0.027 | 0.064 | 0.103 | 0.059 | 0.099 | 0.1 | 0.061 | 0.037 |

Year | Number of Contacts | SE | Grade |
---|---|---|---|

2006 | 0.262 + 0.612I + 0.126J | 1.863503737 | Positive Level 2 |

2007 | 0.284 + 0.617I + 0.099J | 1.814117478 | Positive Level 2 |

2008 | 0.28 + 0.621I + 0.099J | 1.819802604 | Positive Level 2 |

2009 | 0.281 + 0.606I + 0.113J | 1.83159522 | Positive Level 2 |

2010 | 0.325 + 0.60I + 0.074J | 1.748237038 | Bias Positive Level 2 |

2011 | 0.316 + 0.59I + 0.094J | 1.77808089 | Bias Positive Level 2 |

2012 | 0.323 + 0.589I + 0.088J | 1.764297458 | Bias Positive Level 2 |

2013 | 0.333 + 0.602I + 0.065J | 1.732201156 | Bias Positive Level 2 |

2014 | 0.348 + 0.593I + 0.059J | 1.710318666 | Bias Positive Level 2 |

2015 | 0.327 + 0.608I + 0.065J | 1.738912508 | Bias Positive Level 2 |

2016 | 0.36 + 0.576I + 0.064J | 1.704757847 | Bias Positive Level 2 |

2017 | 0.36 + 0.606I + 0.034J | 1.674201471 | Bias Positive Level 2 |

2018 | 0.306 + 0.457I + 0.236J | 1.930387368 | Positive Level 2 |

2019 | 0.267 + 0.453I + 0.281J | 2.013888289 | Positive Level 2 |

2020 | 0.293 + 0.52I + 0.187J | 1.893646336 | Positive Level 2 |

Method | Year | Support Level | Grade | ||
---|---|---|---|---|---|

Level 1 | Level 2 | Level 3 | |||

First order | 2006 | 0.445690966 | 0.933965553 | 0.22989635 | 2 |

2007 | 0.479182183 | 0.947210296 | 0.183612738 | 2 | |

2008 | 0.472278472 | 0.947783832 | 0.18493421 | 2 | |

2009 | 0.473093116 | 0.938308666 | 0.207653618 | 2 | |

2010 | 0.536515722 | 0.95642926 | 0.139262856 | 2 | |

2011 | 0.521495012 | 0.943821035 | 0.174818609 | 2 | |

2012 | 0.532262532 | 0.946631328 | 0.164181644 | 2 | |

2013 | 0.547253568 | 0.961164842 | 0.12383843 | 2 | |

2014 | 0.567672216 | 0.963445389 | 0.111866509 | 2 | |

2015 | 0.538977957 | 0.961906958 | 0.124534978 | 2 | |

2016 | 0.581114654 | 0.957289482 | 0.122448582 | 2 | |

2017 | 0.58593583 | 0.978848992 | 0.066787571 | 2 | |

2018 | 0.48946241 | 0.815112985 | 0.392355718 | 2 | |

2019 | 0.434585901 | 0.790495727 | 0.453868044 | 2 | |

2020 | 0.480836552 | 0.872908538 | 0.324489281 | 2 | |

Second order | 2006 | 0.479041394 | 0.933965553 | 0.281177525 | 2 |

2007 | 0.505602875 | 0.947210296 | 0.231292506 | 2 | |

2008 | 0.498563731 | 0.947783832 | 0.231492137 | 2 | |

2009 | 0.503851796 | 0.938308666 | 0.260084547 | 2 | |

2010 | 0.557345763 | 0.95642926 | 0.186141878 | 2 | |

2011 | 0.548491921 | 0.943821035 | 0.22972998 | 2 | |

2012 | 0.557678475 | 0.946631328 | 0.218335674 | 2 | |

2013 | 0.565671295 | 0.961164842 | 0.167645603 | 2 | |

2014 | 0.58459616 | 0.963445389 | 0.155331083 | 2 | |

2015 | 0.557239545 | 0.961906958 | 0.166971138 | 2 | |

2016 | 0.600423385 | 0.957289482 | 0.173020616 | 2 | |

2017 | 0.595634964 | 0.978848992 | 0.095156117 | 2 | |

2018 | 0.578882899 | 0.815112985 | 0.503330198 | 2 | |

2019 | 0.539906487 | 0.790495727 | 0.554760073 | 2 | |

2020 | 0.542379123 | 0.872908538 | 0.410366993 | 2 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sun, N.; Yao, Z.; Xie, Y.; Wang, T.; Yang, J.; Li, X.; Fu, Q.
Sustainability Analysis of the Water Environment Carrying Capacity of Harbin City Based on an Optimized Set Pair Analysis Posture-Deviation Coefficient Method Evaluation Model. *Water* **2023**, *15*, 1575.
https://doi.org/10.3390/w15081575

**AMA Style**

Sun N, Yao Z, Xie Y, Wang T, Yang J, Li X, Fu Q.
Sustainability Analysis of the Water Environment Carrying Capacity of Harbin City Based on an Optimized Set Pair Analysis Posture-Deviation Coefficient Method Evaluation Model. *Water*. 2023; 15(8):1575.
https://doi.org/10.3390/w15081575

**Chicago/Turabian Style**

Sun, Nan, Zhongbao Yao, Yunpeng Xie, Tianyi Wang, Jinzhao Yang, Xinyu Li, and Qiang Fu.
2023. "Sustainability Analysis of the Water Environment Carrying Capacity of Harbin City Based on an Optimized Set Pair Analysis Posture-Deviation Coefficient Method Evaluation Model" *Water* 15, no. 8: 1575.
https://doi.org/10.3390/w15081575