Improving Analytic Hierarchy Process inside the Analytic Group Decision-Making Approach Method with Two-Dimensional Cloud Model for Water Resource Pollution Risk Warning Evaluation: A Case Study in Shandong Province, China

Abstract

This study proposes a water resource pollution risk warning evaluation method. Firstly, an evaluation system is constructed, consisting of 15 secondary indicators in four aspects: water quality, ecology, utilization protection, and water disasters. Then, an improved AGA-AHP method and coefficient of variation method are used to determine the weights of each indicator. Cloud models are employed to describe the characteristics of standard clouds and evaluation clouds, establishing a two-dimensional cloud model with risk probability and hazard level as variables. Taking a certain region in Shandong Province, China, as an example, the quantitative analysis results indicate that the water pollution risk level in the area is classified as Level IV, with particular attention needed for water quality and management indicators. Simultaneously, a series of measures such as source control, monitoring and early warning, emergency response, and public participation are proposed to further reduce the risk. The research findings demonstrate the following: (1) The establishment of a comprehensive indicator system for multidimensional assessment; (2) The combination of the AGA-AHP method and cloud model for quantitative analysis; (3) The practicality of the method validated through the case study; (4) Providing a basis for subsequent decision-making. This study provides new insights for water environmental risk management, but a further optimization of the model to enhance predictive capability is required when applied in practical scenarios. Nevertheless, the preliminary validation of this method’s application prospects in water resource risk monitoring has been achieved.

1. Introduction

Water resources are one of the essential conditions for achieving sustainable development in a region. However, with accelerated industrialization and increasing urbanization, the quality of water environments is being threatened, and water pollution is becoming increasingly severe. The effective assessment and early warning of water pollution risks are of great significance. It can provide an advance warning of factors that may harm the security of water resources and facilitate timely and effective preventive measures by water resource management authorities to ensure the sustainable utilization of water resources.

Significant progress has been made by global scholars in the field of water environment risk assessment. However, the majority of these works primarily focus on aspects such as indicator selection and quantitative demonstration, with fewer applications and empirical verifications in specific cases [1,2,3,4,5,6,7,8,9,10]. The concept of risk assessment as a management and decision-making tool can be traced back to the 20th century. However, the demand for understanding and evaluating risks can be traced back to an earlier period. China has also made significant achievements in water pollution risk assessment, with a relatively well-established pollution source monitoring database. Over the years, China has invested a considerable amount of resources in real-time monitoring and historical data collection, establishing a solid foundation for pollution source monitoring systems [11,12,13]. Researchers like Xu Jing have made great progress in water pollution risk assessment and early warning [14]. Liao, J et al. have provided more specific early warning methods for specific hazards in the field of risk assessment, providing scientific evidence [15,16,17]. However, existing evaluation methods have certain areas that need further improvement. One of the main concerns is that these methods heavily rely on expert knowledge, resulting in a significant dependence on subjective judgment when assessing risk severity. This subjectivity makes it challenging to define risks accurately and consistently. Another limitation of traditional approaches is their limited capability in dealing with complex problems. Complex risks often involve multiple interconnected factors and dynamic interactions, which can be difficult to capture and analyze effectively using traditional methods [18,19,20]. Consequently, the assessment results may not fully reflect the true complexity and nuances of the risks involved. Additionally, there is a lack of research that applies these evaluation methods to real-world cases. The absence of practical application hinders the validation and verification of these methods in a real-life context. As a result, evaluations may be biased toward theoretical scenarios and may not adequately consider the practical implications and challenges faced in real-world risk assessments [21,22,23]. Addressing these limitations is crucial for enhancing the effectiveness and practicality of risk assessment methods. Future research should focus on developing approaches that reduce the reliance on subjective judgment, improve the ability to handle complex problems, and promote the application of these methods in real-life cases. By doing so, we can achieve more accurate and reliable risk assessments that better reflect the intricacies and realities of the risks we face [24,25]. Shandong Province, as an important grain and cotton production area in China, encompasses various hydrological types and faces different levels of water environmental risks. Industrial zones experience rapid deterioration in water quality, reduced ecological carrying capacity, and high levels of heavy metal contamination in local water bodies. Rural groundwater pollution risks are also becoming increasingly significant. However, there is still a need for in-depth research on how to systematically study water bodies in different regions—using quantitative methods to identify the primary sources of pollution and assessing the risk characteristics—to provide support for management authorities. To address the aforementioned issues, this study takes Shandong Province, China, as an example and proposes an optimized framework, establishing a comprehensive multi-indicator framework for comprehensive assessments. Building upon existing evaluation methods, an improved genetic algorithm is utilized to accurately determine indicator weights, optimizing weight scoring more accurately [26,27,28]. The two-dimensional cloud model is employed to quantitatively describe different levels of risk in the water environment. This model allows for a comprehensive assessment by simultaneously considering multiple factors that contribute to water environmental risks. By integrating qualitative and quantitative information, the model provides a more holistic understanding of the risks involved. This approach offers decision-makers a solid foundation for formulating effective strategies and interventions to mitigate water environmental risks [29,30,31]. Moreover, this study optimizes the selection of indicators and models to continuously improve the quality of the assessment. These improvements contribute to the theoretical foundation and application value compared to traditional methods [32,33,34,35,36].

In summary, this study aims to address the shortcomings of existing methods and provide more reliable references for water environmental management decisions. It endeavors to quantitatively analyze water environmental risks in a specific region, identify pressing issues that need to be addressed, and provide scientific evidence to enhance the effectiveness of water resource protection.

2. Establishment of Evaluation Index System

2.1. Hierarchical Model of Evaluation Indexes

A water resource pollution risk warning refers to the possibility of water resources being threatened by pollution in a certain area. This threat can lead to the deterioration of water quality and availability, thereby jeopardizing the safety and sustainable utilization of water resources. Based on the definition and criteria of water resource pollution hazard risk, a comprehensive evaluation indicator system can be established, including 15 indicators selected from four aspects: water quality assessment indicators, water ecosystem assessment indicators, water resource utilization and protection indicators, and water disaster risk assessment indicators, as shown in Figure 1. In water resource pollution hazard risk warning, factors such as the types of pollution sources, changes in water quality, limitations on water resource availability, ecological environment destruction, and socio-economic losses need to be considered. Therefore, it is possible to establish primary and secondary indicators to assess water resource pollution hazard risk.

2.2. Risk Index Level of Water Pollution Hazards

Based on the unique natural environment and geographical characteristics of water resources, combined with the research findings of numerous scholars, a detailed classification of each indicator has been provided in

Table 1. Classification of index factors.

Index	Ⅰ	Ⅱ	Ⅲ	Ⅳ	Ⅴ
Water quality assessment index U1
Concentration of main pollutants in water bodyU11	Very low concentration, excellent	Low concentration, good	Moderate concentration, average	Higher concentration, worse	Very high concentration, poor
Transparency and turbidity of water bodiesU12	Excellent transparency	High transparency, good	Transparency is moderate and average.	Lower transparency, poor	Very low transparency, poor
pH and REDOX potentialU13	The pH of the water is close to neutral.	The pH of the water is close to neutral.	The pH of the water is slightly acid-based.	The pH value of water is obviously acid-based.	The pH value of the water body deviates significantly from neutral.
Nutrient concentration in waterU14	Aquatic biodiversity is extremely rich.	The aquatic biodiversity is rich.	Aquatic biodiversity is moderate.	Aquatic biodiversity is low.	Aquatic biodiversity is extremely low.
Water ecosystem assessment index U2
Marine biodiversity U21	The water ecosystem structure is complete.	The water ecosystem structure is relatively complete.	The water ecosystem structure is moderate.	The water ecosystem structure is relatively broken.	The structure of the water ecosystem is seriously broken.
Status of water ecosystem structure and functionU22	outstanding	good	normal	range	poor
Water ecological process assessmentU23	outstanding	good	normal	range	poor
Water ecological process assessmentU24	outstanding	good	normal	range	poor
Water resources utilization and protection indicators U3
Water resources supply and demand balance degreeU31	outstanding	good	normal	range	poor
Water resources use efficiencyU32	outstanding	good	normal	range	poor
Implementation of water resources protection measuresU33	outstanding	good	normal	range	poor
Economic benefit index of water resourcesU34	Water resource utilization efficiency is extremely high.	The utilization efficiency of water resources is higher.	The efficiency of water resource utilization is moderate.	The efficiency of water resource utilization is low.	The efficiency of water resource utilization is very low.
Water disaster risk assessment indicators U4
Waterlogging risk assessmentU41	The risk of flooding is extremely low	Low risk of waterlogging	The risk of flooding is moderate	Higher risk of waterlogging	The risk of flooding is extremely high
Flood and drought risk assessmentU42	Flood and drought risk is extremely low	Low flood and drought risk	Flood and drought risks are moderate	The risk of flood and drought is higher	The risk of floods and droughts is extremely high
Water disaster emergency response capability assessmentU43	Water disaster emergency response ability is very strong	Water disaster emergency response ability is strong	Water disaster emergency response ability is moderate	Water disaster emergency response ability is weak	Water disaster emergency response capacity is very weak

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3. Water Resource Pollution Hazard Risk Assessment Method

3.1. Improved AGA-AHP Method

Water pollution risk assessment involves multiple factors and indicators, including water quality status, types of pollution sources, environmental sensitivity, and more. These factors have complex interactions and influence relationships. By using the hierarchical approach, the assessment process can be decomposed into different levels, allowing for the evaluation and analysis of factors at each level, thus better understanding and addressing the complexity and multidimensionality of the problem. The traditional Analytic Hierarchy Process (AHP) method relies on expert judgment or subjective estimation to determine weights, which can introduce subjectivity and bias. It aims to address the challenges of accurately determining weights and dealing with complex multi-level structures in the traditional AHP method [37,38]. The computational steps of the improved AGA-AHP method are as follows:

$$\min =\frac{CR}{RI}$$

$$y_{ij}=\frac{1}{y_{ji}}\in \left[b_{ij}-d{b}_{ij},b_{ij}+d{b}_{ij}\right]\left(i=1~n,j=i+1~n\right)$$

(1)

$$w_i>0{\displaystyle \sum _{i=1}^n{w}_i=1}$$

In the improved AGA-AHP method, the consistency index is denoted as CI, and the random consistency ratio is denoted as RI. The value in the ith row and jth column of the evaluation matrix is represented as y_ij, while the value in the ith row and jth column of the evaluation matrix before the optimization is represented as b_ij. The non-negative parameter d is within the range of [0, 0.5].

3.2. Improved Coefficient of Variation Method

The Coefficient of Variation Method (CVM) is a decision evaluation method based on the variability of indicators. It measures the fluctuation and stability of indicators by calculating the coefficient of variation. A smaller coefficient of variation indicates lower fluctuation and higher stability of the indicator. However, the CVM relies on the mean and standard deviation, neglecting the correlation between indicators and being unable to address the issue of weights. The CVM lacks a clear weight calculation process, making it unable to assign different weights to different indicators and thus unable to fully consider the importance and contribution of each indicator in the decision-making process. On the other hand, the Improved Composite Variable Method (ICVM) is a decision evaluation method based on comprehensive variables. It quantitatively evaluates and ranks decision problems by considering multiple evaluation indicators. In this study, we adopt the improved coefficient of variation method (ICVM), which first normalizes the raw data before computing the coefficient of variation. The specific computation steps are as follows [39,40,41]:

(1)

Assuming that there are m evaluation objects and n evaluation indicators, the original data matrix A is constructed as follows:

$$A={\left(x_{ij}\right)}_{m\times n}$$

(2)

The data are normalized by the extremum method, and the decision matrix is constructed $V={\left(b_{ij}\right)}_{m\times n}$.

(3)

The calculated coefficient of variation V_i is as follows:

$$\left\{\begin{array}{l}V=\frac{{\sigma }_i}{\overline{b_i}}\\ \sigma =\sqrt{{\frac{{\displaystyle \sum _{i=1}^m\left(b_{ij}-\overline{b_i}\right)}}{m-1}}^2}\\ \overline{b_i}={\displaystyle \sum _{n=1}^m{b}_{ij}/n}\end{array}\right.$$

(2)

where σ_i is the standard deviation of the ith evaluation index and $\overline{b_{ij}}$ is the average value of the ith evaluation index.

(4)

The normalized weight e_i of the ith indicator is as follows:

$$e_i=\frac{V_i}{{\displaystyle \sum _{i=1}^n{V}_i}}$$

(3)

3.3. Game Theory Combinatorial Weighting Method

The introduction of game theory aims to combine the advantages of weights calculated using the AGA-AHP method and the weights obtained through the coefficient of variation method. By employing game theory optimization strategies, it allows for the derivation of optimal comprehensive weights for the indicators, thereby enhancing the scientific rigor of the evaluation process. This approach is rooted in the principles of game theory, using the process of game playing among participants to determine the weights for each indicator, reflecting the preferences and interests of the participants toward the indicators. Apologies for the confusion in the previous response, and thank you for clarifying the inclusion of game theory in the context of the improved AGA-AHP method for weight determination in water pollution risk assessment. In this study, an improved AGA-AHP method and an improved coefficient of variation method are employed to calculate the subjective weights (w_i) and objective weights (e_i) of the criteria, respectively. Based on the subjective weight set $w_k=\left\{w_1,w_2,\cdots ,w_n\right\}$, take any linear combination of these two vectors. Let ${\alpha }_k=({\alpha }_1,{\alpha }_2)$ be the combined linear coefficient. Then, the combination of power gives the following: ${\omega }_i={\displaystyle \sum _{k=1}^2{\alpha }_k}{w}_k^T({\alpha }_k>0)$. His optimal game theory strategy is right ${\omega }_i$ and $w_k$. The deviation minimization is performed. The linear combination coefficient is optimized, namely, $Min{‖{\displaystyle \sum _{k=1}^1{\alpha }_k{w}_k^T-w_k^T}‖}^2$. According to the principle of differentiation, the conditions for obtaining the first derivative of the minimum value are as follows [42,43]:

$$\left\{\begin{array}{l}{\alpha }_1{\omega }_1{w}_1^T+{\alpha }_2{\omega }_1{w}_2^T={\omega }_1{w}_1^T\\ {\alpha }_1{\omega }_2{w}_1^T+{\alpha }_2{\omega }_2{w}_2^T={\omega }_2{w}_2^T\end{array}\right.$$

(4)

From Formula (4), we obtain the optimal weight coefficient ${\alpha }_k^{*}$ after the combination coefficient ${\alpha }_k$ is normalized, and then we obtain the optimal comprehensive weight of the evaluation index as follows: ${\omega }^{*}={\displaystyle \sum _{k=1}^2{\alpha }_k^{*}}{w}_k^T$. The above calculation process calculates the comprehensive weight through the game theory optimization strategy.

3.4. Two-Dimensional Cloud Model

The cloud model, proposed by Professor Li Deyi of China in 2009, is a novel uncertainty description model used to handle the relationships among fuzzy, random, and deterministic information [44]. The two-dimensional cloud model is an extension of the traditional cloud model, specifically designed to deal with multidimensional information and multi-criteria decision-making problems. The two-dimensional cloud model (TDCM) is a method used for uncertainty modeling and decision analysis, developed based on the foundation of cloud model theory. Water resource pollution hazard risk warning assesses the level of risk and warning for water resource pollution by considering the combined effects of risk probability and hazard severity as two dimensions. Utilizing the two-dimensional cloud model to establish a water resource pollution hazard risk warning model is a scientifically effective approach.

Assuming N is a bivariate random function following a normal distribution, where Ex and Ey represent the expectations, En_x and En_y represent the standard deviations, and Hex and Hey represent the hyper-entropies, the cloud model consisting of cloud droplets $drop\left(x_i,y_i,{\mu }_i\right)$ that satisfy Equation (5) is referred to as a two-dimensional normal cloud model.

$$\left\{\begin{array}{l}\left(x_i,y_i\right)=N\left(Ex,Ey,E{n}_x,E{n}_y\right)\\ \left(X_i,Y_i\right)=N\left(E{n}_x,E{n}_y,H{e}_x,H{e}_y\right)\\ {\mu }_i=e^{\frac{1}{2}\left[\frac{{\left(x_i-Ex\right)}^2}{X_i}+\frac{{\left(y_i-Ey\right)}^2}{Y_i}\right]}\end{array}\right.$$

(5)

where (x_i, y_i) is the coordinate of the cloud droplet; μ_i is the certainty.

3.5. Comprehensive Evaluation Cloud

For the risk warning of water resource pollution hazards, we can consider the risk probability level and the hazard severity level as two fundamental variables for risk assessment. To evaluate specific engineering projects, we invite experts to rate each indicator on a scale of 1 to 10, with a precision of 0.1. By obtaining expert ratings for the risk probability and hazard severity associated with each indicator, we can form a cloud, thereby creating a risk probability cloud and a hazard severity cloud for that particular indicator. By referring to Han Feng’s literature [45], we can utilize Formulas (6) and (7) along with a Python inverse cloud generator to generate the numerical characteristics of the two-dimensional cloud. Apologies for any confusion caused by the previous response, and thank you for providing further clarification.

$$\left\{\begin{array}{l}Ex=\frac{1}{m}{\displaystyle {\sum }_{k=1}^m{x}_k}\\ En={\left(\frac{\pi }{2}\right)}^{\frac{1}{2}}\times \frac{1}{m}\left|x_k-Ex\right|\\ He=\sqrt{\left|S^2-E{n}^2\right|}\\ S^2=\frac{1}{m-1}{\displaystyle {\sum }_{m-1}^m{\left(x_k-Ex\right)}^2}\end{array}\right.$$

(6)

$$C=\left({\omega }_1, {\omega }_2, {\omega }_3, \dots , {\omega }_{\mathrm{n}}\right)\left(\begin{array}{l}\begin{array}{ccc}E{x}_1& E{n}_1& H{e}_1\end{array}\\ \begin{array}{ccccc}⋮& & ⋮& & ⋮\end{array}\\ \begin{array}{ccc}E{x}_n& E{n}_n& H{e}_n\end{array}\end{array}\right)$$

(7)

where Ex is expectation, En is entropy, He is superentropy, x_k is the score of k experts, S² is sample variance, and m is the number of experts.

3.6. Standard Cloud

Referring to relevant standards such as meteorological disaster warnings and emergency event warnings in China, the interval [0–10] is divided into five standard sub-intervals of equal length with a spacing of 2. These sub-intervals serve as the standard intervals for water pollution risk warning levels, which are denoted as Grade I, Grade II, Grade III, Grade IV, and Grade V. Additionally, Formula (8) is applied to calculate the numerical characteristics of cloud for risk probability and hazard severity for each interval of water pollution risk. The numerical characteristics, value ranges, and risk levels of the standard cloud are presented in

Table 2. Risk warning standards and cloud digital characteristics.

Warning Level	Risk Probability	Degree of Harm	Value Range	Digital Feature
Ⅴ	low	small	[0, 2]	(1, 0.33, 0.05)
Ⅳ	lower	lesser	[2, 4]	(3, 0.33, 0.05)
Ⅲ	normal	normal	[4, 6]	(5, 0.33, 0.05)
Ⅱ	higher	larger	[6, 8]	(7, 0.33, 0.05)
Ⅰ	high	big	[8, 10]	(9, 0.33, 0.05)

.

$$\left\{\begin{array}{l}\overline{E{x}_i}=\frac{G_j^{\max }+G_j^{\min }}{2}\\ \overline{E{n}_i}=\frac{G_j^{\max }+G_j^{\min }}{6}\\ \overline{H{e}_i}=k\end{array}\right.$$

(8)

In the equation, Ex_i, En_i, and He_i represent the expectation, entropy, and hyper-entropy of the standard cloud, respectively. To reduce errors and incorporate practical considerations, the hyper-entropy He_i is set to k = 0.05.

3.7. Risk Warning Standards and Cloud Digital Characteristics

In the level evaluation study, in order to more objectively and accurately reflect the water pollution risk early warning level, the similarity degree can be used to measure the similarity between the comprehensive evaluation cloud and the standard cloud. The higher the similarity degree, the closer the comprehensive evaluation cloud to be evaluated is to the corresponding standard risk early warning cloud level. Due to the excessive computational requirements of the data, Python (JupyterLab3.0) software is being utilized for the calculations. The results of the computations will be rounded to two decimal places. The formula for calculating the similarity degree is as follows:

$$T=\frac{1}{\sqrt{\left(Ex-\overline{E{x}_i}\right)+\left(Ey-\overline{E{y}_i}\right)}}$$

(9)

T is the similarity degree of the integrated cloud, Ex and Ey represent the mathematical expectations of the probability level and damage level of the integrated risk cloud, respectively; they represent the mathematical expectations of the probability level and hazard level of the standard cloud, respectively.

4. Case Analysis

4.1. Study Area Profile

Shandong Province is located in the eastern coastal region of China and is known for its abundant water resources. Particularly in a specific area of Shandong Province, we have selected it as a research subject for conducting water pollution risk warning assessments. This research holds real urgency and necessity, providing a basis for developing scientifically sound control measures. The area in question comprises hills, plains, and coastal regions with rich water resources but also facing the risk of water pollution. Due to factors such as industrial activities, agricultural production, and high population density, water resources in this region are threatened by varying degrees of pollution. Within this area, there are pollution pressures from agricultural and industrial activities, emissions of chemicals and heavy metals into water bodies, as well as agricultural non-point source pollution caused by soil erosion, pesticides, and fertilizer usage. Additionally, there are some specific circumstances—uneven distribution of water pollution risks, varying levels of risk in different regions and water body types, and inadequacies in water pollution prevention and control facilities and management measures—leading to poor controllability of risks, limited emergency plans, and disaster response capabilities, requiring further improvement in handling sudden events. Therefore, selecting the water pollution risk warning in a specific area of Shandong Province as a research subject is of practical urgency and necessity, providing a basis for developing scientifically sound control measures. We will comprehensively consider factors such as water environmental quality, pollution source emissions, water resource utilization patterns, etc., to proactively warn and identify potential water pollution risks and take corresponding measures to protect and manage water resources, ensuring the health and sustainable development of the water environment.

4.2. Analytical Process

To conduct a quantitative analysis of the risk assessment indicators, we will start by analyzing the four Level 1 indicators and fifteen Level 2 indicators. We will invite six experienced industry experts to rate the safety accident consequences and occurrence probabilities of each factor in the water pollution safety risk assessment system in the region. The ratings are presented in

Table 3. Risk grade and probability grade scores.

Risk Factor	X1/X1′	X2/X2′	X3/X3′	X4/X4′	X5/X5′	X6/X6′
U11	7.8/6.5	8.2/6.6	8.0/6.3	8.3/6.7	7.9/6.9	8.5/6.8
U12	7.1/6.9	7.0/6.8	7.3/7.0	7.4/7.3	6.9/6.9	7.2/7.2
U13	6.3/2.3	6.2/2.2	6.2/2.0	5.9/2.3	6.0/1.9	6.1/2.1
U14	7.5/7.2	7.2/7.3	7.6/7.4	7.8/7.5	7.4/6.9	7.3/7.6
U21	5.2/3.1	5.0/3.2	5.3/3.4	5.1/2.9	5.4/3.0	4.9/2.8
U22	5.1/7.2	5.3/7.3	4.9/7.4	5.0/7.2	5.2/6.9	5.4/7.1
U23	7.2/2.7	6.8/2.3	6.9/2.6	7.2/2.4	7.0/2.5	7.3/2.6
U24	7.3/2.4	7.5/2.6	7.8/2.2	7.4/2.5	7.6/2.9	7.5/2.7
U31	7.3/1.8	7.2/1.9	7.3/2.0	7.1/1.8	7.0/2.3	6.9/2.2
U32	6.4/1.6	6.2/1.5	6.6/1.5	6.5/1.7	6.3/1.4	6.2/1.3
U33	5.1/3.5	5.2/3.6	5.0/3.2	4.9/3.7	4.9/3.8	5.2/3.4
U34	3.4/2.8	3.0/2.5	3.1/2.6	2.8/2.3	3.3/2.4	2.9/2.7
U41	2.5/2.6	2.4/3.2	2.2/3.0	2.6/3.1	2.5/2.7	2.3/3.3
U42	4.2/1.8	4.0/1.4	3.9/1.3	3.8/1.5	4.3/1.6	4.4/1.9
U43	2.5/3.2	2.3/3.1	2.5/3.4	2.6/2.9	2.4/3.0	2.5/3.2

Note: Xi and Xi′ are risk and probability scores, respectively.

. By applying Formulas (1) to (4), we can calculate the final weightings. Formula (6) will be used to determine the numerical characteristics of the risk cloud, while Formula (8) will calculate the numerical characteristics of the standard cloud. Finally, Formula (9) will yield the comprehensive risk cloud numerical characteristics. The results can be found in

Table 4. Risk level and Probability level Risk cloud digital characteristics.

Integrated Risk Cloud			Level 1 Risk Cloud				Level 2 Risk Cloud
Overall Index	Risk (Ex1, En1, He1)	Chance (Ex2, En2, He2)	Level 1 Index	Weight	Risk (Ex1, En1, He1)	Chance (Ex2, En2, He2)	Level 2 Index	Weight	Risk (Ex1, En1, He1)	Chance (Ex2, En2, He2)
U	(6.54, 0.43, 0.39)	(6.57, 0.43, 0.38)	U1	0.239	(5.05, 0.54, 0.49)	(6.00, 0.55, 0.44)	U11	0.072	(5.49, 0.61, 0.60)	(6.15, 0.56, 0.49)
							U12	0.060	(4.20, 0.63, 0.53)	(4.10, 0.84, 0.55)
							U13	0.066	(5.41, 0.45, 0.41)	(6.33, 0.36, 0.34)
							U14	0.061	(4.23, 0.35, 0.33)	(6.58, 0.27, 0.26)
			U2	0.298	(7.39, 0.58, 0.49)	(7.79, 0.27, 0.26)	U21	0.069	(7.88, 0.52, 0.45)	(8.00, 0.21, 0.20)
							U22	0.061	(7.29, 0.44, 0.42)	(7.45, 0.27, 0.27)
							U23	0.062	(6.90, 0.79, 0.60)	(7.85, 0.33, 0.32)
							U24	0.062	(7.63, 0.21, 0.21)	(7.75, 0.34, 0.31)
			U3	0.225	(7.68, 0.35, 0.33)	(7.16, 0.43, 0.40)	U31	0.061	(7.78, 0.31, 0.31)	(7.75, 0.40, 0.38)
							U32	0.062	(8.50, 0.33, 0.32)	(7.57, 0.38, 0.35)
							U33	0.074	(5.91, 0.36, 0.34)	(6.82, 0.48, 0.45)
							U34	0.064	(7.56, 0.27, 0.26)	(6.40, 0.75, 0.58)
			U4	0.221	(7.54, 0.33, 0.31)	(7.07, 0.56, 0.48)	U41	0.064	(4.57, 0.32, 0.29)	(4.80, 0.38, 0.34)
							U42	0.065	(7.63, 0.25, 0.24)	(6.47, 0.31, 0.28)
							U43	0.082	(4.73, 0.33, 0.32)	(4.87, 0.47, 0.41)

Note: The significant figures in the table are determined by calculating the results using Python and then preserving them.

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4.3. Analysis Result

The analysis results indicate that the comprehensive risk level of water pollution in the region is Level IV. Looking at each indicator, the risk level for water quality conditions falls between Level III and Level IV, with a calculated result of Level III. The risk level for management level is close to Level III. The risk level for ecological indicators ranges between Level IV and Level V, with a proximity calculation result of Level IV. The risk level for water resource utilization, protection, and water disaster risk assessment falls between Level IV and Level V, with a calculated result of Level IV, as shown in Figure 2 and Figure 3. The analysis suggests that when the risk level is equal to or greater than Level IV, the risk is within an acceptable range but requires focused control and management of water quality conditions and management level indicators. Measures to strengthen the monitoring of key pollutants, such as industrial wastewater discharge, should be implemented. Establishing an early warning mechanism for water quality and responding promptly to emergencies is essential. Improving the quality of work and emergency response capabilities of regulatory authorities is crucial. Public awareness campaigns on water knowledge should be conducted to increase public participation. Additionally, region-specific prevention and control strategies should be scientifically formulated based on the characteristics of water bodies in different areas.

5. Discussion

This study proposes a water pollution risk early warning assessment method, which involves constructing an evaluation system with 15 secondary indicators in four aspects: water quality, ecology, utilization and conservation, and water disasters. The improved AGA-AHP method and coefficient of variation method are applied to determine the weights of each indicator. The cloud model is utilized to describe the characteristics of standard clouds and evaluation clouds. A certain number of experts are invited to rate accidents and probabilities, and a two-dimensional cloud model is established using risk probability and hazard level as variables. The increase in the number of experts may introduce more perspectives and diversity, but it may also lead to increased inconsistency and uncertainty. This study employs statistical analysis, interactive discussions, and other methods to minimize inconsistencies as much as possible and establish the stability and reliability of the results. Taking a specific region in Shandong Province, China, as an example, the quantitative analysis results show that the water pollution risk level in the region is classified as Level IV, with particular attention needed for water quality and management indicators. Additionally, this study proposes a series of measures, such as source control, monitoring and early warning, emergency response, and public participation, to further reduce the risks. The research results demonstrate that: (1) This method establishes a complete indicator system for comprehensive evaluation; (2) The combination of the AGA-AHP method and cloud model enables quantitative analysis; (3) The practicality of the method is validated through a case study; (4) It provides a basis for future decision-making. This study provides new insights into water environmental risk management. However, considering practical circumstances, further optimization of the model is necessary to enhance its predictive capability and analyze its potential applicability in similar locations.

Regarding the discussion of the research results, it is important to consider the background of the study location and the potential applicability to other similar locations. Based on the quantitative analysis results in a specific region of Shandong Province, the water pollution risk level is classified as Level IV, with water quality and management indicators identified as areas requiring particular attention. However, different regions may have varying factors contributing to water pollution risks. Therefore, when applying this research method to other similar locations, targeted analysis and adjustments are necessary. In the analysis of potential applicability to other similar locations, the following aspects need to be considered: geographical and climatic conditions, level of economic development and population density, data availability, and monitoring capacity.

Furthermore, when applying and promoting this research and the proposed method in other locations, the following points should be considered:

Adaptability and feasibility: Management needs and resource conditions vary across different regions. When applying this research method to other locations, it is essential to assess its adaptability and operational feasibility. It may be necessary to make certain adjustments and customization to the method based on specific local requirements and conditions, ensuring its practicality and feasibility.

Policy support and collaboration mechanisms: Effective management of water pollution risks requires policy support and the establishment of collaborative mechanisms across departments and boundaries. When promoting this research and method in other locations, the support and participation of relevant departments and stakeholders are needed to establish collaborative mechanisms that facilitate the implementation of risk management measures and improve their effectiveness.

Continuous improvement and optimization: This research method provides new insights into water pollution risk assessment. However, there is still room for improvement. When promoting the application of this method in other locations, continuous improvement and optimization are necessary to enhance predictive capability and decision support. Consideration can be given to introducing more indicators and models, incorporating new technologies and methods, and continuously refining and strengthening the risk assessment framework.

In summary, the proposed water pollution risk early warning assessment method in this study has been preliminarily validated in a specific region of Shandong Province. However, when promoting the method to other locations, factors such as local characteristics, data availability, monitoring capacity, and management needs need to be considered. Additionally, the support and collaboration of relevant departments and stakeholders are essential to establish effective risk management mechanisms. Future research should focus on further optimizing and improving the method to enhance predictive capability and decision support, providing more effective tools and guidance for water environmental risk management.

6. Conclusions

The study proposed a water pollution risk assessment method based on an improved AGA-AHP (Analytic Hierarchy Process) and a two-dimensional cloud model. Firstly, an evaluation system comprising fifteen secondary indicators in four aspects—water quality, ecology, utilization and conservation, and water disasters—was constructed. Then, the weights of each indicator were determined using the improved AGA-AHP method and coefficient of variation, and the characteristics of the standard cloud and evaluation cloud were described using the two-dimensional cloud model. A two-dimensional cloud model was established with risk probability and hazard level as variables. Taking a specific region in Shandong Province, China, as an example, quantitative analysis was conducted, showing a water pollution risk level of IV, with water quality and management being the key focus indicators. A series of strategies were proposed, such as source control, monitoring and early warning, emergency response, and public participation, to further mitigate the risks. The main contributions and findings of this study are as follows:

(1)

A comprehensive multi-indicator framework was established, which encompassed multiple aspects of water pollution risk assessment. The combination of the improved AGA-AHP method and cloud model enabled quantitative analysis and improved the accuracy and reliability of the evaluation.

(2)

The practicality of the method was demonstrated through a case study, providing a basis for subsequent decision-making. It offered new insights into water environmental risk management, but further optimization of the model is required to enhance predictive capability for better practical application.

(3)

The generalization of the research method to other regions should validate its applicability and effectiveness under different environments and conditions. The evaluation indicators and models should be optimized to improve prediction accuracy and decision support.

(4)

Application and validation of the research method should be conducted through real-world case studies to enhance its practicality and reliability. Further research should investigate the causes and influencing factors of water pollution risk, providing a scientific basis for the development of more effective risk management strategies.

This study provides a novel method and approach for water pollution risk warning and management. With continuous optimization and improvement, we believe that this method will play a greater role in water resource risk management.