Evaluation of the effect of regional collaborative management of water pollution in Nanjing-Zhenjiang-Yangzhou metropolitan area based on grey theory

This paper mainly focuses on the current situation of collaborative water pollution management in the Nanjing-Zhenjiang-Yangzhou Region metropolitan area. For this purpose, a synthetical, innovative and more comprehensive indicator system, based on PSR theory and the degree of regional synergy, which is also suitable for further evaluations towards regional collaborative water pollution management, was constructed by analyzing the existing theories and programs of collaborative regional management. The indicator weights are determined by fuzzy hierarchical analysis. The current situation of water pollution cooperative management in Nanjing-Zhenjiang-Yangzhou metropolitan area is evaluated as good with a probability of 0.9453 in the third grey class by a grey clustering model combining the data from the annual environmental bulletin of the Environmental Protection Bureau of the three cities and 2018 Nanjing Yearbook etc. Finally, several policy suggestions are given.


Introduction
The synergistic management of water pollution in the Nanjing-Zhenjiang-Yangzhou metropolitan region is an important element in the construction of ecological civilization in the Yangtze River Delta basin, and the study of the synergistic management scheme in the region with respect to the water quality characteristics of the Nanjing-Zhenjiang-Yangzhou metropolitan area is an important initiative to protect the ecological environment and manage water pollution in the Yangtze River Delta basin. At the same time, the integration of Nanjing-Zhenjiang-Yangzhou is a major strategic deployment of Jiangsu Province, and it is of great economic benefit to research how to collaboratively manage water pollution in the whole Nanjing-Zhenjiang-Yangzhou metropolitan area with the advantage of Nanjing, which is a mega-city of Nanjing-Zhenjiang-Yangzhou region, so as to promote the synergistic development of the whole Nanjing-Zhenjiang-Yangzhou metropolitan area.

Determination of evaluation Indicator
In order to determine the evaluation index system in a more comprehensive, concise and representative way, and to focus on the evaluation of regional collaborative governance performance, we determine the Nanjing-Zhenjiang-Yangzhou regional collaborative governance model [1] as interactive and consultative based on the judgment that the degree of regional integration of Nanjing-Zhenjiang-Yangzhou is still in the initial promotion period [2] . Therefore, in the process of collaborative governance, the degree of regional synergy is more critical and is listed as a positive indicator. As well as the available literature research results as shown in the table, the Delphi method was used to investigate and obtain the index system for assessing the collaborative governance of watersheds, as shown in the table below.

Related factors
Yang Z, Niu G.M [3] Legal regulations of unified watersheds, basic principles of establishing cross-regional ecological compensation mechanisms, compensation standards, multiple subjects and joint measures Zhang J.T [4] The impact of contradiction and conflict between government regulation scenarios and regional synergy scenarios in water pollution management on the effectiveness of governance Yang H.S, Zhou X.Y [1] The impact of the lack of strong administrative authority and enforcement effectiveness on the effectiveness of collaborative management when local government departments such as water conservancy and environmental protection discuss issues such as water pollution prevention and control Liu H [5] The link between tertiary industry output and water environment quality Ma T [6] Evaluate the government's performance in water pollution control from three aspects: function, effectiveness and potential, and break down indicators such as the satisfaction rate of complaint handling Zhu J.Q [7] Applying the PSR model to the collaborative management evaluation model, the model can relatively scientifically explain the relationship between the three dimensions of pressure, state and response in the collaborative management of water pollution in Nanjing-Zhenjiang-Yangzhou Chen X.M [8] Evaluate pollution management performance with capital investment in synergistic watershed water resources management as an input indicator and economic development as an output indicator Xiang X [9] Using regional economic growth and natural environment protection as ecological civilization evaluation indicators Han L [2] Analysis of the current status of Nanjing-Zhenjiang-Yangzhou integration from the perspective of the degree of economic ties, the degree of industrial synergy and the degree of market integration shows that the integration is still at the preliminary stage of cooperation Synthesizing the findings of the above literature on regional collaborative governance model with the relevant theories of PSR model, we give the following indicators system. 3 Evaluation model construction of regional collaborative water pollution management in Nanjing-Zhenjiang-Yangzhou metropolitan area

Regional Synergy Indicator Evaluation Rating Determination
Before the construction, there are several assumptions is about to set. Let i w : weight of indicator i The regional synergy index R3 is a qualitative index to reflect the degree of concern, coordination and rigor of the synergistic governance of the three cities of Nanjing-Zhenjiang-Yangzhou from the public information. In order to quantitatively analyze the degree of influence of each factor on the target, the qualitative indicators are divided into 10 levels of influence, with values ranging from integer 0 to 10 points, corresponding to levels 1, 2, ……10, respectively. The higher the level indicates the better evaluation obtained by the corresponding indicator data.
Based on the defined measurement values and indicator evaluation system, three evaluators were asked to assign values to the strengths and weaknesses of qualitative indicators based on available data, and the scores were obtained as shown in the table below.

Construction of the sample matrix
To prevent subjectivization of quantitative indicators, this paper only considers the existing government public data of indicators as the input matrix for the sample matrix construction of quantitative indicators.

Dimensionless sample data
The gray variable weight clustering is applicable to the case where the meaning and the scale of indicators are the same. The various influencing factors of each cluster indicators of different levels in the water pollution control may cause inaccurate evaluation results [10] . Thus, it is necessary to proceed the dimensionless processing.
Considering the feasibility of data processing, this paper adopts the maximization formula for the positive indicators and the inverse formula for the negative indicators, so that the direction of the indicators is unified after dimensionless processing.
Letting the normalized matrix be ij n m X x       , the formula for normalizing the maximum value of the positive indicator is The inverse normalized formula for the inverse indicator is The dimensionless sample matrix can be obtained

Determining city weights by the Entropy Weight Method
To obtain the weights of the three cities of Nanjing-Zhenjiang-Yangzhou objectively, this paper takes into account the regional gross domestic production, gross regional product index, year-end household population, local general public budget revenue and budget expenditure of Nanjing-Zhenjiang-Yangzhou from 2015-2019, and uses the entropy weight method to determine the weights of the three cities in each indicator. The data are obtained from the National Bureau of Statistics and the yearbook of Jiangsu Province in relevant years, and the detailed data are shown in Table V. The indicators referred to by the entropy weight method here are the three cities of Nanjing-Zhenjiang-Yangzhou, and the normalized matrix of the three cities' data for each indicator in the above table is calculated：   The city weights of the indicators from 1 to t are summed and normalized to obtain the vector of city weights in the evaluation matrix.
The city data weights are calculated to obtain the weights ′ 0.3564,0.3157,0.3280 for the three cities of Nanjing-Zhenjiang-Yangzhou in the governance scheme.

Determination of indicator weights
In the multi-layer index system, different indicators have different contributions to the evaluation system and there are different degrees of correlation among the indicators, so it is necessary to assign weights to each indicator according to its contribution degree and correlation degree. The fuzzy hierarchical analysis method combines the advantages of hierarchical analysis and fuzzy comprehensive evaluation method, which can be used to measure the weight of qualitative and quantitative, definite and uncertain indicators, and to fuzzify the subjectivity of experts [11] and transform them into accurate decision-making information.

Constructing the fuzzy complementary consistency matrix
A fuzzy complementary consistency matrix characterizing the relative importance of any two factors in the set , , … , can be constructed 1 , 0 1 , 1,2, … , . A larger i j r means that factor i I is more important than factor . In particular, when 0.5 means that both factors are equally important.
The literature [12] provides a method to construct a fuzzy complementary matrix starting from the traditional judgment matrix of hierarchical analysis. The fuzzy consistent judgment matrix is constructed for the first level of judging index factors as follows.

Calculation of index weights
Based on the above definition of fuzzy complementary consistency matrix, the weights of each factor under a certain attribute can be determined by equation (7). Where 1 Considering the resolution of program advantages and disadvantages, taking the base 100 , the weight vector of the first-level indicators is obtained as 100 0.1935, 0.0645, 0.1290, 0.1290, 0.3871, 0.0968 , and the corresponding fuzzy consistent judgment matrix of the second-level indicators is shown in Table VI, and the weights of indicators at all levels are assigned as shown in Table VII.

Establishing a gray evaluation model with mixed centroid whitening weight function
In order to avoid simple and rough evaluation, and to consider the problem of multiple crossovers of gray class whitening weight functions, and to ensure that the probability sum of each gray class of the same index is equal to 1, this paper adopts a hybrid centroid triangular whitening weight function gray clustering evaluation model to evaluate the collaborative governance scheme. The sample vector construction method in this paper has a major feature that ∈ 0,1 for all elements of the sample vector D. In this paper, this range of values is divided into four gray classes: unqualified, qualified, good, and excellent, which correspond to gray classes 1,2,3,4 respectively, as shown in Table VIII. . Therefore, the corresponding gray category of Nanjing-Zhenjiang-Yangzhou metropolitan area water pollution management program is the third category, and the comprehensive assessment level is good.

Conclusions
Located in the Yangtze River basin, the Nanjing-Zhenjiang-Yangzhou metropolitan area was embedded in the integrated development process of the Yangtze River Delta city cluster in 2014, in order to promote urban integration and achieve synergistic cooperation and integrated development among different cities. In this environment, the collaborative water pollution management in Nanjing-Zhenjiang-Yangzhou metropolitan area is also in a difficult situation, and it is urgent to solve the management problem and break the current water pollution dilemma. The conclusion at the end of the paper leads us to make policy recommendations in the following aspects.

Strengthen top-level construction and establish a coordinating body
It is impossible to establish a new regional governing body in the Nanjing-Zhenjiang-Yangzhou region. A more realistic approach is to form a long-term, comprehensive and mutual dialogue regional management group through consultation with a fixed number of representatives from each city, and to establish a communication mechanism for coordinated regional development. The regional management group coordinates their respective interests and resolves disputes in development according to the overall development situation, such as formulating longterm development plans, upgrading and optimizing industries, achieving environmental and ecological protection and sustainable development, so as to avoid duplicate construction, industrial convergence and low resource allocation, and to improve regional resource integration.

Application of modern information technology to achieve information sharing
At present, the water environment pollution problems in Ning, Zhen and Yang cannot be effectively managed, and the root of the problem is that the information cannot be shared in real time effectively. It refers to the use of the Internet and various intelligent sensor devices to form a network system that connects people, things and information to each other, thus realizing digitalization, visualization, intelligence and remote management and control, which truly realizes the collaborative governance of "Internet of everything".

Unification of laws and regulations
The legal regulations of the unified watershed, the basic principles of the establishment of cross-regional ecological compensation mechanism, compensation standards, multiple subjects and joint measures, so that the three cities of Ning, Zhen and Yang will take the construction of the Yangtze River Ecological Civilization Innovation Center as the starting point, better use of legal means to protect the ecology of the Yangtze River Ning, Zhen and Yang section, the Yangtze River protection requirements to the letter.

Establish a reasonable and effective evaluation mechanism
A scientific and reasonable evaluation mechanism can truly evaluate the current status of governance, expose the problems in the process of governance, and provide the right direction for further improvement of governance programs and optimization of governance processes.