1. Introduction
Watershed ecological compensation is a form of payment for environmental services [
1,
2,
3], in which a beneficiary or a destroyer of the ecological environment gives a certain degree of economic compensation to an environmental protector by measuring the value of ecological service to its own value in order to motivate its environmental behavior [
4]. In order to reduce the occurrence of water pollution in basins, the ecological compensation mechanism is designed to force polluters to reduce emissions and compensate for damage to the ecological environment, which has become a popular topic [
5].
As a result of a polluter’s willingness to pay, there would be multiple compensation schemes from which to choose in practical work. In 2007, based on questionnaires and comparative research in three American regions, Kosoy et al. found that the ecological compensation opportunity cost for upstream ecological compensation was greater than the actual payment of downstream ecological compensation. A method of ecological compensation for the basin was then proposed according to the opportunity cost [
6]. Opportunity cost can be defined as the loss of potential gain from other ecological compensation schemes when one scheme is chosen [
7]. Wunder et al. suggested that ecological services should be fully market-oriented, including ecological destruction of the basin and the ecological reconstruction and construction compensation of the basin, which would achieve optimal ecological compensation [
8]. In 2014, Sand et al. studied the ecological compensation mechanism in rural Kenya, and proposed that ecological compensation should be embedded in a broader institutional framework and receive more financial resources to facilitate the adaptation of ecosystem services to climate change [
9]. Furthermore, Cheng et al. reviewed the mature theory and scientific mechanism of ecological compensation in basins and analyzed the defects and shortcomings of the theory of ecological compensation [
10], which will contribute to decisions on compensation schemes.
The reason that we are willing to pay is to elicit the problem that upstream and downstream cities are faced with various compensation plans that have been made by the experts from the ecological compensation work group, and how to make decisions on the choice of these schemes. However, most previous results were obtained by studying one aspect of the ecological compensation scheme of water pollution in a basin separately; meanwhile, the comprehensive influence of various factors is ignored in the selection of ecological compensation schemes [
11], and the analysis of the main behavior of the participation of ecological compensation is lacking. Therefore, the comprehensive evaluation of multiple attributes is required.
Liu et al. and Zhang et al. suggested that the evaluation of the ecological compensation scheme of water pollution in basins was a multi-attribute decision-making problem, and that different compensation modes and compensation capitals, and the combination of compensation time could constitute alternative approaches to ecological compensation [
11,
12]. Accordingly, when we determine the ecological compensation scheme, we need to take into account the impact of the compensation mode, the compensation capital and the compensation time to upstream and downstream regions, and achieve the sustainable development of the whole basin.
Owing to the high degree of uncertainty in the compensation schemes, such as the pollution load, the pollution degree, the compensation capital, and the compensation mode, compensation schemes are difficult to agree on the upstream and the downstream. To address this problem, Zhang et al. proposed a method of decision making based on prospect theory to measure the uncertainty in ecological compensation schemes and improve the accuracy of the decision results [
12]. Prospect theory is a theory in cognitive psychology that describes the way people choose between probabilistic alternatives that involve risk, where the probabilities of outcomes are known [
13,
14,
15]. However, in a study by Zhang [
12], small changes in the upper and lower boundary range were found to lead to a greater impact on the result of compensation schemes, and bring new uncertainty [
16,
17], since the method only used information on the interval and the lower boundary to make the decision.
In this study, we propose that the new uncertainty is mainly caused by the interval number algorithm, which can be overcome by improving the interval number algorithm. Therefore, we use the Monte Carlo technique to simulate random samples of a large number of decision schemes in the interval range. We are able to obtain the decision results of the various schemes, the overall distribution trend of the various schemes, and also to reduce the uncertainty of the traditional interval number algorithm.
By observing the spatial distribution of the projection eigenvalues of all schemes, the random sample projection eigenvalues have the characteristics of total dispersion and local aggregation, which are similar to the clustering problems in system engineering [
18]. Projection pursuit cluster (PPC) is an important system evaluation and decision-making method that has been applied in a large number of studies in the field of water protection and utilization [
18,
19,
20]. Therefore, we propose the sorting decision of the ecological compensation scheme by using the projection trace clustering algorithm to cluster the simulated scheme, and also to propose using the projection pursuit algorithm to cluster the simulated ecological compensation scheme.
The purpose of this paper is to propose a method to solve the problem of multi-attribute scheme in the form of interval number decision-making matrix (DMM) by the Monte Carlo method, and reduce the uncertainty of decision making. At the same time, PPC is used to make the decision of each scheme, obtain the weight of each attribute and subsequently classify the decision classification according to the projection eigenvalues, and carry out the statistical analysis. The rest of this paper is organized, as follows:
Section 2 gives the methodological framework and introduces the main principles of PPC;
Section 3 gives the results of a case study and a discussion, and the decision is made in the case of different random simulations; and,
Section 4 summarizes the main research results of this paper, and suggests that the proposed method of decision making is more accurate and reasonable than other methods. This study is expected to provide guidance for regional socio-economic development.
2. Materials and Methods
Firstly, the interval DMM of the watershed ecological compensation schemes is obtained by using the expert rating method. Secondly, the Monte Carlo method is used to generate a number of random samples in the various attributes of decision intervals, and the processing of the dimensionless is carried out. Then, the PPC object function is constructed, the accelerating genetic algorithm is used to optimize the projection vector, and statistical analysis is carried out to determine the sorting results of each scheme quantitatively. The method is diagrammatically outlined in
Figure 1.
2.1. Randomize Decision-Making Matrix
Let and be the lower bound and upper bound of the jth attribute of the hth scheme in interval DMM, and be the jth attribute of the ith random sample, where i = 1, 2, …, k × n, j = 1, 2, …, m, h = 1, 2, …, k, n is the number of random simulations of each scheme, m is the number of attribute, and k is the scheme number of watershed water pollution decision making.
In the interval of the various attributes, the random number of the uniform distribution is generated by the use of Equation (1) below. The number of random simulations for each scheme are selected as 10, 50, 100, 500, and 1000, respectively, to make the random sampling results statistically significant.
where rand() is a function that can generate [0,1] uniform random number.
2.2. Dimensionless Data Treatment
The dimensionless formulation is given as:
where
and
are the maximum and minimum values of attribute
j in the random samples, respectively.
2.3. Projection Pursuit Cluster
Let
a (
a1,
a2, …,
am) be the m-dimensional unit projection vector, then
zi, the one dimensional projection eigenvalue of
, can be shown as follows:
where,
z = (
z1,
z2, …,
zk×n) is the projection eigenvalue set. According to the projection vector, the weight of each attribute can be calculated by Equation (4).
The PPC theory requires that the distribution of the projection eigenvalue
z(
i) is as dense as possible, and it is best to build up a number of points; and, the overall projection dots are as scattered as possible. According to the maximum entropy principle [
21,
22], the attribute weight of the projection vector distribution should have the maximum entropy. The larger the entropy, the less the constraint and the assumption that people add. Based on this concept, the projection indicator function
Q(
a) can be constructed as:
where,
Sz is the standard deviation of
z(
i) series,
Dz is the local density of
z(
i), and
Hw is the entropy of attribute weights. Those formulas are shown as:
where
Ez is the mean of
z(
i) series,
R = 0.1
Sz denotes the windows radius of local density,
rij = |
z(
i) −
z(
j)|, and
u(
t) is the unit step function, which is equal to 1 when
t ≥ 0, and 0 when
t < 0.
When the value of
Q(
a) reaches a maximum, it obtains the optimal projection vector and clustering results. Then the model can be described as a nonlinear optimization question whose formula is given in Equation (9) below. This study uses the accelerating genetic algorithm to answer this question [
23,
24].
2.4. Compensation Scheme Decision Making
The optimal projection value series is calculated according to Equation (3) by the optimal projection vector a* that is obtained by Equation (9). The mean and standard deviation of each scheme is calculated, and the Duncan significance test is carried out to compare the mean of each scheme in order to guide the practice of policy.
Statistical characteristics and significance tests are performed while using the SPSS 15.0 software (SPSS Inc., Chicago, IL, USA).
2.5. Study Area
The research area is located in the Taihu basin in China. The Taihu basin is divided into the cities of Jiangsu, Zhejiang, Shanghai, and Anhui province, and the basin flows through eight cities, Shanghai, Suzhou, Wuxi, Changzhou, Zhenjiang, Hangzhou, Jiaxing, and Huzhou. This study takes the upstream of Suzhou city and the downstream of Jiaxing city as study areas.
The water quality from Suzhou to Jiaxing is dominantly grade V and above, with an average water quality of grade V observed in 16.7%, higher than grade V in 80%, and grade IV in 3.3%. The water of Jiaxing was so polluted that there was no clean river in the city. The water quality is embodied in the characteristics of organic pollution, and it is completely impossible to meet the basic requirements of drinking water safety. According to the experts from the working group of ecological compensation, the literature [
12] has proposed four alternatives to ecological compensation, as shown in
Table 1. The experts were mainly concerned with the idea that the plan should be acceptable to both upstream and downstream cities, as well as with the level of economic development in both Suzhou and Jiaxing.
Table 1 describes the four schemes, include three attributes:
C1, compensation mode,
C2, compensation amount, and
C3, compensation time.
The four alternatives (schemes) are rated by experts with a score of 1 (worst) to 10 (best); the decision matrix is given in
Table 2. In order to facilitate the comparison of the PPC model with the existing model [
12], the original decision matrix from [
12] is adopted in this paper.
The last line in
Table 2 is a subjective weight range of each attribute, as determined by the same experts from the working group of ecological compensation mentioned above. The subsequent decision study on the ecological compensation scheme of the basin was based on the interval DMM in
Table 2.
4. Conclusions
This paper presents a multi-attribute decision method for the ecological compensation scheme of water pollution in the Taihu basin, China. The proposed method uses Monte Carlo simulation technology to solve the interval multi-attribute decision and PPC method to cluster the projection eigenvalues of various schemes. The proposed method is verified by means of watershed water pollution ecological compensation schemes, and the following conclusions are obtained.
- (1)
The attribute values of the decision schemes are uncertain, and the standard deviation of the decision results is larger. This problem can be solved by simulating a large number of solutions through stochastic simulation techniques. According to the results of various numbers of random simulations, the decision of all the schemes can be analyzed significantly to improve the reliability of the decision results.
- (2)
Using the PPC method can improve the accuracy of the decision result, especially the multi-attribute decision problem of the matrix element for entire interval number or a part. With the increase of the number of simulations, the scatter plot of each scheme demonstrates the superiority of the S2 scheme.
- (3)
The weight of the C2 attribute is the largest, followed by the compensation mode C1 and the compensation time C3, which are consistent with subjective weight. When the number of simulations was 50, 100, 500, and 1000, S2 was significantly better than the other schemes at 0.01 significance levels. It is clear that the combination scheme of money compensation and development in different place is better than that of others, and it is worth using in the decision of ecological compensation of watershed water pollution.
The upstream Suzhou city sets up the economic development zone in the downstream Jiaxing city for the DDP mode and compensates the downstream Jiaxing city for ecological pollution, which not only enables the upstream Suzhou city to gain economic benefits, but also drives the downstream Jiaxing city to develop and restore the downstream city’s ecological environment. Therefore, the combination of the DDP mode and MC mode is an ecological compensation scheme with growth and sustainability, so as to achieve a “win-win” situation for economic development and ecological and environmental protection and bring benefits to regional residents.
Further study of ecological pollution costs and compensation mechanisms should be a bigger priority in regions where environmental protection and remediation is most required.