CN107122851A - A kind of lake water systems connects engineering proposal optimization model Sensitivity Analysis Method - Google Patents

Abstract

Engineering proposal optimization model Sensitivity Analysis Method is connected the present invention relates to a kind of lake water systems, including：Set up index system；Set up Evaluation formula；Determine Vague values；Primary election Vague collection score function models；Index attribute value changing sensitivity is analyzed；Index weightses changing sensitivity is analyzed；Choose preferred plan.The present invention is combined to subjective, objective weighted model, based on the small thought as far as possible of deviation between combining weights and former weight, the Combining weights of indices are asked for, the advantage of subjective weighting method and objective weighted model is so preferably taken into account, obtained combining weights more meet actual demand.Based on cloud model to Vague collection score function models in each index attribute value and the uncertainty and the robust analysis of ambiguity making policy decision result of weighted value, new reference frame is provided for the quality of objective evaluation difference Vague collection score function models, and then contributes to policymaker to select suitable Vague collection score function model to draw best decision scheme.

Description

A Sensitivity Analysis Method for Optimization Model of River and Lake Water System Connectivity Project Scheme

technical field

The invention relates to a method for analyzing the sensitivity of an optimal model of a river-lake water system connection engineering scheme, which is an analysis method for water conservancy projects, and is an analysis method applied to planning of water conservancy projects.

Background technique

Due to the particularity of river and lake water system connectivity issues, attention should not only be paid to the impact of river and lake water system connectivity on the ecological environment and local areas such as transfer-out areas or transfer-out areas, but also its comprehensive impact on areas along the connectivity project and the entire connected system . At present, most studies focus on the exploration of the impact itself. There are relatively few studies on how to realize the quantitative comprehensive evaluation of the impact to optimize the connection project scheme of rivers and lakes. It is necessary to follow the laws of nature and economics, and strengthen the demonstration and selection of connection projects. , attaches great importance to the impact of the connection of river and lake water systems on the ecological environment, and pays attention to the risk assessment research of connection projects. At present, there are many methods such as expert scoring method, AHP gray relational analysis method, fuzzy evaluation, artificial neural network, matter-element analysis and projection pursuit, which can be applied to plan optimization and ranking. Therefore, corresponding research has been carried out in many fields to explore the application characteristics and applicable objects of these evaluation methods.

At present, the fuzzy comprehensive evaluation method is widely used in practical work. It solves the limitation of the classical mathematical model that can only describe the deterministic problem with "either or the other", and uses the fuzzy set theory of "either this or that" to Describe non-deterministic problems. However, traditional fuzzy sets can only reflect the affirmative membership of fuzzy information, and cannot reflect the two aspects of affirmation and negation of fuzzy concepts in the real world and the hesitation between the two, so traditional fuzzy sets are used in engineering scheme optimization It will lead to the loss of part of the decision-maker's information. The Vague set proposed by Gau in 1993 can overcome the above shortcomings and has a stronger ability to express uncertainty. Vague set scoring function method is one of the two commonly used methods. Among them, the scoring function Vague set is the key and core of multi-attribute decision-making. It is the direct concentration and embodiment of fuzzy and uncertain information aggregation processing in Vague set. It affects the pros and cons of the Vague set decision, and even affects the correctness of the decision result. At present, many scholars have constructed multiple scoring functions. Since decision makers have different understandings and detection angles of uncertain information in the Vague value, it has become a research difficulty to find a scoring function that can reasonably reflect objective facts. In the application research of Vague scoring function, the existing research focuses on the application of the method, but does not discuss the rationality of the evaluation results. Therefore, when the multi-attribute decision-making method of Vague set scoring function is used in the planning and construction of river and lake water system connectivity projects, the problem that needs to be solved urgently is to analyze the uncertainty of the evaluation results of these scoring functions. In addition, the index weight has a great influence on the comprehensive evaluation results. The index weight assignment method is generally divided into subjective weighting method and objective weighting method. The index evaluation method is relatively mature, but its shortcoming is that the connotation of each evaluation index is relatively single, and it cannot effectively reflect the mutual influence between different indexes. Although the subjective weighting method reflects the special requirements of decision makers for the indicators of the river and lake system connectivity scheme, it cannot reflect the gradual change of the importance of the evaluation indicators over time; the objective weighting method can objectively reflect the data information and differences of the indicators. But ignoring the importance of the decision-maker's experience, the phenomenon of unreasonable weight may appear.

Contents of the invention

In order to overcome the problems of the prior art, the present invention proposes a method for analyzing the sensitivity of the optimization model of the river-lake water system connectivity engineering scheme. The method described is a method for analyzing the sensitivity of the optimization model of river and lake water system connection engineering schemes based on Vague sets, aiming to solve the uncertainty quantification and model rationality of the application of various Vague set scoring function models in the optimization of river and lake water system connectivity engineering schemes. The question of sexual selection.

The object of the present invention is achieved like this: a kind of river and lake water system connection engineering scheme optimal model sensitivity analysis method, the steps of described method are as follows:

Steps to establish the index system: through literature research, field investigation and evaluation, and according to the resource-society-economy-ecology-environment-engineering model, establish the principles for establishing the index system, construct an evaluation index system for the connection scheme of rivers and lakes, and divide the indicators into Qualitative and quantitative indicators and determine their values;

Steps to establish the combined weighting method: select multiple subjective weighting methods and multiple objective weighting methods, and process the weights calculated by the selected subjective and objective weighting methods according to the probability statistics method to obtain the subjective weight vector and the objective weight vector, and The combination of the two establishes the combined weighting method of the evaluation indicators of the river and lake water system connectivity scheme, and calculates the weight value of each indicator. The specific process is as follows:

Weighting of evaluation indicators for river and lake water system connectivity schemes: respectively select p subjective weighting methods and q objective weighting methods to weight the evaluation indicators of river and lake water system connectivity schemes, and subjective weight vectors ω ₁ , ω ₂ , ..., ω _p and objective weight vectors ω _p+1 , ω _p+2 ,...,ω _p+q , where ω _i =(ω _1i ,ω _2i ,...,ω _ni ) ^T ;

Group the weight vectors of the evaluation indicators of the river and lake water system connectivity schemes: p subjective weight vectors and q objective weight vectors of the river and lake water system connectivity evaluation indicators are respectively used as a sample of uniformly distributed random variables, and their expected values are calculated and normalized, respectively Obtain subjective weight vector ω′ ₁ and objective weight vector ω′ ₂ ;

Based on the subjective weight vector ω′ ₁ and the objective weight vector ω′ ₂ , the combined weight ω of the evaluation index of the connectivity scheme of rivers and lakes is calculated. The calculation formula is as follows, where the probabilities of ω′ ₁ and ω′ ₁ are taken as a and b respectively:

The a and b coefficients are calculated by constructing an optimization model: the objective function is that the deviation between the combined weight vector and the original subjective and objective weight vectors should be as small as possible, as follows:

The above optimization model can be solved by using MATLAB, and can be a, b and ω;

Steps to determine the Vague value: Calculate the relative membership degree of each index, including true membership degree, false membership degree and unknown Degree, so as to determine the Vague value of each river and lake water system connectivity project scheme, the relative degree of membership is calculated as follows:

Assuming that the decision matrix of the river-lake water system connectivity project plan is X={x _ij }, x _ij represents the i-th index attribute value of the jth plan, i=1, 2,..., m; j=1, 2,... , n. Transform the decision matrix X into a relative membership matrix μ={μ _ij } _m×n , and define the support index set, neutral index set and opposition index set of the scheme according to the matrix μ:

If μ _ij ≥ λ ^U , then the i-th index is satisfied with the j-th scheme, or the j-th scheme supports the i-th index i=1, 2,..., m; j=1, 2,..., n;

If μ _ij ≤ λ ^L , then the i-th index is not satisfied with the j-th plan, or the j-th plan is against the i-th index i=1, 2,..., m; j=1, 2,... , n;

If λ ^L ≤ μ _ij ≤ λ ^U , then the i-th index is neutral to the j-th plan, or the j-th plan does not support or oppose the i-th index i=1, 2,..., m; j=1 ,2,...,n;

Let the weight vector of the index be ω=(ω ₁ , ω ₂ ,...,ω _m ), for any project x _j ∈ X of river-lake water system connectivity project, the degree of meeting the requirements on m indicators can be represented by a Vague value , that is, v _j =[t(x _j ), 1-f(x _j )], where t(x _j ) is equal to the sum of corresponding weights of indicators in the support index set of scheme x _j ; f(x _j ) is equal to scheme The sum of the corresponding weights of the indicators in the objection indicator set of x _j ;

The steps of preliminary selection of the Vague set scoring function model: Based on the Vague value of each river and lake water system connectivity project plan, select multiple Vague set scoring function models to calculate the evaluation value of the plan, and use the voting model and the principles of the Vague set scoring function model to analyze each scoring function model The rationality of the model is used to select the model and eliminate the unreasonable model;

The steps of the sensitivity analysis of index attribute value changes: In the case of changes in the index attribute values of a single river-lake water system connectivity scheme, use the initially selected Vague set scoring function model to calculate the evaluation value of the river-lake water system connectivity engineering scheme; based on the cloud model, the preliminary selection The comprehensive evaluation value of the Vague set scoring function model is used as sample data to generate parameter tables and cloud diagrams;

Sensitivity analysis process of indicator attribute value change:

Assume that the possible value interval of the evaluation index r′ ₁₁ of the river-lake water system connectivity project scheme is (0, r″), and the value interval after normalization of the index is within [0, 1];

Assign the initial value r ₀ to r′ ₁₁ , take r ₀ =0.01, and determine the step size as Δr=0.01;

The attribute values of other indicators remain unchanged, and the comprehensive evaluation value of each river and lake water system connectivity project scheme is calculated by using the primary Vague set scoring function model;

Let r′ ₁₁ →r′ ₁₁ +Δr, repeat “other index attribute values remain unchanged, use the primary selection Vague set scoring function model to calculate the comprehensive evaluation value of each river and lake system connectivity project” until r′ ₁₁ = r”;

Repeat the above steps, and count the comprehensive evaluation values of the river and lake water system connectivity project schemes in the entire value interval of the change of other index attribute values in turn;

Based on the comprehensive evaluation value of each river and lake water system connectivity project scheme under the condition of changing index attribute values as sample data, the cloud model E _x , _{E n} , He of each river and lake water system connectivity project scheme is obtained through reverse cloud, and then the cloud map is generated ;

The steps of the sensitivity analysis of index weight value changes: in the case that the weight values of multiple indicators change at the same time, use the preliminary selected Vague set scoring function model to calculate the evaluation value of the river and lake water system connectivity project; based on the cloud model, the primary selected Vague set The comprehensive evaluation value of the set scoring function model is used as sample data to generate a parameter table and a cloud map; the specific process of sensitivity analysis of simultaneous change of multiple weights is as follows:

Assign initial value ω ₀ to ω ₁ , take ω ₀ =0.01;

Use a computer to generate a set of random weights ω ₂ , ω ₃ , ..., ω _j , ..., ω _y , satisfying that the sum of the weights is 1-ω ₀ , forming a set of random weights W ₁ = {ω ₀ , ω ₂ , ω ₃ , ..., ω _j , ...., ω _y };

According to the random weight set obtained above, the comprehensive evaluation value of each river and lake water system connectivity project scheme is calculated by using the primary selection Vague set scoring function model;

Change ω ₁ ＝ω ₁ +ω ₀ , and then repeat the above "using computer to generate a group of random weights ω ₂ , ω ₃ ,..., ω _j ,..., ω _y , satisfying that the sum of weights is 1-ω ₀ , forming A set of random weight sets W ₁ = {ω ₀ , ω ₂ , ω ₃ , ..., ω _j , ..., ω _y }" to "According to the random weight set obtained above, use the primary selection of the Vague set scoring function model Calculate the comprehensive evaluation value of each river and lake water system connectivity engineering scheme", until ω ₁ = 1, the matrix set of comprehensive evaluation value of each river and lake water system connectivity engineering scheme can be obtained;

Analyze the sensitivity of ω ₂ , ω ₃ , ..., ω _j , ..., ω _y respectively;

According to the comprehensive evaluation values of ω ₁ , ω ₂ , ω ₃ ,..., ω _j ,..., ω _y 's connection engineering schemes of rivers and lakes, use them as sample data of the cloud model to generate parameter tables and cloud maps;

Steps for selecting the best plan: compare the robustness of different Vague set scoring functions to the decision-making results of the river and lake water system connectivity project, select the Vague set scoring function with the best The evaluation result of the set scoring function is taken as the final result.

The beneficial effects produced by the present invention are: the present invention combines subjective and objective weighting methods, based on the idea that the deviation between the combined weight and the original weight is as small as possible, and obtains the combined weight of each index, which better takes into account the subjective The advantages of the weighting method and the objective weighting method, the combination weight obtained is more in line with the actual needs. In addition, it focuses on the importance of different evaluation indicators and their impact on the overall evaluation results, and reflects the mutual influence and function of each index, avoiding the separation of each index, and has a better evaluation result. Based on the cloud model, the robustness analysis of the decision-making results of the vague set scoring function model under the uncertainty and ambiguity of each index attribute value and weight value provides a new reference for objectively evaluating the pros and cons of different vague set scoring function models , which in turn helps the decision-maker to select the appropriate Vague set scoring function model to obtain the best decision-making scheme, and provides more comprehensive and scientific decision-making support for the optimization of the river and lake water system connectivity engineering scheme. Optimization and evaluation have practical value, and can be used in the evaluation and optimization of Vague set similarity measurement model and scoring function model.

Description of drawings

The present invention will be further described below in conjunction with drawings and embodiments.

Fig. 1 is the flowchart of the method described in Embodiment 1 of the present invention;

Fig. 2 is the normal cloud distribution diagram of each scheme calculated by the Chen-Tan formula in the example described in Embodiment 1 of the present invention under the change of index attribute value;

Fig. 3 is the normal cloud distribution diagram of each scheme calculated by the Hong-Choi formula in the example described in Embodiment 1 of the present invention under the change of index attribute value;

Fig. 4 is the normal cloud distribution diagram of each scheme calculated by the Xuchanglin formula under the index attribute value change in the example described in the first embodiment of the present invention;

Fig. 5 is the normal cloud distribution diagram of each scheme calculated by Li Peng's formula under the change of index attribute value in the example described in the first embodiment of the present invention;

Fig. 6 is a normal cloud distribution diagram of each scheme calculated by Gao Jianwei's formula in the example described in the first embodiment of the present invention under the change of index attribute value;

Fig. 7 is the normal cloud distribution diagram of each scheme calculated by Wang Wanjun's formula under the change of index attribute value in the example described in the first embodiment of the present invention;

Fig. 8 is a normal cloud distribution diagram of each scheme calculated by Peng Zhansheng's formula in the example of the first embodiment of the present invention;

Fig. 9 is the normal cloud distribution diagram of each scheme calculated by the Chen-Tan formula in the example described in Embodiment 1 of the present invention under the change of index weight value;

Fig. 10 is the normal cloud distribution diagram of each scheme calculated by the Hong-Choi formula under the change of index weight value in the example described in the first embodiment of the present invention;

Fig. 11 is the normal cloud distribution diagram of each scheme calculated by the Xuchanglin formula in the example described in the first embodiment of the present invention under the index weight value change;

Fig. 12 is a normal cloud distribution diagram of each scheme calculated by Li Peng's formula under the change of index weight value in the example described in Embodiment 1 of the present invention;

Fig. 13 is a normal cloud distribution diagram of each scheme calculated by Gao Jianwei's formula in the example described in Embodiment 1 of the present invention under the change of index weight value;

Fig. 14 is the normal cloud distribution diagram of each scheme calculated by Wang Wanjun's formula in the example described in the first embodiment of the present invention;

Fig. 15 is a normal cloud distribution diagram of various schemes calculated by Peng Zhansheng's formula in the example of the first embodiment of the present invention.

detailed description

Embodiment one:

This embodiment is a method for analyzing the sensitivity of the optimization model of the river-lake water system connectivity engineering scheme, and the flow chart is shown in FIG. 1 . The steps of the method described in this embodiment are as follows:

(1) Steps to establish the index system: through literature research, field investigation and evaluation, and according to the resource-society-economy-ecology-environment-engineering model, establish the principles for establishing the index system, construct the evaluation index system for the river and lake water system connectivity scheme, and Indicators are divided into qualitative indicators and quantitative indicators, and their values are determined.

This embodiment takes a certain river and lake water system connection project as an application example. The connectivity project has three schemes P1, P2 and P3,

This embodiment will be described below in conjunction with this application example.

Considering that in the optimal evaluation of river and lake water system connectivity projects, in order to correctly reflect the complex internal relations of resources, society, economy, ecology, environment, resources and engineering technology, and follow the principles of evaluation index system setting, the sustainable development of water resources is used for reference. On the basis of index systems such as utilization, rational allocation of water resources, carrying capacity of water resources, and degree of water resource scarcity, a model of resources-society-economy-ecology-environment-engineering and the actual situation of river and lake water system connectivity projects are used to establish a certain The comprehensive evaluation index system is optimized for the river and lake water system connectivity project, and the index is determined to be qualitative or quantitative.

In the embodiment, an evaluation index system is established, and a total of three layers of indexes are set, and according to the calculation method of the index attribute value,

Set as qualitative and quantitative indicators, as shown in Table 1.

Table 1 Comprehensive evaluation index

(2) Steps to establish a combined weighting method: select multiple subjective weighting methods and multiple objective weighting methods, and process the weights calculated by the selected subjective and objective weighting methods according to the probability statistics method to obtain the subjective weight vector and objective weight Vector, the two are synthesized to establish the combined weighting method of the evaluation index of the river and lake water system connectivity scheme, and the weight value of each index is calculated.

Assuming that the number of indicators for comprehensive evaluation is n, the proposed combined weighting method first uses p kinds of subjective weighting methods and q kinds of objective weighting methods to weight each indicator, and based on the probability statistics method, the subject and object weights The vector groups are processed separately to obtain the subjective weight vector ω′ ₁ and the objective weight vector ω′ ₂ , and then synthesize the two vectors to obtain the final combined weight ω. The specific process is as follows:

(1) The evaluation index weighting of the river and lake water system connectivity scheme. Select p kinds of subjective weighting methods and q kinds of objective weighting methods to weight the evaluation indicators of river and lake water system connectivity schemes, and obtain subjective weight vectors ω ₁ , ω ₂ ,..., ω _p and objective weight vector ω _{p +1} , ω _p+2 , ………, ω _p+q , where ω _i =(ω _1i , ω _2i ,………, ω _ni ) ^T .

(2) Grouping and processing the weight vectors of the evaluation indicators of river and lake water system connectivity schemes. River and lake water system connectivity evaluation indexes p subjective weight vectors and q objective weight vectors are respectively used as a uniformly distributed random variable sample, and their expected values are calculated and normalized to obtain subjective weight vector ω′ ₁ and objective weight vector ω′ ₂ .

(3) Based on the subjective weight vector ω′ ₁ and the objective weight vector ω′ ₂ , calculate the combined weight ω of the evaluation index of the river and lake water system connectivity scheme. The calculation formula is shown in formula (1), where the probabilities of ω′ ₁ and ω′ ₁ are Take a and b.

The a and b coefficients are calculated by constructing an optimization model. The objective function is to minimize the deviation between the combined weight vector and the original subjective and objective weight vectors, as shown in formula (2):

The above optimization model can be solved by using MATLAB, and can be a, b and ω.

The subjective weighting method can choose a variety of subjective weighting methods such as analytic hierarchy process, scoring method, tone operator comparison method, and prioritization diagram method. The objective weighting method can choose objective weighting methods such as entropy weight method and variation coefficient method.

In the example, in order to fully consider the subjective information and objective information, the weights of the first and second layer indicators are determined by the tone operator comparison method, and the third layer indicators are determined by the combined weighting method.

Based on this, the following indicator weight table can be obtained, see Table 2.

Table 2 Index weight table

(3) Steps to determine the Vague value: According to the qualitative and quantitative index attribute values of the evaluation of the river-lake water system connectivity project plan, as well as the calculated weight of each index, calculate the relative membership degree of each index, including the true membership degree (support degree) ), false membership degree (opposition degree) and unknown degree, so as to determine the Vague value of each river and lake water system connectivity project scheme.

The calculation method of relative membership degree is as follows:

Assuming that the decision matrix of the river-lake water system connectivity project plan is X={x _ij }, x _ij represents the i-th index attribute value of the j-th plan, i=1, 2,..., m; j=1, 2, ………, n. Transform the decision matrix X into a relative membership matrix μ={μ _ij } _m×n , and define the support index set, neutral index set and opposition index set of the scheme according to the matrix μ:

(1) If μ _ij ≥ λ ^U (the lower bound of satisfaction acceptable to the decision maker), then the i-th index is satisfied with the j-th plan, or the j-th plan supports the i-th index (i=1, 2, ………, m; j=1, 2,………, n);

(2) If μ _ij ≤ λ ^L (the upper limit of satisfaction acceptable to the decision maker), then the i-th indicator is not satisfied with the j-th scheme, or the j-th scheme is against the i-th indicator (i=1, 2, ... ..., m; j = 1, 2, ... ..., n);

(3) If λ ^L ≤ μ _ij ≤ λ ^U , then the i-th indicator is neutral to the j-th scheme, or the j-th scheme does not support and does not oppose the i-th indicator (i=1, 2,……… , m; j=1,2,………,n);

Let the index weight vector be ω=(ω ₁ , ω ₂ ,………, ω _m ), for any project x _j ∈ X of river and lake system connectivity project, how much it satisfies the decision-maker’s requirements on m indicators It can be represented by a Vague value, that is, v _j =[t(x _j ), 1-f(x _j )], where t(x _j ) is equal to the sum of corresponding weights of indicators in the support indicator set of scheme x _j ; f( x _j ) is equal to the sum of the corresponding weights of the indicators in the objection indicator set of the scheme x _j .

The values of λ ^L and λ ^U are 0.5 and 0.75 respectively, and the Vague values of the three schemes can be obtained, as shown in Table 3.

Table 3 Vague values calculated by different schemes

(4) The steps of preliminary selection of the Vague set scoring function model: Based on the Vague value of each river and lake water system connectivity project plan, select multiple Vague set scoring function models to calculate the evaluation value of the plan, and use the voting model and the principles of the Vague set scoring function model to analyze each The rationality of the scoring function model is used to initially select the model, and the unreasonable model is eliminated.

Vague set scoring function models are generally divided into two types based on the absolute gap and the relative gap between true and false membership.

Representative scoring functions are selected here to analyze their applicability in river and lake water system connectivity engineering schemes. In the following formula is the lower bound on the degree of positive membership derived from the evidence supporting the scheme A _i , is the lower bound on the negative membership derived from the evidence against A _i , is the uncertainty about the scheme A _i , which is equal to

(1) Chen and Tan formula:

(2) Hong and Choi formula:

(3) Liu Huawen formula:

(4) Liu and Wang formula:

(5) Zhou Xiaoguang's formula:

(6) Xuchanglin formula:

(7) Zhang Enyu's formula:

(8) Li Peng formula:

(9) Wang Wanjun formula:

(10) Gao Jianwei formula:

(11) Peng Zhansheng formula:

(12) Wang Weiping formula:

According to the definition of the scoring function, the larger the value of the scoring function, the more suitable the project plan is for the needs of decision makers. Therefore, the optimal plan can be selected according to the optimization or ranking of the scoring function value.

According to the above scoring function, the corresponding scoring function value can be obtained, as shown in Table 4.

Table 4 Different scoring function values of different schemes and the ranking of schemes

From the total calculation results, Liu Huawen's formula, Liu-Wang's formula, Zhang Enyu's formula, and Wang Weiping's formula are ranked as P2>P3>P1. Among them, the scores of P2 and P3 calculated by Liu Huawen formula and Zhang Enyu formula are nearly equal; the scores of P2 calculated by Liu-Wang formula and Wang Weiping formula are higher than the scores of P3. The P1 score is lower than the P2 and P3 scores.

According to the voting model to analyze the Vague value of different proposals, assuming that the number of voters is 100, and the judgment of the plan is divided into three situations: support, opposition and abstention, then the number of people who support P1 is 53 people, the number of opponents is 21 people, and abstentions The number of people is 26; the number of P2 support is 67, the number of opposition is 16, and the number of abstentions is 17; the number of P3 support is 75, the number of opposition is 20, and the number of abstentions is 5.

Analyzing in sequence, Liu Huawen's formula, Liu-Wang's formula, and Zhang Enyu's formula show that the number of supporters of P3 is more than that of P2, so the score value is higher than the latter, but the calculation result of the score value is just the opposite. The main reason is that these three formulas successively refine the abstention part of the Vague set, and propose a scoring function method based on the relative gap between true and false membership degrees. However, this method actually exaggerates the impact of unknown information on decision-making results. The main consideration is It is the influence of supporting opinions on decision-makers, ignoring the influence of opposing opinions on decision-making effects. It is a more optimistic decision-making method. In some cases, it will also get results that go against people’s intuitive judgment. It is concluded that P2 is better than P3 unreasonable judgment. Therefore, it should not be used in the optimization and sequencing of river and lake water system connectivity projects.

The reason why Wang Weiping’s formula obtains calculation results that are contrary to common sense is that the scoring function of this formula constructs a segmented scoring function according to the decision-maker’s neutrality, aversion and pursuit mentality. Although this method can better reflect the decision-maker’s preference mentality, However, this scoring function tends to cause information preference extremes in information decision-making, that is, when the supporting evidence is dominant, the unascertained information is all radical supporting evidence when the pursuit mentality is used for decision-making; It is theoretically unreasonable to follow all unconfirmed information with opposing evidence.

Although Zhou Xiaoguang’s formula shows that the ranking of the schemes is: P3>P2>P1, the scoring values of the three schemes are 0.932, 0.972 and 0.998 respectively, which are very close, and the resolution of the scheme ranking is not high. The reason for the analysis is that the higher the degree of uncertainty, the greater the impact on the value of the calculation results, thus exaggerating the impact of uncertainty information or waiver.

Combined with the voting model, the Chen-Tan formula, Hong-Choi formula, Xu Changlin formula, Li Peng formula, Wang Wanjun formula, Gao Jianwei formula, and Peng Zhansheng formula are more reasonable. In the above formulas, the Chen-Tan formula and the Hong-Choi formula only consider the true and false membership degrees. The starting point of the Chen-Tan formula is that the more advantages the true membership degree has than the false membership degree, the more it meets the requirements of decision makers; Hong The starting point of the -Choi formula is that the more known information, the more satisfied the decision maker's requirements. These two formulas cannot deal with the same scoring value, and ignore the impact of unknown information on decision-making.

(5) Steps for sensitivity analysis of index attribute value changes: In the case of changes in the index attribute value of a single river-lake water system connectivity scheme, use the primary selected Vague set scoring function model to calculate the evaluation value of the river-lake water system connectivity project scheme; based on the cloud model, The comprehensive evaluation value of the initially selected Vague set scoring function model is used as sample data to generate parameter tables and cloud diagrams.

Sensitivity analysis of indicator attribute value changes:

Sensitivity analysis of index attribute values is to consider only the changes in the evaluation index attribute values of one river-lake water system connectivity project each time, and keep the other evaluation index attribute values unchanged, and calculate the ranking changes of each plan to determine the value that keeps the optimal plan unchanged interval. Introduce cloud model theory to analyze single-index sensitivity analysis, the detailed process is as follows:

(1) Assume that the possible value range of the evaluation index r′ ₁₁ of the river-lake water system connectivity project scheme is (0, r″), and the value range after normalization of the index is within [0, 1].

(2) Assign an initial value r ₀ to r′ ₁₁ , generally r ₀ =0.01, and the step size is determined to be Δr=0.01.

(3) Other index attribute values remain unchanged, and the comprehensive evaluation value of each river and lake water system connectivity project scheme is calculated by using the primary Vague set scoring function model.

(4) Let r′ ₁₁ →r′ ₁₁ +Δr, repeat step (3) until r′ ₁₁ =r″.

(5) Repeat the above steps, and sequentially count the comprehensive evaluation values of the river and lake water system connectivity project schemes in the entire value range where the attribute values of other indicators change.

(6) Based on the comprehensive evaluation value of each river and lake water system connectivity engineering scheme under the condition of changing index attribute values as sample data, the cloud model (E _x , _{E n} , He ), and then generate a cloud map.

For the P1, P2 and P3 water system connectivity engineering schemes, on the basis of the standardization of the attribute values of the decision-making indicators of the engineering schemes, the possible value range of all indicators is set to be 0.01-1.0. In order to make the robustness of the decision-making results of P1, P2 and P3 schemes under different scoring function methods more intuitive, under the comprehensive evaluation methods of seven scoring functions, the comprehensive evaluation value of the scheme under index changes is the sample data, and through the reverse cloud And the cloud models (E _x , _{E n} , He ) of each scheme of forward cloud computing, the results are shown in Table 5, and the generated normal cloud diagrams are shown in Figures 2 to 8.

Table 5 Cloud models of various schemes under the comprehensive evaluation method of different formulas under the change of index value

(6) The steps of the sensitivity analysis of index weight value changes: in the case that the weight values of multiple indexes change at the same time, the evaluation value of the river-lake water system connectivity project scheme is calculated by using the primary selected Vague set scoring function model. Based on the cloud model, the parameter table and cloud map are generated by using the comprehensive evaluation value of the primary selected Vague set scoring function model as sample data.

The specific steps of the sensitivity analysis of simultaneous changes in index weight values are as follows:

(1) Assign an initial value ω ₀ to ω ₁ , generally take ω ₀ =0.01.

(2) Use a computer to generate a set of random weights ω ₂ , ω ₃ , ..., ω _j , ..., ω _y , satisfying that the sum of the weights is 1-ω ₀ , forming a set of random weights W ₁ ={ω ₀ , ω ₂ , ω ₃ , ..., ω _j , ...., ω _y }.

(3) According to the random weight set obtained above, the comprehensive evaluation value of each river and lake water system connectivity project scheme is calculated by using the scoring function model of the primary Vague set.

(4) Change ω ₁ =ω ₁ +ω ₀ , and then repeat the above steps (2)~(3) until ω ₁ =1, then the matrix set of comprehensive evaluation values for each river and lake system connectivity project scheme can be obtained.

(5) Similarly, analyze the sensitivity of ω ₂ , ω ₃ , ..., ω _j , ..., ω _y respectively.

(6) According to the comprehensive evaluation value of ω ₁ , ω ₂ , ω ₃ ,..., ω _j ,..., ω _y for the connection engineering schemes of rivers and lakes, use it as the sample data of the cloud model to generate the parameter table and cloud map .

When analyzing the sensitivity of index weight changes, assuming that the index attribute values of each plan remain unchanged, the decision results of Chen-Tan formula, Hong-Choi formula, Xu Changlin formula, Li Peng formula, Gao Jianwei formula, Wang Wanjun formula, Peng Zhansheng formula, etc. For analysis, take all the comprehensive evaluation values of the three schemes under the weight change as samples, and obtain cloud models with different scoring functions. The parameters are shown in Table 6, and the distribution is shown in Figures 9 to 15.

Table 6 The cloud model of each scheme under the comprehensive evaluation method of different formulas under the change of weight value

(7) Steps for selecting the best plan: compare the robustness of different Vague set scoring functions to the decision-making results of river-lake water system connectivity projects, select the Vague set scoring function with the best robustness in decision-making results, and use the most robustness The evaluation result of the best Vague set scoring function is taken as the final result.

The sensitivity of the decision-making results of the engineering scheme can be analyzed from the following two aspects by using the cloud model parameters and the cloud map:

(1) Under the comprehensive evaluation method of a Vague set scoring function, horizontally compare the ranking stability among the alternative engineering schemes. First, sort according to the expected Ex of the schemes. The greater the expectation, the better the stability; if the expected _{Ex is the} same , the smaller the entropy Entropy E _n (that is, the better the stability), the better the sorting stability. If the expected _{Ex and entropy E n are the} same, the smaller the hyper-entropy He (ie, the smaller the randomness), the better the sorting stability .

(2) When it is difficult to determine the robustness of a certain scoring function by using the above-mentioned horizontal comparison, and then compare the stability of the decision-making results between the comprehensive evaluation methods of the scoring functions of each vague set according to the cloud map vertically, if the cloud distribution of the optimal scheme is different from that of other schemes The less overlap, the more robust the decision results obtained by the method.

The sensitivity analysis of index attribute value changes is as follows:

It can be seen from Table 6 that: in the case of changes in various indicators, 1) According to the calculation of the comprehensive evaluation value results based on the Chen-Tang formula, Hong-Choi formula, Li Peng formula and Peng Zhansheng formula, the expectation of the P3 scheme is the highest, followed by the P2 scheme, and the P1 scheme The expectation is the lowest, and the entropy and hyper-entropy of the three schemes are not much different, which shows that the three schemes maintain their expected stability. The expectation is not much different, the expectation of the P1 scheme is the lowest, and the entropy and super-entropy of the P3 and P1 schemes are not much different, which shows that the two schemes maintain their expected stability. The entropy and hyper-entropy of the P2 scheme are much lower than the other two schemes. It shows that the P2 scheme is more robust to keep expectations stable; 3) According to the analysis of the calculation results of Gao Jianwei's formula, the P3 scheme has the highest expectation, the P2 scheme takes the second place, and the P1 scheme has the lowest expectation. The entropy of the P1 and P2 schemes is similar, and the P3 scheme has a slightly higher entropy , which shows that the P1 and P2 schemes have higher expected stability values than P3, and the three schemes have similar hyperentropy, indicating that the randomness is similar; 4) According to the calculation results of Wang Wanjun's formula, the P2 scheme has the highest expectation, and the P1 and P3 schemes have similar expected values , the entropy and hyper-entropy of the P2 and P3 schemes are not much different, indicating that the stability of the two schemes is similar to maintaining the expectation, and the entropy and hyper-entropy of the P1 scheme are higher than the other two schemes, indicating that the stability of the P1 scheme is poor.

In order to analyze the results more intuitively, the cloud model distributions of the comprehensive evaluation values calculated by different methods are shown in Figures 2 to 8. It can be seen from the 7 cloud diagrams:

1) According to the five formulas of Chen-Tang formula, Hong-Choi formula, Li Peng formula, Peng Zhansheng formula, Gao Jianwei formula and other formulas, the three schemes maintain their expected stability almost the same, and the comprehensive evaluation value of P1 scheme and P3 scheme is almost no The overlapping part shows that the ranking of the P1 scheme and the P3 scheme is stable. The robustness of the P3 scheme is better than that of the P1 scheme. The comprehensive evaluation values of the P2 scheme and the P1 scheme and the P3 scheme have a certain overlap. The overlap between the P2 scheme and the P3 scheme is smaller than the overlap with the P1 scheme, and the overlap between the P2 scheme and the P1 scheme is less than the overlap with the P3 scheme calculated by Li Peng's formula, and the overlapping ratio of the P2 scheme with the P1 and P3 schemes is calculated by the other three formulas Almost equal, but the overlap of the Chen-Tan formula is larger than that of Gao Jianwei's and Peng Zhansheng's formulas.

2) According to the analysis of the comprehensive evaluation results calculated by Xu Changlin's formula, the P2 scheme overlaps almost all of the P1 and P3 schemes, and the overlap between the P1 scheme and the P3 scheme is relatively large, which shows that the ranking of the P1 scheme, P2 scheme and P3 scheme is unstable and prone to occurrence Changes; According to the analysis of the comprehensive evaluation results calculated by Wang Wanjun's formula, the P2, P3 and P1 schemes completely overlap, and the P2 and P3 schemes also almost completely overlap, which also shows that the ranking of the three schemes is unstable and prone to change.

The weight sensitivity analysis is as follows:

From the analysis of Table 7 and Figures 9 to 15, in the case of changes in index weight values,

1) According to the Chen-Tan formula, the expectation of the P3 scheme is slightly higher than that of the P2 scheme, the expectations of the P2 and P3 schemes are much higher than the P1 scheme, and the entropy of the P3 scheme and the P2 scheme is lower than that of the P1 scheme, indicating that the P3 scheme and the P2 scheme are stable is higher than that of the P1 scheme, but the hyper-entropy of the P2 scheme and P3 scheme is lower than that of P1, indicating that these two schemes are more random. It can be seen from the cloud map that the overlapping parts of the three schemes are relatively large, so the ranking of the three schemes is not very stable;

2) From the Hong-Choi formula, the P3 scheme has the highest expectation, followed by the P2 scheme, and the P1 scheme has the lowest expectation. From the analysis of entropy and hyperentropy, the stability and robustness of the P3 scheme is higher than that of the P1 and P2 schemes. It can be seen that the overlapping parts of the three schemes are large, and the ranking of the three schemes is not particularly stable;

3) According to the analysis of comprehensive evaluation results of Xu Changlin formula, Li Peng formula, and Wang Wanjun formula, the expectations of P2 scheme and P3 scheme are close, and the entropy and hyper-entropy are also very close. The expectation of P1 scheme is much lower than that of P2 scheme and P3 scheme. The value is higher than the P2 scheme and the P3 scheme, indicating that the P1 scheme is more unstable. Since the sample standard deviation value is smaller than the entropy value, the hyper-entropy is a complex number, indicating that its randomness is not large. It can be seen from the cloud map that the P2 scheme and the P3 scheme overlap There are many parts, and the order of the two is unstable;

4) Judging from Gao Jianwei's formula and Peng Zhansheng's formula, the expectations of the P3 and P2 schemes are much higher than the expectations of P1, and the entropy of the P2 and P3 schemes is less than that of the P1 scheme, indicating that the P2 and P3 schemes are more stable than the P1 scheme, and the P1 hyper-entropy is lower than that of the P1 scheme. The P2 and P3 schemes indicate that the expectation of P1 is relatively stable. From the cloud map, it can be seen that the overlapping parts of the P2 and P3 schemes are large, indicating that the ranking of the P2 and P3 schemes is unstable, and the overlap between the P1 scheme and the P2 and P3 schemes is small.

Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention without limitation, although the present invention has been described in detail with reference to the preferred arrangement scheme, those of ordinary skill in the art should understand that the technical solution of the present invention (such as The selection of models, the use of various formulas, the sequence of steps, etc.) can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention.

Claims (1)

1. a river and lake water system connectivity engineering scheme optimization model sensitivity analysis method, is characterized in that, the steps of described method are as follows: Steps to establish the index system: through literature research, field investigation and evaluation, and according to the resource-society-economy-ecology-environment-engineering model, establish the principles for establishing the index system, construct an evaluation index system for the connection scheme of rivers and lakes, and divide the indicators into Qualitative and quantitative indicators and determine their values; Steps to establish the combined weighting method: select multiple subjective weighting methods and multiple objective weighting methods, and process the weights calculated by the selected subjective and objective weighting methods according to the probability statistics method to obtain the subjective weight vector and the objective weight vector, and The combination of the two establishes the combined weighting method of the evaluation indicators of the river and lake water system connectivity scheme, and calculates the weight value of each indicator. The specific process is as follows: Weighting of evaluation indicators for river and lake water system connectivity schemes: respectively select p subjective weighting methods and q objective weighting methods to weight the evaluation indicators of river and lake water system connectivity schemes, and subjective weight vectors ω ₁ , ω ₂ ,..., ω _p and objective weight vectors ω _{p +1} , ω _{p +2} , ..., ω _p+q , where ω _i = ( ω _{1 i} , ω _{2 i} , ..., ω _ni ) ^T ; Group the weight vectors of the evaluation indicators of the river and lake water system connectivity schemes: p subjective weight vectors and q objective weight vectors of the river and lake water system connectivity evaluation indicators are respectively used as a sample of uniformly distributed random variables, and their expected values are calculated and normalized, respectively Get the subjective weight vector and the objective weight vector ; Based on subjective weight vector and the objective weight vector Calculate the combined weight ω of the evaluation index of the river and lake water system connectivity scheme, the calculation formula is as follows, where with The probabilities of are taken as a and b respectively: The a and b coefficients are calculated by constructing an optimization model: the objective function is that the deviation between the combined weight vector and the original subjective and objective weight vectors should be as small as possible, as follows: The above optimization model can be solved by using MATLAB, and can be a , b and ω; Steps to determine the Vague value: Calculate the relative membership degree of each index, including true membership degree, false membership degree and unknown Degree, so as to determine the Vague value of each river and lake water system connectivity project scheme, the relative degree of membership is calculated as follows: Assuming that the decision matrix of the river-lake system connectivity project is X ={ x _ij }, x _ij represents the i -th index attribute value of the j -th scheme, i =1, 2, ..., m ; j =1, 2, ... , n ; Transform the decision matrix X into a relative membership degree matrix μ ={ μ _ij } _{m × n} , and define the support index set, neutral index set and opposition index set of the scheme according to the matrix μ : If μ _ij ≥ λ ^U , then the i -th index is satisfied with the j -th scheme, or the j -th scheme supports the i -th index i =1, 2,..., m ; j =1, 2,..., n ; If μ _ij ≤ λ ^L , then the i -th index is dissatisfied with the j -th plan, or the j -th plan is against the i -th index i =1, 2,..., m ; j =1, 2,... , n ; If λ ^L ≤ μ _ij ≤ λ ^U , then the i -th index is neutral to the j -th plan, or the j -th plan does not support or oppose the i -th index i =1, 2, ..., m ; j =1 , 2,..., n ; Let the weight vector of the index be ω=(ω ₁ , ω ₂ ,...,ω _m ), for any project x _j ∈ X of river-lake water system connectivity project, the degree of meeting the requirements on m indicators can be expressed by a Vague value , that is, v _j =[ t ( x _j ), 1- f ( x _j )], where t ( x _j ) is equal to the sum of corresponding weights of indicators in the support index set of scheme x _j ; f ( x _j ) is equal to scheme The sum of the corresponding weights of the indicators in the objection indicator set of x _j ; The steps of preliminary selection of the Vague set scoring function model: Based on the Vague value of each river and lake water system connectivity project plan, select multiple Vague set scoring function models to calculate the evaluation value of the plan, and use the voting model and the principles of the Vague set scoring function model to analyze each scoring function model The rationality of the model is used to select the model and eliminate the unreasonable model; The steps of the sensitivity analysis of index attribute value changes: In the case of changes in the index attribute values of a single river-lake water system connectivity scheme, use the initially selected Vague set scoring function model to calculate the evaluation value of the river-lake water system connectivity engineering scheme; based on the cloud model, the preliminary selection The comprehensive evaluation value of the Vague set scoring function model is used as sample data to generate parameter tables and cloud diagrams; Sensitivity analysis process of indicator attribute value change: Assumed river and lake system connectivity project evaluation index The possible value range of is (0, r ″), and the value range after normalization of the indicator is within [0, 1]; Give Assign the initial value r ₀ , take r ₀ =0.01, and determine the step size as Δ r =0.01; The attribute values of other indicators remain unchanged, and the comprehensive evaluation value of each river and lake system connectivity project scheme is calculated by using the primary Vague set scoring function model; make , repeating "other index attribute values remain unchanged, and the comprehensive evaluation value of each river and lake water system connectivity project is calculated using the primary Vague set scoring function model" until ; Repeat the above steps, and count the comprehensive evaluation values of the river and lake water system connectivity project schemes in the entire value interval of the change of other index attribute values in turn; Based on the comprehensive evaluation value of each river and lake water system connectivity project scheme under the condition of changing index attribute values as sample data, the cloud model E _x , E _n , He of each river and lake water system connectivity project scheme is obtained through the reverse cloud _, and then the cloud map is generated ; The steps of index weight value sensitivity analysis: when the weight values of multiple indexes change at the same time, use the preliminary selected Vague set scoring function model to calculate the evaluation value of the river and lake water system connectivity project; based on the cloud model, the primary selected Vague set The comprehensive evaluation value of the scoring function model is used as sample data to generate parameter tables and cloud images; the specific process of simultaneous change sensitivity analysis of multiple weights is as follows: Assign initial value ω ₀ to ω ₁ , take ω ₀ =0.01; Use a computer to generate a set of random weights ω ₂ , ω ₃ ,..., ω _j ,..., ω _y , satisfying that the sum of the weights is 1- ω ₀ , forming a set of random weights W ₁ ={ ω ₀ , ω ₂ , ω ₃ ,……, ω _j ,……., ω _y }; According to the random weight set obtained above, the comprehensive evaluation value of each river and lake water system connectivity project scheme is calculated by using the primary selection Vague set scoring function model; Change ω ₁ = ω ₁ + ω ₀ , and then repeat the above "using computer to generate a group of random weights ω ₂ , ω ₃ ,..., ω _j ,..., ω _y , satisfying that the sum of the weights is 1— ω ₀ , forming A set of random weight sets W ₁ ={ ω ₀ , ω ₂ , ω ₃ ,..., ω _j ,..., ω _y }" to "According to the random weight set obtained above, use the primary selection of the Vague set scoring function model to calculate The comprehensive evaluation value of each river and lake water system connectivity engineering scheme", until ω ₁ =1, the comprehensive evaluation value matrix set of each river and lake water system connectivity engineering scheme can be obtained; Analyze the sensitivity of ω ₂ , ω ₃ ,..., ω _j ,..., ω _y respectively; According to the comprehensive evaluation value of ω ₁ , ω ₂ , ω ₃ ,..., ω _j ,..., ω _y for the connection engineering scheme of each river and lake system, use it as the sample data of the cloud model to generate the parameter table and cloud map; Steps for selecting the best plan: compare the robustness of different Vague set scoring functions to the decision-making results of the river and lake water system connectivity project, select the Vague set scoring function with the best The evaluation result of the set scoring function is taken as the final result.