# Application of Neural Network Sample Training Algorithm in Regional Economic Management

Authors: Yan He
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In order to solve the limitations of the traditional method of determining expert weights in AHP and improve the level of the regional economy, this paper proposes a neural network algorithm based on AHP. This paper first calculates the interest correlation coefficient among experts, then obtains the comprehensive evaluation value of all experts according to the evaluation value matrix, and then determines the evaluation weight of each expert in the expert group. Finally, the comprehensive weight of each index is obtained by weighting the index weight obtained from the traditional AHP and the expert evaluation weight. Then, the evaluation value obtained by the improved AHP is used as a prior sample to train and test the BP neural network, and a classifier that can be popularized is obtained. The experimental results show that the overall evaluation value of circular economy of 9 construction enterprises is at a medium level, only 2 enterprises have an evaluation value of more than 50, and one enterprise has an evaluation value of only 35, indicating that the overall implementation of circular economy of these 9 construction enterprises is still at a low level, with great room for development and improvement.Conclusion. The economic management method based on a neural network algorithm can make the evaluation results more accurate and reliable and has high popularization and application value.


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## Body

## 1. Introduction

With the increasingly severe situation of resource shortage, the circular economy has attracted more and more attention from all walks of life. It has become one of the effective models to alleviate the contradiction between resource shortage and economic development and achieve sustainable development. With the continuous development of computer technology and scientists’ in-depth research on human brain science, it will play an important role to use a neural network to imitate human thinking to deal with problems in economic management [1]. The neural network is a complex dynamic system. The future development direction of the artificial neural network is to connect neural network with traditional technology, reduce its complexity and make it easy to understand and operate, as shown in Figure 1. Using an artificial neural network to deal with the scientific prediction and optimal decision-making of economic management has broad prospects for development. The application and development of the artificial neural network method in the field of economic management is mainly reflected in the expansion of the application field and the combination with other economic management research methods. As an important force to promote the rapid development of the national economy, the development level of its circular economy determines the sustainable development ability of China’s economy to a certain extent [2]. The artificial neural network method is suitable for dealing with nonlinear mapping relations, nonlinear simulation computing ability, self-learning, and self-organization functions, which makes it have a wide range of adaptability and capacity. It has unique advantages in dealing with qualitative indicators and hierarchical relationship variables. When combined with other quantitative analysis methods, the application range of the artificial neural network method is broader. Therefore, an in-depth study on the development of economic management and evaluation of its development status is of great significance to improve the efficiency of the circular economy of construction enterprises and the development level of the circular economy in China.Figure 1
Neural network sample training.


## 2. Literature Review

The background of neural network research can be traced back to the end of the 19th century and the interdisciplinary research on physics, psychology, and neurophysiology at the beginning of the 20th century [3]. These early studies systematically analyzed the general theories of learning, sensation, and reflex based on biological neural networks but did not make a mathematical generalization of the working mechanism of biological neurons. After Khalimon and others proposed the analytic hierarchy process (AHP) in 1980, Chinese and foreign scholars have carried out a series of studies using this method, and the results are quite rich. Due to the strong subjectivity of this method, scholars have also improved and innovated on the basis of AHP [4]. In foreign studies, Ma and others took an information technology service industry as an example and combined fuzzy logic theory with AHP to evaluate the importance of each component of human capital [5]. Vizzaccaro and others corrected the AHP by determining the expert evaluation weight through the projection method and obtained a good improvement effect [6]. Bakshi and others used the improved AHP for natural disaster assessment. Their innovation is mainly reflected in that they do not directly construct a judgment matrix based on expert scores but obtain a judgment matrix by comparing it with the highest score of the index set in advance, avoiding the subjectivity of the assessment to a certain extent [7]. Xu and others combined fuzzy AHP with the fuzzy TOPSIS method to evaluate the quality of medical services and concluded that medical services should be improved from the aspects of specialization, interactivity, and service accuracy [8]. Blanco-Urrejola and others studied the location of solar energy in a region by calculating the weights of various indicators in combination with GIS and AHP [9]. In terms of research on the evaluation of the circular economy, there are mainly lifecycle assessment (LCA), energy analysis, materials flow analysis (MFA), ecological footprint, comprehensive evaluation methods, etc. Qian and others used the life cycle method to evaluate building energy, providing effective information for decision makers to make energy repair decisions [10]. Kuo and others studied the material circulation mode of the French copper industry through the dynamic material flow analysis model, focusing on the impact of the economic system, resource consumption, product manufacturing, and waste generation on pollution [11]. Bradha and others used the ecological footprint method to evaluate the existing resource protection policies. The sensitivity analysis of the calculation results shows that the ecological footprint method has a good ability to evaluate the negative impact of policies [12]. Boboshko and others used the emergy analysis method to accumulate the total input of raw materials, labor, and resources through emergy equivalents and evaluated the resource utilization and transfer efficiency in the industrial ecological economy [13]. On the basis of current research, this paper proposes a method based on an improved AHP-BP neural network algorithm. Firstly, the interest correlation coefficient among experts is calculated, then the comprehensive evaluation value of all experts is obtained according to the evaluation value matrix, and then the evaluation weight of each expert in the expert group is determined. Finally, the comprehensive weight of each index is obtained by the weighted average of the index weight obtained from the traditional AHP and the expert evaluation weight. Then, the evaluation value obtained by the improved AHP is used as a prior sample to train and test the BP neural network, and a classifier that can be popularized is obtained. It is of great significance to improve the circular economy efficiency of construction enterprises and the development level of the circular economy.


## 3. Research Methods

### 3.1. Improved AHP Method Based on Stakeholder Perspective

The traditional AHP method scores the evaluation objects by multiple experts and then simply takes the mean value of the score to build a judgment matrix to calculate the weight of indicators at all levels. However, when there is an interesting relationship between experts and the evaluation object, they will strive for more say by improving their own advantages and suppressing competitors, resulting in the loss of fairness in the calculation of index weights [14]. Therefore, based on the perspective of stakeholders, this paper proposes an improved AHP method to give different weights to experts who may score as common stakeholders and potential competitors, and then weighted average the index weights obtained from their scores to obtain the comprehensive weights of each index, making the weight calculation more fair.


#### 3.1.1. Calculate Expert Evaluation Weight Based on Stakeholder Perspective

In the multi-index evaluation system composed ofN experts o1, o2, …, on and selected M indexes x1, x2, …, xm, setij = xj(oi) (i = 1, 2, …, n, j = 1, 2, …, m) as the value of expert oi under the index xj. The evaluation data matrix can be expressed as follows:(1)A=xijn×m=x11x12⋯x1mx21x22⋯x2m⋯⋯⋯⋯xn1xn2⋯xnm.Without losing generality, assume thatM indicators are extremely large (benefit type), and assume that the data in a is the normalized data. It can be seen from the evaluation data matrix A that the closer the values of the evaluation indicators (row vectors in matrix A) given by the two experts are, the more likely they are to have common interests.


#### 3.1.2. BP Neural Network Model

This paper adopts BP neural network, which is a multilayer feedforward neural network. The conversion function of its neurons is a nonlinear sigmoid function. In this paper,f(x) = 1/(1 + e − x) function is used. The basic idea of the BP neural network is to minimize the sum of squares of errors in the output layer of the network by adjusting the weights and thresholds of the network so that the output value is as close to the target value as possible.The learning process of the BP neural network is the process of constantly changing weights and thresholds to minimize the error value [15].The specific steps of the improved AHP-BP neural network algorithm in the evaluation of circular economy are shown in Figure2.(1)
Establish the evaluation index system of circular economy and collect data(2)
Data preprocessing, dividing the data into the training set and test set(3)
Calculate the evaluation weight of each expert based on the perspective of stakeholders(4)
Calculate the weight of each index of AHP by using the scores of each expert(5)
Weighted average of the expert evaluation weight and AHP index weight obtained in steps (3) and (4) to calculate the comprehensive weight of each index(6)
The evaluation value of the circular economy is obtained by multiplying the index data of the evaluation object and the comprehensive weight of the index(7)
Taking the results obtained in step (6) as input, the BP neural network model is trained with training set samples(8)
The BP neural network model is used to verify the test set samples and analyze the results, which is popularized and appliedFigure 2
Steps of improving AHP-BP neural network algorithm.


### 3.2. Case Study

#### 3.2.1. Index Data of Circular Economy

Before training the neural network, this paper first standardized the sample data to eliminate the dimensional influence. When the larger the index value is, the better the evaluation is, the data standardization method adopted is:x∗=0.1+xi−ximin/ximax−ximin×0.9; when the smaller the index value, the better the evaluation, the data standardization method adopted is: x=0.1+ximax−xi/xmax−ximn×0.9. x∗ represents the standardized value of index xi, ximin represents the minimum value of the i-th index, and ximaxrepresents the maximum value of the i-th index [16].See Table1 for the dimensionless index data after processing the original data.Table 1
Sample data of circular economy evaluation indicators of construction enterprises.
Number/index12345678910U110.10.4130.7470.7420.5840.7550.90.8820.8720.893U120.10.1460.2320.2540.2670.3930.5660.6860.8620.9U130.1290.I0.2080.2310.2820.3660.5120.7170.8540.9U140.5410.7340.90.2490.1940.10.1720.2720.2660.437U210.480.6860.480.4170.3930.10.1160.3740.3980.9U220.1110.10.2040.2440.2710.4640.5300.8070.7730.9U230.1070.10.1940.230.260.4320.5320.8750.7690.9U240.1270.1250.1890.10.2360.3170.1880.90.7480.800U310.10.1610.1530.2270.3540.560.6780.8610.6680.9U320.2090.330.3240.4530.580.3360.450.90.3370.1U330.130.I0.4060.5070.490.7980.7770.90.5960.612U340.2200.8480.8380.3740.4520.4750.10.90.8710.795U350.2450.I0.6300.3840.2950.630.90.5540.5240.429U360.1970.1960.10.2820.2370.3630.610.5170.7270.9U370.4040.5210.10.2680.3810.5210.6990.3080.5250.9U410.10.3690.7240.7260.5140.7020.90.6790.8540.801U420.1150.1250.1450.10.1960.2530.4450.5850.7470.9U430.2220.3120.4830.4340.3270.10.90.8840.8160.874U440.1690.2650.4580.2020.350.4180.90.320.3010.1U450.1090.10.3350.4860.4040.8090.7920.90.6970.772U460.5970.90.7790.3610.4770.3810.8430.10.3580.222U470.3250.6390.5410.10.6670.6160.6680.6960.7190.9U510.6070.740.90.1060.10.5550.5910.6970.4380.516U520.10.5410.740.3210.3790.3820.8860.4850.7480.534U530.4860.90.5390.3650.4140.8380.1840.3450.6690.612


#### 3.2.2. Calculation of AHP Index Weight

For the evaluation index, compare the scores of experts in pairs to obtain the index judgment matrix of each expert at all levels. Taking one expert as an example, the judgment matrix of the first level index is(2)U=113153531135751317913151713151719131.The approximate eigenvectors of the judgment matrix are [0.156, 0.322, 0.413, 0.066, 0.043], as shown in Table2.(3)λmax=∑i=1n∑j=1naim¨winwi=5.0634,CI=λmax−nn−1=0.01268,RI=CICR=0.012681.12=0.0113<0.10.Table 2
Normalization and eigenvector of a primary index judgment matrix.
Criterion layerU judgment matrixU1U2U3U4U5Sum of linesW¯iFeature vectorWi=W¯i/∑​j=1nW¯iU10.1050.1660.1120.1840.2000.7670.156U20.3150.4980.1860.3060.2801.5850.322U30.5240.1660.5600.4290.3602.0390.413U40.0350.1000.0800.0610.1200.3240.066U50.0210.0700.0620.0200.0400.2130.043The consistency ratio is less than 0.10. Through the consistency test, the expert’s AHP level-1 index weightwi can be obtained. Similarly, the AHP level-1 index weight of the other 9 experts can be obtained.By weighted averaging the AHP primary index weight and its evaluation weight of the above-given 10 experts, the primary index weight of the index system can be obtained asu = (0.12, 0.31, 0.38, 0.11, 0.08). According to the same method, the secondary index weight can be obtained, and then the comprehensive weight can be determined [17].After calculation, the overall ranking of the comprehensive evaluation hierarchy has passed the overall consistency test. It can be considered that the index weights at all levels are reasonable and effective, and the comprehensive weights of the indicators at all levels of the evaluation index system can be obtained.Comprehensive evaluation results of circular economy of construction enterprises. Calculate through the formulaY = W × X, where y is the evaluation result vector; W is the weight vector of 25 evaluation indexes; X is the dimensionless sample data [18]. Therefore, the circular economy evaluation value of 59 construction enterprises is [0.1738, 0.2256, 0.3168, 0.4059, 0.3445, 0.3510, 0.4962, 0.6077, 0.6891, 0.6606, 0.7608, 0.2096, 0.319, 0.4018, 0.4923, 0.4528, 0.4486, 0.5857, 0.6903, .7191, 0.7359, 0.7972, 0.6597, 0.7608, 0.2126, 0.3148, 0.3985, 0.4904, 0.4376, 0.4502, 0.5820, 0.8002, 0.6597, 0.7608, 0.5807, 0.6943, 0.7191, 0.7400, 0.7972, 0.6591, 0.7608, 0.2107, 0.3237, 0.3927, 0.5014, 0.4535, 0.5872, 0.7958, 0.7608, 0.5835, 0.5608, 0.4835, 0.3881, 0.5370, 0.4941, 0.4990, 0.4559, 0.4634, 0.4128].


#### 3.2.3. Establishment of BP Neural Network Model

(1) Determine Network Hierarchy. Any given continuous function Φ = X ⟶ Y, X ∈ Rn, Y∈[0, 1]n, then Φ can be accurately implemented by a three-layer network. Therefore, the BP neural network constructed in this paper has three layers, including input layer, middle hidden layer, and output layer.(2) Determine the Number of Network Output Input Nodes. In this paper, the number of nodes n in the input layer of the BP neural network is the same as the number of evaluation indicators, i.e., 25; the output of the BP neural network is the evaluation value of circular economy for construction enterprises, so the number of nodes in the output layer is m = 1.(3) Determine the Number of Hidden Layer Neurons. At present, there is no clear theoretical basis for how to determine the number of hidden layer nodes. It is generally believed that too few hidden layer elements will lead to insufficient fitting, and too many will lead to overfitting and reduce the generalization of the network [19]. The following methods are usually used to determine the number of hidden layer nodes j: j=m+n+a;j=log2n;j=mn. Where n is the number of input nodes, M is the number of output nodes, and a is a constant between 1 and 10. Based on experience, j = 10 is selected in this paper.(4) Training Sample Data. The first 50 of the sample data of 59 construction enterprises are selected as the training set, that is, the input vector X = [X1, X2, …, X50]T. The circular economy evaluation value of construction enterprises numbered 1–50 obtained by the improved AHP method in the sample is used as the output target value of the neural network, that is, the target output vector t training = [t1, t2, …, t50]T, t test = [t51, t67, …, t59]T, and then the BP neural network is created through the Matlab toolbox and trained.(5) Parameter Setting of Training Function. Select “TRAINRP” for training function; the adaptive function is “LEARNGDM,” the executive function is “MSE,” the transfer function is “LOGSIG,” the number of neurons is “10,” and the training accuracy is e = 0.00001; training times N = 10000 (default values are selected for other parameters).(6) Training Results. The training results show that after 10 steps of training, the square sum of network training error MSE meets the requirements of target error. The output value of the network after training is very close to the expected value. If the accuracy requirements are met, the network can be used for simulation [20]. According to the above steps, the neural network evaluation test was conducted on 50 construction enterprise samples in the training set, and the relative error of the training results is shown in Table 3.Table 3
Training results of BP neural network.
Sample no12345678910Expected value0.17380.22560.31680.40590.34450.3510.49620.60770.68910.6606Training value0.237480.222030.231140.387590.304150.328260.508220.647750.758980.69606Relative error−0.063680.003570.085660.018310.040350.02274−0.01202−0.04005−0.06988−0.03546Sample No11121314151617181920Expected value0.76080.20960.31960.40180.49230.45280.44860.58570.69030.7191Training value0.774430.2337720.3070.370770.462530.42930.41810.59590.711170.7409Relative error−0.01363−0.024170.01260.031030.029770.02350.0305−0.0102−0.02087−0.0218Sample No21222324252627282930Expected value0.73590.79720.65970.76080.21260.31480.39850.49040.43760.4502Training value0.775730.82620.670360.771760.256210.340430.45360.478150.422230.4739Relative error−0.03983−0.029−0.01066−0.01096−0.04361−0.02563−0.05510.012250.01537−0.0237Sample no31323334353637383940Expected value0.5820.80020.65970.76080.58070.69430.71910.740.79720.6591Training value0.549040.833520.66670.784860.595680.648580.730670.787831.00030.70266Relative error0.03296−0.03332−0.007−0.02406−0.014980.04572−0.01157−0.04783−0.2031−0.04356Sample no41424344454647484950Expected value0.76080.21070.32370.39270.50140.45350.58720.79580.76080.5835Training value0.775050.224930.345430.466470.472140.470.624170.814850.805760.5976Relative error−0.01425−0.01423−0.02173−0.073770.02926−0.0165−0.03697−0.01905−0.04496−0.0141


## 3.1. Improved AHP Method Based on Stakeholder Perspective

The traditional AHP method scores the evaluation objects by multiple experts and then simply takes the mean value of the score to build a judgment matrix to calculate the weight of indicators at all levels. However, when there is an interesting relationship between experts and the evaluation object, they will strive for more say by improving their own advantages and suppressing competitors, resulting in the loss of fairness in the calculation of index weights [14]. Therefore, based on the perspective of stakeholders, this paper proposes an improved AHP method to give different weights to experts who may score as common stakeholders and potential competitors, and then weighted average the index weights obtained from their scores to obtain the comprehensive weights of each index, making the weight calculation more fair.


### 3.1.1. Calculate Expert Evaluation Weight Based on Stakeholder Perspective

In the multi-index evaluation system composed ofN experts o1, o2, …, on and selected M indexes x1, x2, …, xm, setij = xj(oi) (i = 1, 2, …, n, j = 1, 2, …, m) as the value of expert oi under the index xj. The evaluation data matrix can be expressed as follows:(1)A=xijn×m=x11x12⋯x1mx21x22⋯x2m⋯⋯⋯⋯xn1xn2⋯xnm.Without losing generality, assume thatM indicators are extremely large (benefit type), and assume that the data in a is the normalized data. It can be seen from the evaluation data matrix A that the closer the values of the evaluation indicators (row vectors in matrix A) given by the two experts are, the more likely they are to have common interests.


### 3.1.2. BP Neural Network Model

This paper adopts BP neural network, which is a multilayer feedforward neural network. The conversion function of its neurons is a nonlinear sigmoid function. In this paper,f(x) = 1/(1 + e − x) function is used. The basic idea of the BP neural network is to minimize the sum of squares of errors in the output layer of the network by adjusting the weights and thresholds of the network so that the output value is as close to the target value as possible.The learning process of the BP neural network is the process of constantly changing weights and thresholds to minimize the error value [15].The specific steps of the improved AHP-BP neural network algorithm in the evaluation of circular economy are shown in Figure2.(1)
Establish the evaluation index system of circular economy and collect data(2)
Data preprocessing, dividing the data into the training set and test set(3)
Calculate the evaluation weight of each expert based on the perspective of stakeholders(4)
Calculate the weight of each index of AHP by using the scores of each expert(5)
Weighted average of the expert evaluation weight and AHP index weight obtained in steps (3) and (4) to calculate the comprehensive weight of each index(6)
The evaluation value of the circular economy is obtained by multiplying the index data of the evaluation object and the comprehensive weight of the index(7)
Taking the results obtained in step (6) as input, the BP neural network model is trained with training set samples(8)
The BP neural network model is used to verify the test set samples and analyze the results, which is popularized and appliedFigure 2
Steps of improving AHP-BP neural network algorithm.


## 3.1.1. Calculate Expert Evaluation Weight Based on Stakeholder Perspective

In the multi-index evaluation system composed ofN experts o1, o2, …, on and selected M indexes x1, x2, …, xm, setij = xj(oi) (i = 1, 2, …, n, j = 1, 2, …, m) as the value of expert oi under the index xj. The evaluation data matrix can be expressed as follows:(1)A=xijn×m=x11x12⋯x1mx21x22⋯x2m⋯⋯⋯⋯xn1xn2⋯xnm.Without losing generality, assume thatM indicators are extremely large (benefit type), and assume that the data in a is the normalized data. It can be seen from the evaluation data matrix A that the closer the values of the evaluation indicators (row vectors in matrix A) given by the two experts are, the more likely they are to have common interests.


## 3.1.2. BP Neural Network Model

This paper adopts BP neural network, which is a multilayer feedforward neural network. The conversion function of its neurons is a nonlinear sigmoid function. In this paper,f(x) = 1/(1 + e − x) function is used. The basic idea of the BP neural network is to minimize the sum of squares of errors in the output layer of the network by adjusting the weights and thresholds of the network so that the output value is as close to the target value as possible.The learning process of the BP neural network is the process of constantly changing weights and thresholds to minimize the error value [15].The specific steps of the improved AHP-BP neural network algorithm in the evaluation of circular economy are shown in Figure2.(1)
Establish the evaluation index system of circular economy and collect data(2)
Data preprocessing, dividing the data into the training set and test set(3)
Calculate the evaluation weight of each expert based on the perspective of stakeholders(4)
Calculate the weight of each index of AHP by using the scores of each expert(5)
Weighted average of the expert evaluation weight and AHP index weight obtained in steps (3) and (4) to calculate the comprehensive weight of each index(6)
The evaluation value of the circular economy is obtained by multiplying the index data of the evaluation object and the comprehensive weight of the index(7)
Taking the results obtained in step (6) as input, the BP neural network model is trained with training set samples(8)
The BP neural network model is used to verify the test set samples and analyze the results, which is popularized and appliedFigure 2
Steps of improving AHP-BP neural network algorithm.


## 3.2. Case Study

### 3.2.1. Index Data of Circular Economy

Before training the neural network, this paper first standardized the sample data to eliminate the dimensional influence. When the larger the index value is, the better the evaluation is, the data standardization method adopted is:x∗=0.1+xi−ximin/ximax−ximin×0.9; when the smaller the index value, the better the evaluation, the data standardization method adopted is: x=0.1+ximax−xi/xmax−ximn×0.9. x∗ represents the standardized value of index xi, ximin represents the minimum value of the i-th index, and ximaxrepresents the maximum value of the i-th index [16].See Table1 for the dimensionless index data after processing the original data.Table 1
Sample data of circular economy evaluation indicators of construction enterprises.
Number/index12345678910U110.10.4130.7470.7420.5840.7550.90.8820.8720.893U120.10.1460.2320.2540.2670.3930.5660.6860.8620.9U130.1290.I0.2080.2310.2820.3660.5120.7170.8540.9U140.5410.7340.90.2490.1940.10.1720.2720.2660.437U210.480.6860.480.4170.3930.10.1160.3740.3980.9U220.1110.10.2040.2440.2710.4640.5300.8070.7730.9U230.1070.10.1940.230.260.4320.5320.8750.7690.9U240.1270.1250.1890.10.2360.3170.1880.90.7480.800U310.10.1610.1530.2270.3540.560.6780.8610.6680.9U320.2090.330.3240.4530.580.3360.450.90.3370.1U330.130.I0.4060.5070.490.7980.7770.90.5960.612U340.2200.8480.8380.3740.4520.4750.10.90.8710.795U350.2450.I0.6300.3840.2950.630.90.5540.5240.429U360.1970.1960.10.2820.2370.3630.610.5170.7270.9U370.4040.5210.10.2680.3810.5210.6990.3080.5250.9U410.10.3690.7240.7260.5140.7020.90.6790.8540.801U420.1150.1250.1450.10.1960.2530.4450.5850.7470.9U430.2220.3120.4830.4340.3270.10.90.8840.8160.874U440.1690.2650.4580.2020.350.4180.90.320.3010.1U450.1090.10.3350.4860.4040.8090.7920.90.6970.772U460.5970.90.7790.3610.4770.3810.8430.10.3580.222U470.3250.6390.5410.10.6670.6160.6680.6960.7190.9U510.6070.740.90.1060.10.5550.5910.6970.4380.516U520.10.5410.740.3210.3790.3820.8860.4850.7480.534U530.4860.90.5390.3650.4140.8380.1840.3450.6690.612


### 3.2.2. Calculation of AHP Index Weight

For the evaluation index, compare the scores of experts in pairs to obtain the index judgment matrix of each expert at all levels. Taking one expert as an example, the judgment matrix of the first level index is(2)U=113153531135751317913151713151719131.The approximate eigenvectors of the judgment matrix are [0.156, 0.322, 0.413, 0.066, 0.043], as shown in Table2.(3)λmax=∑i=1n∑j=1naim¨winwi=5.0634,CI=λmax−nn−1=0.01268,RI=CICR=0.012681.12=0.0113<0.10.Table 2
Normalization and eigenvector of a primary index judgment matrix.
Criterion layerU judgment matrixU1U2U3U4U5Sum of linesW¯iFeature vectorWi=W¯i/∑​j=1nW¯iU10.1050.1660.1120.1840.2000.7670.156U20.3150.4980.1860.3060.2801.5850.322U30.5240.1660.5600.4290.3602.0390.413U40.0350.1000.0800.0610.1200.3240.066U50.0210.0700.0620.0200.0400.2130.043The consistency ratio is less than 0.10. Through the consistency test, the expert’s AHP level-1 index weightwi can be obtained. Similarly, the AHP level-1 index weight of the other 9 experts can be obtained.By weighted averaging the AHP primary index weight and its evaluation weight of the above-given 10 experts, the primary index weight of the index system can be obtained asu = (0.12, 0.31, 0.38, 0.11, 0.08). According to the same method, the secondary index weight can be obtained, and then the comprehensive weight can be determined [17].After calculation, the overall ranking of the comprehensive evaluation hierarchy has passed the overall consistency test. It can be considered that the index weights at all levels are reasonable and effective, and the comprehensive weights of the indicators at all levels of the evaluation index system can be obtained.Comprehensive evaluation results of circular economy of construction enterprises. Calculate through the formulaY = W × X, where y is the evaluation result vector; W is the weight vector of 25 evaluation indexes; X is the dimensionless sample data [18]. Therefore, the circular economy evaluation value of 59 construction enterprises is [0.1738, 0.2256, 0.3168, 0.4059, 0.3445, 0.3510, 0.4962, 0.6077, 0.6891, 0.6606, 0.7608, 0.2096, 0.319, 0.4018, 0.4923, 0.4528, 0.4486, 0.5857, 0.6903, .7191, 0.7359, 0.7972, 0.6597, 0.7608, 0.2126, 0.3148, 0.3985, 0.4904, 0.4376, 0.4502, 0.5820, 0.8002, 0.6597, 0.7608, 0.5807, 0.6943, 0.7191, 0.7400, 0.7972, 0.6591, 0.7608, 0.2107, 0.3237, 0.3927, 0.5014, 0.4535, 0.5872, 0.7958, 0.7608, 0.5835, 0.5608, 0.4835, 0.3881, 0.5370, 0.4941, 0.4990, 0.4559, 0.4634, 0.4128].


### 3.2.3. Establishment of BP Neural Network Model

(1) Determine Network Hierarchy. Any given continuous function Φ = X ⟶ Y, X ∈ Rn, Y∈[0, 1]n, then Φ can be accurately implemented by a three-layer network. Therefore, the BP neural network constructed in this paper has three layers, including input layer, middle hidden layer, and output layer.(2) Determine the Number of Network Output Input Nodes. In this paper, the number of nodes n in the input layer of the BP neural network is the same as the number of evaluation indicators, i.e., 25; the output of the BP neural network is the evaluation value of circular economy for construction enterprises, so the number of nodes in the output layer is m = 1.(3) Determine the Number of Hidden Layer Neurons. At present, there is no clear theoretical basis for how to determine the number of hidden layer nodes. It is generally believed that too few hidden layer elements will lead to insufficient fitting, and too many will lead to overfitting and reduce the generalization of the network [19]. The following methods are usually used to determine the number of hidden layer nodes j: j=m+n+a;j=log2n;j=mn. Where n is the number of input nodes, M is the number of output nodes, and a is a constant between 1 and 10. Based on experience, j = 10 is selected in this paper.(4) Training Sample Data. The first 50 of the sample data of 59 construction enterprises are selected as the training set, that is, the input vector X = [X1, X2, …, X50]T. The circular economy evaluation value of construction enterprises numbered 1–50 obtained by the improved AHP method in the sample is used as the output target value of the neural network, that is, the target output vector t training = [t1, t2, …, t50]T, t test = [t51, t67, …, t59]T, and then the BP neural network is created through the Matlab toolbox and trained.(5) Parameter Setting of Training Function. Select “TRAINRP” for training function; the adaptive function is “LEARNGDM,” the executive function is “MSE,” the transfer function is “LOGSIG,” the number of neurons is “10,” and the training accuracy is e = 0.00001; training times N = 10000 (default values are selected for other parameters).(6) Training Results. The training results show that after 10 steps of training, the square sum of network training error MSE meets the requirements of target error. The output value of the network after training is very close to the expected value. If the accuracy requirements are met, the network can be used for simulation [20]. According to the above steps, the neural network evaluation test was conducted on 50 construction enterprise samples in the training set, and the relative error of the training results is shown in Table 3.Table 3
Training results of BP neural network.
Sample no12345678910Expected value0.17380.22560.31680.40590.34450.3510.49620.60770.68910.6606Training value0.237480.222030.231140.387590.304150.328260.508220.647750.758980.69606Relative error−0.063680.003570.085660.018310.040350.02274−0.01202−0.04005−0.06988−0.03546Sample No11121314151617181920Expected value0.76080.20960.31960.40180.49230.45280.44860.58570.69030.7191Training value0.774430.2337720.3070.370770.462530.42930.41810.59590.711170.7409Relative error−0.01363−0.024170.01260.031030.029770.02350.0305−0.0102−0.02087−0.0218Sample No21222324252627282930Expected value0.73590.79720.65970.76080.21260.31480.39850.49040.43760.4502Training value0.775730.82620.670360.771760.256210.340430.45360.478150.422230.4739Relative error−0.03983−0.029−0.01066−0.01096−0.04361−0.02563−0.05510.012250.01537−0.0237Sample no31323334353637383940Expected value0.5820.80020.65970.76080.58070.69430.71910.740.79720.6591Training value0.549040.833520.66670.784860.595680.648580.730670.787831.00030.70266Relative error0.03296−0.03332−0.007−0.02406−0.014980.04572−0.01157−0.04783−0.2031−0.04356Sample no41424344454647484950Expected value0.76080.21070.32370.39270.50140.45350.58720.79580.76080.5835Training value0.775050.224930.345430.466470.472140.470.624170.814850.805760.5976Relative error−0.01425−0.01423−0.02173−0.073770.02926−0.0165−0.03697−0.01905−0.04496−0.0141


## 3.2.1. Index Data of Circular Economy

Before training the neural network, this paper first standardized the sample data to eliminate the dimensional influence. When the larger the index value is, the better the evaluation is, the data standardization method adopted is:x∗=0.1+xi−ximin/ximax−ximin×0.9; when the smaller the index value, the better the evaluation, the data standardization method adopted is: x=0.1+ximax−xi/xmax−ximn×0.9. x∗ represents the standardized value of index xi, ximin represents the minimum value of the i-th index, and ximaxrepresents the maximum value of the i-th index [16].See Table1 for the dimensionless index data after processing the original data.Table 1
Sample data of circular economy evaluation indicators of construction enterprises.
Number/index12345678910U110.10.4130.7470.7420.5840.7550.90.8820.8720.893U120.10.1460.2320.2540.2670.3930.5660.6860.8620.9U130.1290.I0.2080.2310.2820.3660.5120.7170.8540.9U140.5410.7340.90.2490.1940.10.1720.2720.2660.437U210.480.6860.480.4170.3930.10.1160.3740.3980.9U220.1110.10.2040.2440.2710.4640.5300.8070.7730.9U230.1070.10.1940.230.260.4320.5320.8750.7690.9U240.1270.1250.1890.10.2360.3170.1880.90.7480.800U310.10.1610.1530.2270.3540.560.6780.8610.6680.9U320.2090.330.3240.4530.580.3360.450.90.3370.1U330.130.I0.4060.5070.490.7980.7770.90.5960.612U340.2200.8480.8380.3740.4520.4750.10.90.8710.795U350.2450.I0.6300.3840.2950.630.90.5540.5240.429U360.1970.1960.10.2820.2370.3630.610.5170.7270.9U370.4040.5210.10.2680.3810.5210.6990.3080.5250.9U410.10.3690.7240.7260.5140.7020.90.6790.8540.801U420.1150.1250.1450.10.1960.2530.4450.5850.7470.9U430.2220.3120.4830.4340.3270.10.90.8840.8160.874U440.1690.2650.4580.2020.350.4180.90.320.3010.1U450.1090.10.3350.4860.4040.8090.7920.90.6970.772U460.5970.90.7790.3610.4770.3810.8430.10.3580.222U470.3250.6390.5410.10.6670.6160.6680.6960.7190.9U510.6070.740.90.1060.10.5550.5910.6970.4380.516U520.10.5410.740.3210.3790.3820.8860.4850.7480.534U530.4860.90.5390.3650.4140.8380.1840.3450.6690.612


## 3.2.2. Calculation of AHP Index Weight

For the evaluation index, compare the scores of experts in pairs to obtain the index judgment matrix of each expert at all levels. Taking one expert as an example, the judgment matrix of the first level index is(2)U=113153531135751317913151713151719131.The approximate eigenvectors of the judgment matrix are [0.156, 0.322, 0.413, 0.066, 0.043], as shown in Table2.(3)λmax=∑i=1n∑j=1naim¨winwi=5.0634,CI=λmax−nn−1=0.01268,RI=CICR=0.012681.12=0.0113<0.10.Table 2
Normalization and eigenvector of a primary index judgment matrix.
Criterion layerU judgment matrixU1U2U3U4U5Sum of linesW¯iFeature vectorWi=W¯i/∑​j=1nW¯iU10.1050.1660.1120.1840.2000.7670.156U20.3150.4980.1860.3060.2801.5850.322U30.5240.1660.5600.4290.3602.0390.413U40.0350.1000.0800.0610.1200.3240.066U50.0210.0700.0620.0200.0400.2130.043The consistency ratio is less than 0.10. Through the consistency test, the expert’s AHP level-1 index weightwi can be obtained. Similarly, the AHP level-1 index weight of the other 9 experts can be obtained.By weighted averaging the AHP primary index weight and its evaluation weight of the above-given 10 experts, the primary index weight of the index system can be obtained asu = (0.12, 0.31, 0.38, 0.11, 0.08). According to the same method, the secondary index weight can be obtained, and then the comprehensive weight can be determined [17].After calculation, the overall ranking of the comprehensive evaluation hierarchy has passed the overall consistency test. It can be considered that the index weights at all levels are reasonable and effective, and the comprehensive weights of the indicators at all levels of the evaluation index system can be obtained.Comprehensive evaluation results of circular economy of construction enterprises. Calculate through the formulaY = W × X, where y is the evaluation result vector; W is the weight vector of 25 evaluation indexes; X is the dimensionless sample data [18]. Therefore, the circular economy evaluation value of 59 construction enterprises is [0.1738, 0.2256, 0.3168, 0.4059, 0.3445, 0.3510, 0.4962, 0.6077, 0.6891, 0.6606, 0.7608, 0.2096, 0.319, 0.4018, 0.4923, 0.4528, 0.4486, 0.5857, 0.6903, .7191, 0.7359, 0.7972, 0.6597, 0.7608, 0.2126, 0.3148, 0.3985, 0.4904, 0.4376, 0.4502, 0.5820, 0.8002, 0.6597, 0.7608, 0.5807, 0.6943, 0.7191, 0.7400, 0.7972, 0.6591, 0.7608, 0.2107, 0.3237, 0.3927, 0.5014, 0.4535, 0.5872, 0.7958, 0.7608, 0.5835, 0.5608, 0.4835, 0.3881, 0.5370, 0.4941, 0.4990, 0.4559, 0.4634, 0.4128].


## 3.2.3. Establishment of BP Neural Network Model

(1) Determine Network Hierarchy. Any given continuous function Φ = X ⟶ Y, X ∈ Rn, Y∈[0, 1]n, then Φ can be accurately implemented by a three-layer network. Therefore, the BP neural network constructed in this paper has three layers, including input layer, middle hidden layer, and output layer.(2) Determine the Number of Network Output Input Nodes. In this paper, the number of nodes n in the input layer of the BP neural network is the same as the number of evaluation indicators, i.e., 25; the output of the BP neural network is the evaluation value of circular economy for construction enterprises, so the number of nodes in the output layer is m = 1.(3) Determine the Number of Hidden Layer Neurons. At present, there is no clear theoretical basis for how to determine the number of hidden layer nodes. It is generally believed that too few hidden layer elements will lead to insufficient fitting, and too many will lead to overfitting and reduce the generalization of the network [19]. The following methods are usually used to determine the number of hidden layer nodes j: j=m+n+a;j=log2n;j=mn. Where n is the number of input nodes, M is the number of output nodes, and a is a constant between 1 and 10. Based on experience, j = 10 is selected in this paper.(4) Training Sample Data. The first 50 of the sample data of 59 construction enterprises are selected as the training set, that is, the input vector X = [X1, X2, …, X50]T. The circular economy evaluation value of construction enterprises numbered 1–50 obtained by the improved AHP method in the sample is used as the output target value of the neural network, that is, the target output vector t training = [t1, t2, …, t50]T, t test = [t51, t67, …, t59]T, and then the BP neural network is created through the Matlab toolbox and trained.(5) Parameter Setting of Training Function. Select “TRAINRP” for training function; the adaptive function is “LEARNGDM,” the executive function is “MSE,” the transfer function is “LOGSIG,” the number of neurons is “10,” and the training accuracy is e = 0.00001; training times N = 10000 (default values are selected for other parameters).(6) Training Results. The training results show that after 10 steps of training, the square sum of network training error MSE meets the requirements of target error. The output value of the network after training is very close to the expected value. If the accuracy requirements are met, the network can be used for simulation [20]. According to the above steps, the neural network evaluation test was conducted on 50 construction enterprise samples in the training set, and the relative error of the training results is shown in Table 3.Table 3
Training results of BP neural network.
Sample no12345678910Expected value0.17380.22560.31680.40590.34450.3510.49620.60770.68910.6606Training value0.237480.222030.231140.387590.304150.328260.508220.647750.758980.69606Relative error−0.063680.003570.085660.018310.040350.02274−0.01202−0.04005−0.06988−0.03546Sample No11121314151617181920Expected value0.76080.20960.31960.40180.49230.45280.44860.58570.69030.7191Training value0.774430.2337720.3070.370770.462530.42930.41810.59590.711170.7409Relative error−0.01363−0.024170.01260.031030.029770.02350.0305−0.0102−0.02087−0.0218Sample No21222324252627282930Expected value0.73590.79720.65970.76080.21260.31480.39850.49040.43760.4502Training value0.775730.82620.670360.771760.256210.340430.45360.478150.422230.4739Relative error−0.03983−0.029−0.01066−0.01096−0.04361−0.02563−0.05510.012250.01537−0.0237Sample no31323334353637383940Expected value0.5820.80020.65970.76080.58070.69430.71910.740.79720.6591Training value0.549040.833520.66670.784860.595680.648580.730670.787831.00030.70266Relative error0.03296−0.03332−0.007−0.02406−0.014980.04572−0.01157−0.04783−0.2031−0.04356Sample no41424344454647484950Expected value0.76080.21070.32370.39270.50140.45350.58720.79580.76080.5835Training value0.775050.224930.345430.466470.472140.470.624170.814850.805760.5976Relative error−0.01425−0.01423−0.02173−0.073770.02926−0.0165−0.03697−0.01905−0.04496−0.0141


## 4. Result Analysis

Click “Simulate” in the Matlab toolbox and input the index sample data of construction enterprises numbered 51–59. The evaluation results are [0.5200, 0.4457, 0.3538, 0.5398, 0.4815, 0.4776, 0.40945, 0.4477, 0.4610]. Compared with the expected output value, the error is shown in Table4. It can be seen that the maximum relative error between the output value and the expected value obtained by BP neural network simulation is 0.0482, which is completely acceptable in the evaluation of the circular economy. It can be seen that the neural network has high evaluation efficiency and small error and can be popularized and applied in the evaluation of circular economy in construction enterprises in the future. Save the trained neural network. When evaluating the circular economy of other construction enterprises in the future, just input the index data of the enterprise and start the network to obtain the evaluation results.Table 4
Test results of BP neural network.
Number515253545556575859Expected value0.56080.48350.38810.5370.49410.4990.45590.46340.4128Output value0.52000.44570.35380.53980.48150.47760.40950.44770.4610Relative error0.04080.03780.0343−000280.01260.02140.04640.0157−0.0482In order to understand the evaluation results more intuitively, the comprehensive evaluation values of the circular economy obtained from the above simulation are multiplied by 100. The results are shown in Figure3. It can be seen that the overall evaluation value of the circular economy of the nine construction enterprises is at the medium level, only two of them have an evaluation value of more than 50, and one of them has an evaluation value of only 35. Therefore, the implementation of a circular economy in these nine construction enterprises is still at a low level, with great room for development and improvement.Figure 3
Comprehensive evaluation value of circular economy of construction enterprises numbered 51–59.


## 5. Conclusion

This paper creatively puts forward an improved AHP method. Firstly, the expert evaluation weight is calculated from the perspective of stakeholders, and then the AHP weight of each index is obtained according to the scores of each expert, and the comprehensive weight of each index is determined by the weighted average with the evaluation weight of experts, so as to make the weight calculation more reasonable. At the same time, this paper combines the improved AHP method with BP neural network and constructs an evaluation model based on the improved AHP-BP neural network algorithm to achieve complementary advantages. The improved AHP reduces the impact of experts’ subjective factors on the evaluation, and BP neural network effectively improves the convenience of evaluation. Finally, this paper takes the evaluation of the circular economy of construction enterprises as an example to carry out an empirical analysis. The results show that the model not only fully reflects the evaluation opinions of experts but also avoids the conflict of interest between experts and reduces the randomness of subjective evaluation. In addition, the learning ability of the BP neural network model makes the evaluation results more accurate and reliable, which shows that the model constructed in this paper has high popularization and application value.



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*Source: 7666331-2022-08-24.xml*