It can be divided into subjective, objective, and a combination of subjective and objective methods.
1 Common subjective empowerment methods
In general, the subjective weighting method is mainly based on the knowledge experience or preference of decision makers and experts when determining the weight, and compares the indicators according to their importance, assigns weights or calculates their weights. It believes that the essence of weights is the evaluation index. Quantitative reflection of the relative importance of the evaluation target. Such methods are relatively subjective and arbitrary, but the ranking of index weights is basically in line with the actual situation of the evaluation object. At present, the commonly used subjective weighting methods can be classified into four categories: expert estimation method, analytic hierarchy process, binomial coefficient method, and ring-comparison scoring method.
(1) Expert estimation method
The expert estimation method is based on the experts in the relevant field subjectively judge the importance of each indicator based on their own experience and knowledge, and the final weight distribution value of the indicator can be directly obtained by the average of the weight values independently given by K experts [1] , or Use the frequency statistics method to determine the weight, that is, for each indicator, the K weight distribution values are grouped according to a certain group distance, and the frequency of the weight in each group is calculated. The group median value of the group with the largest frequency is the final value of the corresponding indicator. weight value [ 2 ].
As early as 1986, F. Shands et al. [ 3 ] used the expert estimation method to determine the index weight of the teacher performance evaluation system, and submitted the evaluation index to several field experts in the form of a questionnaire for two rounds of scoring to assign the weight, and finally got The performance evaluation model of the school has achieved good results in the actual application of the school. In the past two years, Chinese scholar Liu Lu et al. [ 4 ] also used this method in the determination of index weights for energy-saving evaluation of heating systems. The weights of each index were determined by the average value of the weight coefficients given by many experts in the field, and compared with Comparing the comprehensive evaluation results of the analytic hierarchy process and the coefficient of variation method, the results show that the expert estimation method is most consistent with the actual system operation. This is mainly because there are many realistic influencing factors in the operation of the heat source system, and the experts will be relatively comprehensive. These factors are thus assigned weights more reasonably.
The advantages of the expert estimation method are mainly reflected in three aspects: first, to make full use of the experience and knowledge of experts, and to comprehensively consider various external factors based on expert experience, and the reliability of the method is high; second, the calculation of index weights is based on the traditional It is mainly descriptive statistics, such as calculating the mean value and statistical frequency, which is simple and direct; third, it is not limited by whether there is sample data, and can make probabilistic estimates for a large number of non-technical indicators that cannot be quantitatively analyzed. This method also has certain defects: first, the distribution of weights is completely affected by expert experience and knowledge, and different expert composition may produce different evaluation results, which has a large degree of subjective randomness; second, when there are many indicators, It is not easy to ensure the consistency of the judgment and thinking process, and it is difficult to be objective and reasonable.
Generally speaking, this method has a wide range of applications and is suitable for various evaluation systems with a moderate number of indicators, especially for those practical problems where there is no sample data and it is difficult to establish a mathematical model.
(2) Analytic Hierarchy Process
The basic idea of AHP is to decompose the indicators of complex problems into several orderly hierarchical structures according to the mutual affiliation relationship. The internal indicators of each layer are compared by experts in the field according to a certain ratio scale. Subjective judgment is quantified to form a judgment matrix, and then mathematical methods are used to calculate the weight value of each indicator in each layer of judgment matrix relative to the previous layer, and finally the total level of hierarchy is sorted to calculate the weight coefficient of all indicators relative to the total target[5 ] . At present, there are more than 20 methods for calculating the index weight coefficients in the judgment matrix, including eigenvector method, least square method, square root method, linear programming method, etc. There are certain differences in the order of index weight determined by different methods.
Analytic Hierarchy Process is widely used in the determination of index weights in various evaluation systems. For example, as early as the last century, R. Shen et al. [ 6 ] used this method to evaluate the labor force intensity in the industry. The judgment matrix was obtained by synthesizing the quantitative evaluation of the relative importance of indicators by dozens of experts in the field, and then using the eigenvector The index weight is calculated by the method, and passed the consistency test, and the evaluation model constructed has achieved good results in practical application. Chinese scholars such as Chu Cunkun [ 7 ] applied it to the three-level evaluation index system of the subject service model of university libraries based on qualitative indicators, and achieved good evaluation results.
The advantages of AHP are mainly reflected in three aspects: first, it quantifies the qualitative judgment of decision makers based on subjective experience knowledge, organically combines qualitative analysis and quantitative analysis, and gives full play to the advantages of both. On the other hand, through objective deduction and accurate calculation, the decision-making process has a strong scientific nature, so that the decision-making results have high credibility; the second is to classify complex evaluation problems into levels It can be decomposed to form a hierarchical hierarchical structure, which makes the evaluation of complex problems clearer, clearer, and hierarchical; third, it is not limited by whether there is sample data, and can solve practical problems that cannot be handled by traditional optimization techniques. However, this method also has certain limitations. First, the determination of index weights mainly depends on expert experience and knowledge. Different experts’ choices may lead to differences in weight distribution results, which are subjective and uncertain. Second, hierarchical analysis The judgment matrix of the method is prone to serious inconsistencies. When there are many indicators on the same layer, and because the nine-level ratio scaling method is difficult to accurately grasp, decision makers can easily make contradictory and confusing relative importance judgments. In response to this problem, Ma Nongle et al. [ 8 ] proposed to use the three-level scaling method to replace the nine-level scaling method to construct the judgment matrix, which is easier to measure the importance of indicators and does not require consistency testing; but the result of this The weight distribution of each indicator is concentrated, and it is easy to have the situation that the weights of multiple indicators are difficult to distinguish.
In general, AHP has a wide range of applications, and is especially suitable for evaluation systems with a moderate number of indicators that lack sample data, have complex evaluation target structures, and domain experts have a clear understanding of the relative importance of indicators.
(3) Binomial coefficient method
The basic idea of the binomial coefficient method is to firstly compare the importance of n indicators independently by K experts, and obtain the index values of each index representing the priority order through the double cycle ratio and statistical processing, and then according to the size of the index value Arrange the indicators in order from the middle to both sides to form an indicator priority sequence, and renumber the indicators in the sequence from left to right to obtain the indicator sequence
, so that according to the principle of the binomial coefficient, the weight distribution value of the th indicator is .
The binomial coefficient method used to determine the index weight was originally proposed by Chinese scholar Cheng Mingxi in 1983, and it has been widely used in China. For example, Zhao Shuli used the method in the multi-index evaluation of laboratory equipment investment in the early stage. Firstly, the priority of each index is determined by the average score of each index by several experts, and then the weight of each index is calculated according to the binomial expansion coefficient. in accordance with. In recent years, Liu Fuqiang et al. [ 11 ] have used it to determine the index weights of factors affecting the excavation period of pumping storage projects. Due to the large number of influencing factors of pumping storage projects, it is difficult to subjectively quantify the relative weight values of the factors, so relying on domain experts Directly judge the priority of indicators, and then use the binomial coefficient to calculate the weight. The final evaluation result of the influencing factors is consistent with the evaluation result using the entropy weight method.
The advantages of the binomial coefficient method mainly include four aspects: first, it organically combines qualitative analysis with quantitative calculation, quantifies subjective experience knowledge, and increases the scientificity and rationality of the evaluation process; second, it does not need to determine the importance of indicators For specific quantification, it is only necessary to judge the relative size of the indicators, which is relatively easy for experts to judge and will not produce contradictory and confusing judgments; the third is to use the binomial expansion for weight calculation, which is simple and easy to operate; The limitation of sample data can solve practical problems that cannot be handled by traditional optimization techniques. However, this method also has certain defects: first, the determination of the weight mainly depends on the subjective judgment of experts’ experience and knowledge, which has randomness and uncertainty; second, when using the binomial coefficient formula to calculate the weight of indicators with different priorities In the case of the same weight, the weight values calculated by the two symmetrical indicators in the indicator priority sequence will be the same, and there will be a certain deviation from the actual situation; the third is that this method only pays attention to the level order of the importance of the indicators, and does not pay attention to the indicators. The degree of difference in the relative importance between them, the weight distribution will be biased.
In general, this method has no restrictions on whether there is sample data, and has a wide range of applications, especially for those multi-factor evaluation problems with a moderate number of indicators that lack precedent and lack of quantitative weighting experience.
(4) Ring-to-ring scoring method
The basic idea of the ring-comparison scoring method is to compare the importance of the index with the next adjacent index in sequence based on the experience and knowledge of the experts, and determine the importance ratio between the adjacent indexes based on the judgment of multiple experts, and then take the last index as the benchmark , reversely calculate the comparison weight of each index, and further normalize to obtain the weight of each index.
The ring-comparison scoring method was first proposed by Chinese scholar Lu Mingsheng in 1986, and has been widely used at home and abroad. For example, Chen Zhigang used this method in the evaluation of Shanghai’s innovative city stage, relying on experts to determine the ring ratio value of the evaluation indicators, and then corrected and normalized to obtain the index weights. The final evaluation results were consistent with the actual situation of Shanghai at that time. Development matches. J. Xie et al. also adopted this method when evaluating highway emergency plans. First, experts compare the indicators from top to bottom to determine their importance, and then perform benchmarking and normalization to obtain weights. The evaluation results are consistent with realistic choices. Consistent with the effectiveness of the method.
The advantages of the ring-comparison scoring method are mainly reflected in four aspects: first, the organic combination of qualitative judgment and quantitative calculation makes the evaluation process more organized and scientific; The process is relatively simple; the third is to determine the relative importance of indicators one-way in sequence, which is not easy to cause conflicts in judgment, and does not need to carry out the consistency test in AHP, which can effectively solve complex decision-making problems; fourth, it is not affected by whether there are samples The limitation of data can solve practical problems that cannot be handled by traditional optimization techniques. However, this method also has certain defects: first, it requires high expert knowledge, and requires experts to have a clear understanding of the importance of evaluation indicators and to conduct accurate quantitative comparisons for each pair of adjacent indicators, otherwise it is easy to use The weight distribution of the entire index system produces large deviations; second, the determination of weights mainly depends on subjective experience and knowledge, which has great uncertainty and subjective arbitrariness.
In general, this method has no restrictions on whether there is sample data, and has a wide range of applications, especially for various evaluation problems that can make more accurate quantitative judgments on the relative importance of adjacent evaluation indicators.
2 Common objective empowerment methods
The objective weighting method relies on certain mathematical theories and determines the weight of indicators based entirely on the quantitative analysis of the actual data of the indicators, which ensures the absolute objectivity of the weights and has higher requirements for the sample data. However, the objective weighting method ignores subjective information such as human experience, and there may be a phenomenon that the weight distribution result is contrary to the actual situation, and it depends on the actual business field and lacks versatility. At present, the main objective weighting methods are: variation coefficient method, multivariate statistical method based on principal component analysis and factor analysis, vector similarity method, gray relational degree method, entropy value method, rough set method and neural network method.
(1) Variation coefficient method
The idea of the coefficient of variation method is to determine the weight of the index by calculating the degree of difference in the measured data of each index. If the internal data of the index is more different, the greater the role of the index in distinguishing the evaluation object, the greater the weight distribution value. large [ 15 ]. The mathematical theory on which the coefficient of variation method is based on determining the weight mainly includes standard deviation and dispersion maximization, that is, through the calculation and normalization of the standard deviation (maximum deviation) of the internal data of each index, the weight distribution of each index is obtained.
The coefficient of variation method is widely used in the weighting of the index system. For example, Shi Shixin et al. [ 16 ] used this method in the evaluation of the benefits of small watershed governance. Through the dimensionless processing of the index sample data and the calculation of the standard deviation of the data , the index weight is obtained through normalization processing, and the evaluation results obtained by relying on this evaluation model can objectively reflect the actual situation. In recent years, H. Zheng et al. [ 17 ] used it in the determination of the weight of wind farm economic operation evaluation indicators. First, the consistency and dimensionless processing of a large number of sample data of the actual operation and monitoring of wind farms in the past ten years, Then the weight is determined by calculating the standard deviation of each index data, and the effectiveness of the evaluation system is verified based on the evaluation and comparison of the three wind farms.
The advantages of the coefficient of variation method are reflected in three aspects: first, the calculation method of the index weight is relatively simple, convenient and practical; second, the full use of sample data objectively reflects the size of the discrimination ability of each index, ensuring the absolute objectivity of the index weight; This method has no limit to the number of evaluation indicators and has a wide range of applications. However, this method also has certain defects: First, the evaluation results are highly correlated with the selection of data samples, and different data samples may produce different weight distribution results. When the sample size is small and not universal, The accuracy of the method will be very low; second, it has no ability to solve the outliers in the sample data. If there are outliers, the method will have a large error in determining the weight; third, it cannot reflect the internal relationship of the indicators. It only analyzes and judges each index separately; the fourth is purely objective calculation, which cannot reflect the understanding of decision makers on the importance of the index.
Therefore, this method is suitable for the comprehensive evaluation where the independence between evaluation indicators is strong, the sample data of the indicators is universal, relatively complete and the sample size is large, and there are no outliers in the sample data.
(2) Multivariate statistical method
Multivariate statistical method refers to the method of using multivariate statistical analysis to calculate sample data to determine the weight of indicators, including principal component analysis and factor analysis.
1) Principal Component Analysis
The basic principle of principal component analysis is to use the idea of dimensionality reduction to convert a group of indicators with certain correlation into another group of irrelevant few comprehensive indicators, namely principal components, according to the variance contribution rate of indicators, and further The normalization process gets the weight of each index.
The principal component analysis method has been widely used since its appearance. For example, the early Chinese scholar Jin Xingri used this method in the comprehensive evaluation of the economic benefits of industrial enterprises. Through the analysis of the sample data of the main economic benefit indicators of Yanbian General Factory from 1990 to 1995 After standardization and principal component analysis, four principal components and the weight of each index are obtained to determine the evaluation model, and the final evaluation result is consistent with the evaluation by the ideal solution. In the past two years, B. Prado et al. [ 20 ] used this method when assessing the climate variables of the city of Minnes, Germany. Through the principal component analysis of the relevant sample data from 2008 to 2012, a principal component was used to explain the overall Variable evaluation model, the evaluation results are consistent with the actual situation.
The advantages of principal component analysis are mainly reflected in three aspects: first, it replaces more correlation indicators with fewer independent indicators, which solves the problem of information overlap between indicators and simplifies the indicator structure; second, the weight of indicators is Relying on objective data, it is calculated and determined by the variance contribution rate of each principal component, which avoids the influence of subjective factors and is more objective and reasonable; third, there are no specific restrictions on the number of indicators and samples, and the scope of application is wide. However, this method also has four defects: first, the calculation process of index weight is relatively complicated, and the result of weight determination has a great correlation with the selection of samples; second, certain sample data information is lost, and some indicators with practical significance are in the This method may be eliminated, which may cause deviations from the actual situation; third, it assumes that the indicators are linearly related, and many non-linear relationship index systems in practical problems will produce deviations when using this method; fourth, rely purely on objective data to determine Weight, ignoring subjective experience and knowledge, the evaluation results may be contrary to the actual situation.
In general, the principal component analysis method is suitable for determining the weight of indicators in a complex evaluation system where the sample data is relatively complete and representative, and there is a certain correlation between indicators and the relationship between indicators is basically linear.
2) Factor Analysis
The basic idea of factor analysis method [ 21 ] is similar to that of principal component analysis method. It also transforms the relevant indicators into a few irrelevant indicators, and then determines the index weight according to the variance contribution rate of each factor. The difference is that the principal component analysis method linearly combines the original indicators, while the factor analysis method splits the original indicators into common factors and special factors unique to each indicator to linearly represent, and the factor representation has a more clear actual meaning.
Factor analysis is widely used in various comprehensive evaluation problems, especially in the evaluation and analysis of related issues in the field of social economy. For example, Wan Jianqiang, an early Chinese scholar, used this method in the evaluation of the operating performance of listed companies. Through standardization and factor analysis of the 1999 annual report data of 13 representative listed companies in the building materials industry, the first four have explanations. The independent comprehensive factors of significance replace the original 11 indicators for comprehensive evaluation, and the evaluation results are consistent with the actual economic rankings of each enterprise. In the past two years, A. Bai et al. used it in the evaluation of national economic rankings, used the IMF data set to conduct factor analysis on 15 economic indicators in 20 countries, and used 3 comprehensive factors to explain and represent all indicators and conduct Comprehensive evaluation, the final calculated ranking is almost consistent with that provided by the world ranking, confirming the feasibility of the method.
The advantages and disadvantages of the factor analysis method in determining the index weight are similar to those of the principal component analysis method, but the number of factors is smaller than the original index number, and the number of principal components can be equal to the original index number, so the missing information of the factor analysis method is generally More than the principal component analysis method, its accuracy is generally not as good as the principal component analysis method, and the calculation process is more complicated, and the factor analysis method strictly requires that there be correlations between the indicators of the evaluation system. However, the factor analysis method can clearly explain the specific content of the original indicators, can explain the reasons for the correlation between indicators, and can have a deeper understanding of the content of the indicators.
In general, the factor analysis method is more suitable for complex evaluation problems that require in-depth analysis of social and economic phenomena and other related evaluation objects, where there is a large correlation between indicators, and a large number of representative and complete data samples.
3) Vector similarity method
The basic principle of the vector similarity method is to use the feature vector composed of the sample data of each index and the reference vector composed of the ideal values of all indexes to solve the similarity, and the vector similarity reflects the contribution of each index to the best performance of the system degree, and normalize it to get the weight of each index.
The vector similarity method used to determine the index weight was first proposed by Chinese scholar Jiao Liming et al. [ 24 ], and was subsequently applied to comprehensive evaluation by many scholars in China. For example, Jiao Liming et al. [ 25 ] used this method to evaluate the effectiveness of the air defense brigade system, extracted 6 groups of representative sample data, processed the data dimensionlessly, and calculated the data vector of each index and the standardized The similarity of the ideal reference vector is further normalized to obtain the weight of each index, which effectively evaluates the system performance. Xie Ping[ 26 ] used it to evaluate the eutrophication of lakes, took the measured water quality data of 30 lakes across the country as data samples, and made the vector composed of the sample data of each evaluation index and the ideal reference vector of all levels of indicators dimensionless The vector similarity is calculated, and the index weight is obtained through normalization processing. The evaluation results are highly consistent with the previous evaluation results using fuzzy methods, random methods, etc.
The advantages of the vector similarity method are mainly reflected in three aspects: First, the calculation is simple and easy to operate. The similarity calculation is performed on the vector composed of the index data vector and the ideal value of all indexes, and the ideal reference vector composed of all indexes is cleverly used to pass the dimensionless After conversion, it becomes a unit vector with all element values of 1, which is the same as the ideal value of the same index and the similarity of the data solution of this index, which reduces the number of calculations; second, the result is easy to understand, and the method takes into account the optimal solution. The relationship between them has strong practicability; the third is to make full use of the sample data, without the interference of human factors, and has strong objectivity; the fourth is that there is no specific limit on the number of indicators and sample size, and the scope of application is wide. But at the same time, this method also has certain defects: first, the accuracy of the method will be affected by the data samples, and when the sample size is small and not representative, the accuracy of the evaluation results of this method will be very low; The problem of duplication of information caused by the correlation of different factors can easily cause the weight of some related indicators to become larger due to repeated calculations; the third is to use objective data for weight calculations, ignoring subjective experience and knowledge, which may lead to situations that are contrary to reality .
In general, this method is more suitable for a comprehensive evaluation system that has an appropriate amount of relatively complete sample data, and the sample data is typical and representative, and the evaluation indicators are relatively independent.
4) Gray relational degree method
The basic idea of the gray relational degree method is to combine the data comparison with the trend of the geometric curve to calculate the weight, that is, to use the degree of correlation between each plan and the optimal plan to determine the index weight. Specifically, the method calculates the contribution of each index to the optimal performance of the entire system through the gray correlation judgment matrix and correlation coefficient of each plan and the ideal plan, and further normalizes to obtain the index weight.
Gray relational degree analysis is widely used in practical decision-making problems in many disciplines. As early as the 1980s, Chinese scholar Ma Zhiying and others used this method in the evaluation of cotton varieties. Taking the trait data of 7 cotton varieties in the cotton disease-resistant area of the Yellow River Basin in 1986 as samples, the data were dimensionless. After processing, the gray correlation coefficient between each variety and the ideal variety is calculated, and the weight of each index is obtained through normalization processing. The final evaluation result is consistent with the result of fuzzy comprehensive evaluation. Later, C.Ho [ 29 ] used it in the evaluation of bank operating performance. The data samples were the financial documents of three Taiwan banks, and the index weight was calculated by using similar steps as Ma Zhiying et al. [ 28 ], and based on this An evaluation model is established to evaluate the three banks, and the evaluation results are consistent with the analysis results of the financial statements, which shows the effectiveness of the method.
The advantages of the gray relational degree analysis method are mainly reflected in four aspects: first, the calculation process of the method is relatively simple, considering the relationship with the ideal decision-making scheme, the results are intuitive and easy to understand; second, there is no need for a large number of samples, only a small number of representative Only a single data sample is sufficient, and there is no limit to the number of indicators; third, the method has a certain degree of fault tolerance, because the calculation of the correlation degree uses the maximum difference and the minimum difference between the two poles, so that some data are partially missing or human error. The resulting data inaccuracy problem can be weakened, making the analysis results relatively reasonable; Fourth, relying on sample data for weight calculation, avoiding the interference of human factors, and strong objectivity. This method also has certain defects: first, the value of the resolution coefficient when calculating the gray correlation coefficient is determined subjectively by humans, and there is no fixed standard, and the difference in value will affect the final weight distribution and reduce the credibility; second, The accuracy of the method will be affected by the samples, and different sample selections may lead to differences in the final evaluation results; third, the method cannot solve the problem of information overlap caused by the correlation between indicators; fourth, it does not consider subjective experience knowledge, and the evaluation results may be different. contrary to the actual situation.
In general, this method has a wide range of applications, and there is no limit to the number of indicators and samples. It is more suitable for a comprehensive evaluation system with relatively complete sample data, representative and typical samples, and relatively independent indicators.
5) Entropy method
The basic idea of the entropy value method is to reflect the degree of discrimination of the index to the evaluation object from the perspective of the degree of disorder of the index, that is, the index entropy. The smaller the entropy value of an index, the more orderly the sample data of the index. The greater the difference, the greater the ability to distinguish the evaluation object, and the greater the corresponding weight. This method first calculates the entropy value of each index according to the entropy value function, and then normalizes the entropy value into index weight.
Since the entropy method was proposed, it has been widely used in the evaluation of problems in many fields. For example, in the early days, Zhu Shunquan et al. [ 31 ] used this method to evaluate the financial status of listed companies. Taking the data of 15 evaluation indicators of 20 companies in the "China Securities Journal" in 2000 as a sample, the data were first dimensionless After processing, calculate the entropy value of each index and further normalize the weight of the index, and obtain the comprehensive evaluation value of each company after simple weighting, and the evaluation result is reasonable. Later, A.Gorgij et al. [ 32 ] also used this method in the assessment of groundwater quality. In 2016, 21 groundwater samples in Iran's Azashah Plain were sampled and evaluated for water quality, and calculated by a similar entropy method The first step is to calculate the weight of each index, and further use the comprehensive evaluation model to evaluate the water quality level of each sample. The evaluation result is consistent with the evaluation of the spatial autocorrelation coefficient.
The entropy value method has three advantages in determining the index weight: first, the calculation process of the method is relatively simple, and the index weight is determined from the perspective of the degree of distinction between the index and the evaluation object, the result is intuitive and easy to understand, and the method is practical; Relying on sample data for weight calculation avoids the interference of subjective factors and has strong objectivity; third, the method has no limit on the number of indicators and has a wide range of applications. However, this method also has three shortcomings: first, the accuracy of the method will be affected by the data samples, and different sample selections may produce different weight distribution results, and there are high requirements for the completeness of the sample data and sample size; First, it cannot reflect the correlation between indicators and cannot solve the problem of information overlap; third, it cannot reflect the understanding of decision makers on the importance of each indicator, which may be contrary to the facts to a certain extent.
Therefore, this method is more suitable for a relatively independent comprehensive evaluation system among indicators with large sample size, complete sample data information and universality.
6) Rough set method
The basic idea of using the rough set method to determine the index weight is to first classify the evaluation objects according to all the indexes in the system, reduce one index at a time, and consider the change degree of the reduced object classification compared with the original classification, the index is important Sex is directly proportional to the degree of change. The concept of the importance of attributes (indicators) in rough set can be attributed to the definition of algebraic representation and the definition of information representation, and further derives a variety of subdivision weighting methods based on the ideas of the equivalence relationship, superiority relationship and tolerance relationship of indicators . The difference between the rough set weighting method from the perspective of index equivalence relationship, dominance relationship and tolerance relationship mainly lies in the different standards on which the object classification is based. The evaluation object is divided according to the degree of superiority in the conditional attribute set, and the tolerance relationship is divided according to the degree of difference between the objects. The equivalence relationship requires the data to be processed to be discrete, while the data in the dominance relationship can be continuous, while the tolerance relationship is mainly used to deal with the absence of sample data.
The rough set method is widely used in the determination of index weights for various evaluation problems. For example, IP.WC, etc. used this method in the evaluation of water quality, taking the water quality measured data in April and May of the Han River Basin from 1992 to 1997 as For the sample of the conditional attribute set, the equal-weighted summed average of each index value in each time period is used as the decision attribute. First, the sample data is discretized, and then the importance of each index is calculated based on the algebraic rough set method of the equivalence relationship. The index weights obtained through normalization processing, the final calculated water quality comprehensive evaluation grades in each time period are in line with the actual situation. Zou Bin et al. used it to evaluate energy consumption in East China, and took the energy consumption data of 8 provinces (cities) in East China in the 2011 China Energy Statistical Yearbook as a sample to divide the dominant categories on the attribute set (no need to discretize the sample data ), and calculate the weight of each index according to the definition of algebraic attribute importance, the evaluation result is consistent with the result of the gray relational degree weighting method, which is reasonable and reliable.
The advantages of the rough set method in index weighting are mainly reflected in five aspects: First, it can handle a wide range of data types, including discrete data and continuous data. Second, it has strong fault tolerance, can handle missing sample data, and effectively solves the problem of weighting under data loss; third, the importance of information representation can make up for the weight of indicators in the importance of algebraic representation The defect that may be 0 improves the accuracy of the method; fourth, the method has no limit on the number of indicators, and has a wide range of applications; fifth, it completely relies on objective data for weight calculation, avoiding the interference of subjective factors. However, this method also has certain defects: first, the accuracy of the method will be affected by the data samples, and different sample selections may produce different decision-making results; second, it cannot solve the problem of information overlap caused by the correlation between indicators; third, it does not Objective weighting requires prior information, and the calculated results may contradict the understanding of the decision maker.
In general, the rough set method is the most widely used in the objective weighting method, and it is suitable for multi-attribute decision-making problems where the data samples are universal and the indicators with a large sample size are relatively independent.
7) Neural network method
The most commonly used neural network method is the BP neural network algorithm. The basic idea of weighting [ 36 ] is to carry out nonlinear parallel learning training on a large number of data samples according to a certain learning mechanism, and specifically to output data according to the accuracy requirements of the error. Continuous iterative adjustment of the difference with the known sample output data to obtain the connection weight matrix between the input layer and the hidden layer that meets the requirements, and sum the absolute value of the connection weights from each input layer node to all hidden layer nodes. The weight of the indicator is obtained by normalization.
The neural network method is currently being used more and more in the determination of index weights. For example, J. Ch et al. [ 37 ] used this method in the evaluation of e-government websites in the early stage, taking the correlation of 20 e-government websites in Ningbo City The data is used as a training sample (11 evaluation indicators and expert evaluation results are used as specific sample data), the weight of each index is calculated through training, and the evaluation model is used in the evaluation of another 10 e-government websites. The evaluation results are compared with the expert evaluation. unanimous. Later, S. Silva et al. [ 38 ] used this method to evaluate the stability of extra virgin olive oil. The training samples consisted of 18 kinds of extra virgin olive oil stored under dark and light conditions (including 11 evaluation indicators and The evaluation results obtained from the experimental data), the weights of each index were calculated by training, and the evaluation model was used in the evaluation of 10 groups of olive oil stability outside the training samples. The consistency between the evaluation results and the test classification shown in the experiment was greater than 90%, indicating that This method has higher accuracy.
The advantages of the neural network method are mainly reflected in three aspects: first, it can deal with nonlinear complex system evaluation problems, and can perform dynamic evaluation, and has a powerful function for system analysis and processing; second, through the learning and training of samples, it can obtain The relative importance information of the indicators is reasonable, scientific and practical after actual testing, which ensures the objectivity and practicability of the indicator weights; thirdly, there is no limit to the number of evaluation indicators, and the application range is very wide. However, this method also has certain defects: first, it is completely based on training samples, so it has high requirements for samples. The bigger the better), the reliability of the results can be guaranteed; to a certain extent, subjective experience knowledge is ignored, and the evaluation results may be contrary to the subjective preferences of decision makers.
In short, the neural network method has a strong ability to deal with the evaluation of complex systems, and is more suitable for determining the weight of indicators in various complex systems with a large amount of sample data and a wide coverage, and the indicators are relatively independent.
3 Common comprehensive integrated empowerment methods
The comprehensive integrated weighting method is a comprehensive method to determine the index weight by combining the subjective weighting method and the objective weighting method according to different preference coefficients. Based on the information representation of expert experience knowledge and the subjective intention of decision makers in the subjective weighting method, and based on the information representation of the internal relationship between indicators and evaluation objects in the objective weighting method, the comprehensive integrated weighting method combines the two through certain mathematical operations. They are effectively combined to achieve the effect of complementary advantages. At present, there are many forms of comprehensive integration weighting methods based on different principles, but they can be roughly classified into four categories, namely the comprehensive integration weighting method based on addition or multiplication synthesis normalization, and the comprehensive integration weighting method based on the sum of squared deviations. Weighting method, comprehensive integrated weighting method based on game theory, comprehensive integrated weighting method based on goal optimization.
The comprehensive integration weighting method based on addition or multiplication synthesis and normalization is to directly add or multiply the index weights obtained by the subjective and objective weighting methods in the form of the same preference, and perform normalization processing to obtain the comprehensive weight of each index. Weights. For example, in supply chain risk assessment, L. Yang et al. used this method to multiply the subjective weight determined by the AHP and the objective weight determined by the coefficient of variation method, and then normalized to obtain the comprehensive weight of each index. The evaluation results With higher precision.
The comprehensive integrated weighting method based on the sum of squared deviations is to solve the problem that can make the comprehensive evaluation value of the decision-making program as dispersed as possible, that is, the total sum of squared deviations between the comprehensive evaluation values of each program is the largest Subjective and objective weight distribution coefficient. For example, B. Meng et al. used this method in bank credit risk assessment, and calculated the optimal adjustment coefficient of subjective and objective weights according to the principle of maximizing the square sum of the overall deviation of the evaluation values of different objects by the subjective and objective weighting method. The comprehensive weight of each index is obtained through chemical analysis, and the evaluation result has higher accuracy than the subjective and objective single weighting method.
The comprehensive integrated weighting method based on game theory is to seek a compromise or consistency between different subjective and objective weights, to keep the original information of subjective and objective weights as much as possible, and to solve the weight distribution coefficient that minimizes the deviation from subjective and objective weights. For example, C. Lu et al. [ 41 ] used the idea of this method to calculate the subjective weight of the indicators determined by the AHP and the objective weight determined by the coefficient of variation method in the evaluation of the development level of educational informatization, and then normalized The comprehensive integration weight of each index is obtained through the process of simplification, and the model has achieved good results in the evaluation of the development level of educational informatization in schools in 11 areas of Suzhou.
The comprehensive integrated weighting method based on objective optimization is based on the principle of optimal comprehensive decision-making results to solve the distribution of subjective and objective weight coefficients, including two specific solving methods: the maximum comprehensive target value and the maximum deviation from the negative ideal solution. For example, in the evaluation of learning cities, J. Yan et al. calculated and assigned the subjective and objective weight coefficients based on the principle of maximizing the overall comprehensive evaluation value based on the subjective weight of the indicators obtained by the expert estimation method and the objective weight obtained by the entropy method. , and based on this model, the four learning cities are evaluated more accurately.
In short, all kinds of comprehensive weighting methods have a certain theoretical basis, and solve them specifically through mathematical ideas such as linear equations and matrix operations. Some methods are simple to integrate and calculate, while others bring relatively large calculations to the evaluation process. However, there is no absolute difference between the methods, and there is no consistent conclusion on which comprehensive weighting method to choose for which evaluation problem in practical applications. In addition, compared with the subjective and objective weighting methods, the evaluation results obtained by the comprehensive weighting method are relatively more scientific and reasonable, but there may also be large random deviations, which may cause the results to be inconsistent with the actual situation, and it cannot completely replace the single weighting method. It is necessary to have a rational understanding when choosing the method of empowerment in the research of practical problems.
Excerpted from: Liu Qiuyan, Wu Xinnian. Review on the Method of Determining Index Weights in Multi-factor Evaluation [J]. Knowledge Management Forum, 2017, 2(06): 500-510. DOI: 10.13266/j.issn.2095-5472.2017.054.