Dynamic index weight correction method and device for comprehensive evaluation and medium

Abstract

The invention relates to an index weight dynamic correction method and device for comprehensive evaluation and a medium. The method comprises the steps that all indexes needed by the comprehensive evaluation at the initial moment and index values and weight values of all the indexes are obtained; according to the change of the index required at the current moment relative to the index required at the previous moment, constructing a column connection table for representing the change degree of each index; calculating a posterior probability matrix representing the posterior probability of each index through the Bayesian probability based on the concatenation table; correcting the posterior probability matrix through a correction matrix obtained based on a Probit function to obtain a correction probability matrix; performing standard normal correction on the correction probability matrix; and obtaining a weight value of each index at the current moment based on a result after standard normal correction. According to the invention, dynamic correction of the index weight is realized.

Description

Technical Field

[0001] The present invention relates to the field of comprehensive evaluation, and in particular to a method, device and medium for dynamically correcting index weights for comprehensive evaluation. Background Art

[0002] With the rapid development of the big data era, society is facing an unprecedented flood of data. Weight allocation methods have been widely used in many fields. For labeled data, machine learning models can identify key features and automatically adjust weights through feedback mechanisms to optimize the model's predictive performance. This type of method is widely used in classification and regression tasks. Its core is to use known target variables to determine the importance of features and assign corresponding weights accordingly.

[0003] However, in practical applications, it is often difficult to obtain sufficient labeled data, especially in scenarios involving complex multimodal, multidimensional indicator systems and user portraits. For unlabeled or unstructured data, the effectiveness of traditional weight assignment methods based on label feedback is significantly reduced. In such cases, the determination of weights depends more on the intrinsic characteristics and potential laws of the data rather than external label feedback. In addition, although traditional weight determination methods can extract information from the internal structure of the data to a certain extent, they are usually based on static models and are difficult to cope with complex scenarios. In particular, when faced with frequent changes in user behavior and market demand, static models are difficult to adapt to the dynamic changes and complex interactions of data, and thus their long-term effectiveness is limited. Given the comprehensiveness and complexity of the indicator system, the weight of a certain indicator should be adjusted and corrected accordingly with the development of economy and technology. Therefore, it is particularly important to build and develop an efficient, reasonable and universal indicator weight dynamic correction system. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a method, device and medium for dynamically correcting indicator weights for comprehensive evaluation.

[0005] The specific plan is as follows:

[0006] A method for dynamically correcting indicator weights for comprehensive evaluation comprises the following steps:

[0007] S1: Obtain all the indicators required for comprehensive evaluation at the initial moment, as well as the indicator value and weight value of each indicator;

[0008] S2: Based on the change of the required indicators at the current moment relative to the required indicators at the previous moment, a contingency table is constructed to characterize the degree of change of each indicator;

[0009] S3: Based on the contingency table, the posterior probability of each indicator is calculated by Bayesian probability, and then the posterior probability matrix is ​​constructed based on the posterior probabilities of all indicators;

[0010] S4: Correcting the posterior probability matrix by using a correction matrix obtained based on the Probit function to obtain a corrected probability matrix;

[0011] S5: Perform standard normal correction on the corrected probability matrix;

[0012] S6: Based on the results of standard normal correction, the weight value of each indicator at the current moment is obtained.

[0013] Furthermore, all the indicators required at the initial moment in step S1 are obtained by screening all the indicators involved in the comprehensive evaluation, and the screening process is carried out through the rough set theory.

[0014] Furthermore, all indicators in step S1 include indicators of at least two levels; when screening all indicators involved in the comprehensive evaluation, the first-level indicators are screened first, and then all second-level indicators contained in the screened first-level indicators are screened, and so on.

[0015] Furthermore, the weight value of each indicator at the initial moment is obtained by the expert scoring method, that is, after constructing a contingency table to represent the expert evaluation results of each indicator, the influence of each indicator is calculated by a measurement method based on the rank effect value as the standard, and the rank effect value of each indicator is normalized to obtain the weight value of each indicator.

[0016] Furthermore, the method for constructing the contingency table in step S2 is: obtaining the scoring results of multiple experts at the current moment for each indicator required at the current moment; when the indicator did not appear at the previous moment, the expert's scoring result for the indicator at the current moment is the value interval to which the indicator value of the indicator belongs; when the previous moment also includes the indicator, the expert's scoring result for the indicator at the current moment is the change interval of the indicator at the current moment relative to the previous moment; constructing a contingency table based on the scoring results of all experts for each indicator required at the current moment; the rows in the contingency table represent indicators, the columns represent value intervals or change intervals, and the values ​​of the elements in the table represent the number of expert scoring results for the corresponding indicators in all expert scoring results that are corresponding value intervals or change intervals.

[0017] Furthermore, when performing standard normal correction on the corrected probability matrix in step S5, the cumulative distribution function of the standard normal distribution is selected for mapping.

[0018] A terminal device for dynamically correcting indicator weights for comprehensive evaluation includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method described above in the embodiment of the present invention are implemented.

[0019] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described above in an embodiment of the present invention are implemented.

[0020] The present invention adopts the above technical solution, which can realize the reasonable allocation and dynamic correction of weights in an unlabeled situation by analyzing data characteristics and combining changes in external factors. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Shown is a flow chart of a method according to a first embodiment of the present invention. DETAILED DESCRIPTION

[0022] To further illustrate various embodiments, the present invention provides drawings. These drawings are part of the disclosure of the present invention, which are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these contents, ordinary technicians in this field should be able to understand other possible implementations and advantages of the present invention.

[0023] The present invention will now be further described with reference to the accompanying drawings and specific implementation methods.

[0024] Embodiment 1:

[0025] The embodiment of the present invention provides a method for dynamically correcting the weight of indicators for comprehensive evaluation, such as Figure 1 As shown, the method comprises the following steps:

[0026] S1: Obtain all the indicators required for comprehensive evaluation at the initial moment, as well as the indicator value and weight value of each indicator.

[0027] The comprehensive evaluation in this embodiment is explained by taking the comprehensive performance evaluation of Xiamen's high-quality development in 2022 as an example. The method adopted in this embodiment can also be applied to the comprehensive evaluation of other businesses, such as the comprehensive evaluation of users and environment, etc., without limitation. All the indicators required at the initial moment of acquisition can be all the indicators involved in the comprehensive evaluation of the business.

[0028] Furthermore, among all the indicators involved in the comprehensive evaluation, some indicators may be of particularly low importance. If such indicators are taken into consideration, the subsequent results will be affected. Therefore, this embodiment also includes screening all the indicators involved in the comprehensive evaluation to remove the indicators of low importance. In addition, since all indicators may include at least two levels of indicators, when screening indicators, the first-level indicators are first screened, and then all the second-level indicators contained in the first-level indicators obtained by screening are screened, and so on, until the last level of indicators are screened.

[0029] In this embodiment, the index screening process is screened by rough set theory, that is, the importance of each index is measured by rough set theory, and the importance of the index is evaluated by removing specific indicators from the index decision set and observing the changes in the classification results. The rough set theory is introduced below.

[0030] A and B represent the classification derived from the indicator decision set D (A∈D, B∈D), then the approximate set of A under B is expressed as:

[0031]

[0032] Among them, POS A (B) represents the positive domain of index set B in index set A, that is, the set of all the indexes in U that can be uniquely classified into index set B according to the classification of index set A. For the classification derived from index set B, the importance μ of any index a∈A in index set A is A,B The calculation formula for (a) is:

[0033]

[0034] Among them, card(.) represents the cardinality of the set; γ A (B) represents the coverage of the indicator set B, and its value range is 0≤γ A (B)≤1, the value depends on the indicator set A.

[0035] In the framework of rough set theory, we explore whether the positive area in the classification method used for indicator set B is affected after removing a specific indicator a from indicator set A. A,B The larger (a) is, the greater the influence of indicator a is, that is, the stronger its importance is; otherwise, the importance of indicator a is weaker. In the actual decision-making process, if the importance of indicator a is low, its influence can be considered to be ignored, thereby achieving the compression of indicator items.

[0036] In this way, we can rank the importance of all indicators in indicator set A. Regardless of whether indicator set A contains numerical values, voice, text, pictures or videos, we can set a suitable importance threshold, compare the importance of each indicator with the importance threshold in turn, and only retain indicators that are greater than the importance threshold.

[0037] When obtaining the weight value of each indicator, the existing methods for determining the indicator weight value can be summarized into three basic types: a weighting method based on subjective judgment, a weighting method relying on objective data, and a comprehensive weighting method integrating subjective and objective factors.

[0038] (1) Subjective weighting method

[0039] The subjective weighting method is a method of comparing and assigning values ​​to the degree of importance, cognition or preference of each indicator based on the knowledge, cognition or preference of the decision maker or evaluator, and then calculating the weight.

[0040] The core ideas of subjective weighting methods mainly include two types: one is to obtain relative importance and assign corresponding scores through comparison or multiple comparisons, and generate weight coefficients through normalization, including expert scoring method, Delphi method, chain scoring method and binomial coefficient method; the other method is to construct a judgment matrix by pairwise comparison, and obtain weight coefficients by solving the eigenvector. The hierarchical analysis method, fuzzy hierarchical analysis method and fuzzy comprehensive evaluation method all rely on this construction of judgment matrix to obtain weights. The judgment matrix method is a commonly used subjective weighting method. According to the different settings of the judgment scale, it can be divided into complementary judgment matrix theory and method, fuzzy complementary judgment matrix theory and method and hybrid judgment matrix theory and method.

[0041] (2) Objective weighting method

[0042] Objective weighting method means that the original data is formed by the actual data of each attribute in the decision-making scheme, and the weight of each attribute should be determined according to the difference in attribute values ​​of each scheme under the attribute. Objective weighting plays a core role in multi-objective decision analysis. In order to accurately determine the weights, scholars have adopted a series of quantitative methods to analyze the correlation between attributes and the degree of variation of attribute values. These methods provide decision makers with a set of scientific and systematic weight allocation schemes when facing multi-objective decisions, which helps to achieve better scheme selection.

[0043] Objective weighting methods are mainly divided into two categories: one is the objective weighting method based on "global difference", which mainly includes: TOPSIS method, mean square error method, variance maximization method, deviation maximization method, differential maximization method, DEA theory and method, and some commonly used linear programming methods and goal programming methods. The core idea is to consider that under the optimal weight coefficient, the ranking results of all decision plans have the largest difference or the highest degree of dispersion, and the ranking of decision plans reaches the "global" optimal; the second is the objective weighting method based on "local difference", which mainly includes factor analysis, principal component analysis, entropy value method, cluster analysis, coefficient of variation method, grey correlation analysis, rough set theory and rank effect, etc. The core idea is basically to give priority to the influence of certain "main" attributes, "related" attributes or "local" information on the ranking of decision plans.

[0044] (3) Comprehensive empowerment method

[0045] Subjective weighting methods may deviate from objective reality due to the personal preferences of decision makers. Although objective weighting methods are based on data, they are complex to calculate and difficult to reflect the subjective cognition of decision makers. In order to balance the advantages and disadvantages of these two methods, scholars have proposed a comprehensive weighting method, which aims to more comprehensively reflect the subjective and objective factors in the decision-making process. The main methods are: variance maximization weighting method, optimal coordination weighting method, combined target programming method, and combined least squares method.

[0046] In this embodiment, the expert scoring method is used to obtain the weight value of each indicator. When calculating the indicator weight, it is necessary to study the database in the form of a questionnaire. The contingency table is one of the main display forms and analysis bases of questionnaire data. The contingency table derived from the questionnaire data can also be used as a frequency table of observation data. Furthermore, we can analyze the importance of indicators based on the contingency table.

[0047] Assume that individuals in the population can be classified according to two factors A * and Classification, A * There are r levels q1,q2,…,q r , There are c levels α1, α2, …, α c , draw a sample of size n from the population, where there are n i j individuals belong to the class and n ij Indicates frequency, r×c n ij Arranged as a two-dimensional contingency table with r rows and c columns, referred to as an r×c table.

[0048] If the two factors A in the contingency table * and Represented as an indicator set and the value range of each indicator (the value range of each indicator is the same), and because The median value α j It is arranged by size, so it is called an R×C two-factor one-way ordered contingency table based on questionnaire data, as shown in Table 1.

[0049] Table 1

[0050]

[0051] Table 1 ij The indicator is q i And the level value is a j The cardinality of the set of all objects, that is, the observation frequency, in this embodiment, specifically means that there are several expert evaluation indicators q i The index value of belongs to the interval a j In Table 1, represents the sum of the jth column, represents the sum of the i-th row, represents the sum of all elements in the contingency table, denoted by q i =(n i1 ,n i2 ,…,n ic ), i=1,2,…,r; α j =(n 1j ,n 2j ,…,n rj ), j = 1, 2, ..., c, r represents the total number of indicators, i represents the index number, q i represents the i-th indicator, j represents the scoring interval number when the expert scores, a j represents the jth scoring interval, and c represents the total number of scoring intervals when the experts score.

[0052] The measurement method based on the rank effect value is to calculate the impact of the indicator using the average rank as the weight. j =(n 1j ,n 2j ,…,n rj ), j = 1, 2, ..., c is regarded as a specific value interval, and the value in this interval is called rank, and such an interval is called rank interval. The width of the jth rank interval is the total frequency in the jth interval Therefore, the j-th rank interval is:

[0053]

[0054] The average rank of the jth rank interval is expressed as j=1,2,…,c can be expressed as as a weight vector, where:

[0055]

[0056] Factor A * The i-th level of the ordered factor The rank sum is denoted as R i ,i=1,2,…,r,because:

[0057]

[0058] Here we call R i Factor A * The i-th level is affected by the ordered factor The rank effect of the influence, where R i The larger it is, the greater its importance is and the greater the impact of the indicator is.

[0059] Then normalize the rank effect of indicators at all levels to obtain the weights of indicators at all levels:

[0060]

[0061] From this we can get

[0062] In the expert scoring method, experts often only score the bottom-level indicators and do not score the parent-level indicators, such as only scoring the third-level indicators and not the first- and second-level indicators. Therefore, the above calculation process can only directly calculate the weight of the third-level indicators, but cannot directly settle the weights of the first- and second-level indicators.

[0063] For the primary and secondary indicators, since it is not possible to directly obtain the expert scores of the corresponding indicators, in this embodiment, the frequencies of the primary and secondary indicators in the corresponding contingency tables are calculated based on the frequencies of the third-level indicators contained in the primary and secondary indicators in the corresponding contingency tables. The specific calculation formula is:

[0064]

[0065] in, represents the frequency of the kth primary indicator or the second-level indicator in the jth scoring area, p k represents the total number of third-level indicators contained in the kth first-level indicator or second-level indicator, i represents the sequence number of the third-level indicator contained in the kth first-level indicator or second-level indicator, n ij It represents the frequency of the i-th third-level indicator contained in the k-th first-level indicator or second-level indicator in the j-th scoring area, σ j It represents the standard deviation of the frequency of all the third-level indicators contained in the kth first-level indicator or second-level indicator in the jth scoring area.

[0066] After calculating the frequencies of all primary and secondary indicators in different value ranges, we can obtain the contingency table corresponding to the primary and secondary indicators. Then, based on the obtained contingency table, we can calculate the weights of the primary and secondary indicators using formulas (3)-(6).

[0067] The weights obtained in the above steps are adjusted through the rank effect to smooth out the differences in scoring preferences among experts, ensuring that the relative importance of each indicator is not affected by the expert scoring preferences. This makes the weights more objective and reasonable while ensuring the theoretical agreement of the indicator weights.

[0068] S2: According to the change of the required indicators at the current moment relative to the required indicators at the previous moment, a two-factor single-item ordered contingency table is constructed to characterize the degree of change of each indicator.

[0069] In multi-index decision analysis, expert scoring is a commonly used method to obtain the weight of indicators. By collecting the scores of multiple experts on the importance of each indicator, and optimizing the expert scores with mathematical methods (such as weighted average, hierarchical analysis method, etc.), the preliminary weight distribution of each indicator can be obtained. When constructing a contingency table, this embodiment first obtains the scoring results of multiple experts at the current moment for each indicator required at the current moment. Considering that the required indicators selected at the current moment may change compared to the required indicators at the previous moment, the expert scoring situation is divided into two situations: when the indicator does not appear at the previous moment, the expert's scoring result for the indicator at the current moment is the value interval to which the indicator value of the indicator belongs; when the previous moment also includes the indicator, the expert's scoring result for the indicator at the current moment is the change interval of the indicator at the current moment relative to the previous moment. Then, a two-factor single-item ordered contingency table is constructed based on the scoring results of all experts for each indicator required at the current moment; the rows in the contingency table represent indicators, the columns represent value intervals or change intervals, and the values ​​of the elements in the table represent the number (frequency) of expert scoring results of the corresponding indicator in all expert scoring results for the corresponding value intervals or change intervals. The contingency table formed by the expert scoring results in this embodiment is shown in Table 2, and the number of indicators required at the current moment is M, and the number of items scored by experts for each indicator is N.

[0070] Table 2

[0071]

[0072] S3: Based on the contingency table, the posterior probability matrix representing the posterior probability of each indicator is calculated through Bayesian probability.

[0073] Bayesian theory provides a framework based on probabilistic reasoning for updating estimates of the probability of random events. For two random events X and Y, the Bayesian formula defines the probability of event X given that event Y has already occurred, i.e., the posterior probability, which is expressed as follows:

[0074]

[0075] Among them, P(X|Y) represents the posterior probability, also known as the conditional probability of X given Y; P(Y|X) represents the likelihood probability, that is, the probability of event Y occurring under the condition that event X occurs; P(X) represents the prior probability of event X; and P(Y) represents the marginal probability of event Y.

[0076] According to the concept of conditional probability, it is assumed that the sample space contains all independent events X1, X2, …, X n , and P(X i )>0,(i=1,2,…,n),i represents the sequence number of the event,n represents the total number of events,then the probability of event Y occurring can be calculated by the total probability formula:

[0077]

[0078] Using the Bayesian formula, we can calculate for each independent event X in the sample space i The probability under the condition that event Y occurs, that is, the posterior probability:

[0079]

[0080] In the above formula, P(X i ) represents event X i The prior probability of P(Y|X) is the likelihood probability, P(Y) is called the marginal probability, and P(X i |Y) is the posterior probability, that is, given that Y occurs, X i The conditional probability of occurrence.

[0081] The Bayesian updating process involves combining prior probabilities with new evidence to calculate posterior probabilities. This process is particularly important in weight revision because it allows us to adjust the weights of indicators based on expert ratings and historical data. In this way, we are able to more accurately reflect the importance of indicators in the current decision-making environment.

[0082] In order to dynamically modify the weight values ​​of each indicator at the current moment, we first need to calculate the likelihood probability. Assuming there are N modification levels, the scores of all experts on each indicator can form a 1×N vector r i , where i = 1, 2, ..., M. These scoring vectors can form an M×N matrix R.

[0083]

[0084] Among them, n ij It represents the score frequency of the i-th indicator at the j-th correction level.

[0085] Likelihood probability P(u j |q i ) means that given the i-th index q i Under the condition that j The probability of occurrence. Through the matrix R, we can calculate the likelihood probability P(u j |q i ), whose formula is:

[0086]

[0087] in, Represents the total score frequency of the ith indicator at all correction levels.

[0088] Bayesian probability theory enables us to calculate the modified level u through the total probability formula j Probability of occurrence:

[0089]

[0090] Where P(q i ) represents the prior probability of the ith indicator, which can be estimated through expert scoring or other information sources.

[0091] Furthermore, each indicator q i At a given correction level u j The probability of occurrence under the condition, that is, the posterior probability, is given by the following formula:

[0092]

[0093] According to formula (13), we construct the posterior probability matrix A, which contains the posterior probabilities of all indicators at all correction levels:

[0094]

[0095] S4: The posterior probability matrix is ​​corrected by a correction matrix obtained based on the Probit function to obtain a corrected probability matrix.

[0096] The Probit function is represented by Φ -1 (x), which is the inverse function of the cumulative distribution function Φ(x), also known as the percentile function or inverse cumulative distribution function. The main function of this function is to return the corresponding random variable value x given a quantile (i.e. probability value). In the context of the standard normal distribution, the Probit function is used to map the probability to the corresponding quantile.

[0097] The core formula of the inverse transform method is:

[0098] x=Φ -1 (P) (15)

[0099] Among them, Φ -1 represents the percentile function of the standard normal distribution, P is a given probability value, and x is the corresponding variable value. In particular, we focus on a specific sequence of probability values

[0100] To calculate the corresponding x value, we can use the standard normal distribution table, calculation tools or statistical software to find or calculate Φ by following the steps below: -1 (P) value:

[0101] 1) For Find or calculate The value of x1 is recorded as ω1;

[0102] 2) For Find or calculate The corresponding value of x2 is recorded as ω2;

[0103]

[0104] n) For Find or calculate The value of x is obtained n Denoted as ω n .

[0105] The above process provides an accurate and reliable way to determine the value of a variable given a probability, based on the properties of the standard normal distribution.

[0106] In this embodiment, the correction matrix obtained based on the Probit function is set to ω=[ω1,ω2,…,ω N ] T By modifying the correction matrix, the posterior probability matrix can be made more consistent with the standard distribution. The modified probability matrix is ​​B = [P U (q1),P U (q2),…P U (q M )] T , and its correction process is expressed as:

[0107] B=A*ω (16)

[0108] in

[0109] S5: Perform standard normal correction on the corrected probability matrix.

[0110] The cumulative distribution function (CDF) is expressed as Φ(x) = cdf(x), which is the integral of the probability density function and is used to describe the probability that the random variable X is less than or equal to x. If the random variable Y follows a uniform distribution on the interval [0,1], we can normalize any random variable X to a uniform distribution on the interval [0,1] through the cumulative distribution function. The central limit theorem states that the sum of multiple independent and identically distributed random variables approximately follows a normal distribution, which is the default assumption when the properties of random variables are not understood. The cumulative distribution function expression of the normal distribution is:

[0111]

[0112] Among them, μ and σ 2 represent the mean and variance of the normal distribution respectively.

[0113] In this embodiment, the cumulative distribution function Φ(x) of the standard normal distribution is selected for mapping to obtain the final modified probability matrix B * :

[0114]

[0115] This mapping process not only provides a unified metric, but also ensures that the statistical properties of the revised probabilities are consistent with the standard normal distribution.

[0116] The embodiments of the present invention realize the intelligent and dynamic weight allocation, significantly improve the accuracy and adaptability of weight allocation, and can effectively assist decision makers to make more reasonable decisions in complex and changing environments.

[0117] Example Analysis

[0118] This embodiment selects the comprehensive evaluation of Xiamen’s high-quality development as a case for weight correction.

[0119] Table 3

[0120] (I) Determination of the weight of the comprehensive evaluation index system for Xiamen’s high-quality development in 2022

[0121] This embodiment adds relevant indicators based on the characteristics of Xiamen, selects 7 first-level indicators, 15 second-level indicators and 49 third-level indicators, as shown in Table 3, and then determines the high-quality development evaluation index system of Xiamen.

[0122] Table 3

[0123]

[0124]

[0125] Regarding the data collection of the weights of each indicator, we distributed questionnaires online and offline, and collected a total of 73 valid expert questionnaires. The steps for determining the weights are as follows:

[0126] First, we counted the experts’ scores and used a 9-point questionnaire to obtain the experts’ quantitative evaluation scores on the relative importance of each level 3 indicator, and counted the total number of experts on each score of each level 3 indicator. That is, the number of experts who evaluate the relative importance score of the jth third-level indicator is w, w = {1, 2, ..., 9}. The larger w is, the more important the third-level indicator is, as can be seen from the frequency distribution table of Xiamen's high-quality development expert scores in 2022 in Table 4. Further, the number of experts is counted and the rank effect related statistics are calculated. Finally, the rank effect weight is calculated, the rank effect of the third-level indicator is normalized, and the weight of each third-level indicator is obtained. According to the above formulas (3)-(6), the weights of the first-level and second-level indicators are finally calculated, and the final weight values ​​are shown in Table 3.

[0127] Table 4

[0128]

[0129] Through the rank effect adjustment, the preference differences in expert scoring are eliminated, ensuring that the relative importance of each indicator is not affected by subjectivity, thereby enhancing the objectivity and rationality of weight distribution on the basis of theoretical agreement. Based on this adjustment, the weights of each three-level indicator in the comprehensive evaluation system of high-quality development are obtained.

[0130] It can be seen that due to the excessive number of three-level indicators, the absolute difference in indicator weights is small. Among them, the indicator weight of per capita disposable income of residents is the largest, which is 2.7%; the per capita GDP, ecological environment satisfaction, social security and employment expenditures accounted for the proportion of general public budget expenditures and the emission intensity of major air pollutants from fixed pollution sources are second, with values ​​of 2.6%, 2.4%, 2.4% and 2.4% respectively. These indicators are important reflections of the economy, people's livelihood security and the environment. The indicator with the smallest weight is agricultural labor productivity, with a value of 1.3%. The three-industry structure of Xiamen is 0.4:41.0:58.6, and the primary industry accounts for a low proportion of about 0.4%, so this indicator objectively reflects the development of Xiamen's economic industry.

[0131] Similarly, among the secondary indicator weights, the indicator with the largest weight is economic development, with a value of 8.8%. As a solid foundation for high-quality development, economic development is an important indicator in the comprehensive evaluation index system of Xiamen's high-quality development. In addition, the indicator weights of economic stability (8.3%), social ecology (8.2%), resource sharing (7.8%), innovative industries (7.7%), natural ecology (7.5%) and regional coordination (6.9%) are higher than the average. These indicators are important reflections of Xiamen in terms of material and spiritual aspects, and are also important indicators in the comprehensive evaluation index system of Xiamen's high-quality development.

[0132] Among the primary indicators, comprehensive quality and efficiency (22.3%), shared development (19.5%), green development (15.3%) and innovative development (13.2%) have a large weight in the comprehensive evaluation of Xiamen's high-quality development; coordinated development and open development are also important indicators, with weights of more than 10%; and subjective feelings have the lowest weight, with a value of 7.2%. High-quality development reflects the development of the new development concept, which is the development in which innovation becomes the first driving force, coordination becomes an endogenous feature, green becomes a universal form, openness becomes the only way, and sharing becomes the purpose. On the whole, the calculated weights can better reflect the relative importance of each indicator, embody the important concept of high-level and sustainable development, and better reflect the important measurement indicators of Xiamen's high-quality development status, which is more in line with the requirements of this study.

[0133] Based on this, we can further use the indicator data from 2018 to 2021 provided by various departments of the Xiamen Municipal Government as the basis, use the power coefficient method to non-dimensionalize the data, and combine the weights calculated in the previous article to synthesize the indicators, comprehensively calculate the comprehensive indicators of high-quality development and the scores of the seven first-level indicators and their subordinate second-level and third-level indicators, and describe and analyze them. I will not go into details here.

[0134] (II) Weight revision of the comprehensive evaluation index system for high-quality development of Xiamen in 2023

[0135] Based on the weight determination of the comprehensive evaluation index system of Xiamen's high-quality development in 2022, a comprehensive performance evaluation index system of Xiamen's high-quality development in 2023 is constructed, which can be specifically decomposed into 7 first-level indicators, 15 second-level indicators and 52 third-level indicators. This embodiment collects and integrates the detailed data provided by various departments in Xiamen, and selects data from 2018 to 2022 for comparative analysis.

[0136] Regarding the data collection of each indicator weight, questionnaires were distributed online and offline, and a total of 91 valid expert questionnaires were collected. Based on the new round of expert scoring, the questionnaire design was based on the revised suggestions of importance, combined with the ideas of Bayesian theory, to optimize and adjust the original indicator weights, thereby obtaining the updated indicator weights. The steps for determining weight optimization and revision are as follows:

[0137] First, the expert scoring results were counted. This empirical questionnaire was designed using the Likert five-level scale, with the five options in the questionnaire denoted as u j , j = 1, 2, 3, 4, 5, and obtain the experts’ opinions on 15 secondary indicators (q i , i=1,…,15) and count the frequency of expert scores for each option on each secondary indicator n(U j |Q i ). Through the frequency of different options on each secondary indicator, the conditional probability table of the five options under different secondary indicators is finally obtained as shown in the secondary indicator weight frequency statistics table in Table 5.

[0138] Table 5

[0139]

[0140]

[0141] According to the above table and the modified results of the secondary weights calculated according to formulas (10)-(18), the secondary indicator weights of the comprehensive evaluation index system of high-quality development are obtained. The primary indicator weights and the tertiary indicator weights are merged and evenly decomposed according to the expert scoring results of the secondary indicator weights, and finally calculated according to the same solution idea. The final weight results are shown in Table 6.

[0142] Table 6

[0143]

[0144]

[0145]

[0146] As can be seen from Table 6, among the secondary indicator weights, the indicator with the largest weight is economic development, with a value of 8.6%. As a solid foundation for high-quality development, economic development is an important indicator in the comprehensive evaluation index system of Xiamen's high-quality development. In addition, the indicator weights of social ecology (8.2%), economic stability (8.0%), innovative industries (7.8%), resource sharing (7.6%), and natural ecology (7.5%) are higher than the average. These indicators are important reflections of Xiamen in terms of material and spiritual aspects, and are also important indicators in the comprehensive evaluation index system of Xiamen's high-quality development.

[0147] The secondary weights of the comprehensive evaluation index system in 2023 show some changes in Xiamen's high-quality development. Economic development still occupies the largest weight, at 8.6%, a slight decrease from 8.8% in 2022. The weights of social ecology and economic stability have decreased slightly compared with 2022. At the same time, the weight of innovative industries has increased, from 7.7% in 2022 to 7.8%. The weights of resource sharing and natural ecology have also increased slightly. These changes may reflect Xiamen's emphasis on scientific and technological innovation and its continued attention to ecological balance and social stability in the process of high-quality development. The 2023 index system shows that Xiamen is striving to achieve more comprehensive and sustainable high-quality development in many aspects while maintaining its economic foundation.

[0148] Among the primary indicators, comprehensive quality and efficiency (20.8%), shared development (19.1%), green development (15.5%) and innovative development (14.2%) have a large weight in the comprehensive evaluation of Xiamen's high-quality development; coordinated development and open development are also important indicators, with weights of more than 10%; and subjective feelings have the lowest weight, with a value of 7.2%. High-quality development reflects the development of the new development concept, which is the development in which innovation becomes the first driving force, coordination becomes an endogenous feature, green becomes a universal form, openness becomes the only way, and sharing becomes the development based on purpose. On the whole, the calculated weights can better reflect the relative importance of each indicator, embody the important concept of high-level and sustainable development, and better reflect the important measurement indicators of Xiamen's high-quality development status, which is more in line with the requirements of this study.

[0149] Among the first-level indicators, comprehensive quality and efficiency, shared development, green development and innovative development are still the core areas of concern for Xiamen's high-quality development, but their specific weight distribution has undergone some adjustments. Compared with 2022, the weight of comprehensive quality and efficiency has dropped from 22.3% to 20.8%, the weight of shared development has dropped from 19.5% to 19.11%, the weight of green development has increased from 15.3% to 15.5%, and the weight of innovative development has increased from 13.2% to 14.2%. This shows that in 2023, the emphasis on innovation and green development has increased, while the weights for comprehensive quality and efficiency and shared development have slightly decreased. Coordinated development and open development are still important indicators in 2023, with weights above 10%, but compared with 2022, the weights have not changed significantly. The weight of subjective feelings is 7.2% in 2023, slightly lower than 7.2% in 2022, but still relatively low compared with other indicators. The 2023 evaluation index system reflects the emphasis on innovation and green development, while maintaining the focus on comprehensive quality and efficiency, shared development, coordinated development, and open development. These adjustments may reflect a more sophisticated and comprehensive consideration of sustainable and high-quality development under the new development concept.

[0150] It can be seen that due to the excessive number of three-level indicators, the absolute difference in indicator weights is small. Among them, the indicator weight of per capita disposable income of residents is the largest, which is 2.6%; the per capita regional GDP, ecological environment satisfaction, social security and employment expenditures accounted for the proportion of general public budget expenditures and the emission intensity of major air pollutants from fixed pollution sources are second, with values ​​of 2.6%, 2.4%, 2.3% and 2.4% respectively. These indicators are important reflections of the economy, people's livelihood security and the environment. The indicator with the smallest weight is the three indicators in confidence intensity, with a value of 0.8%. In addition, agricultural labor productivity is 1.3%.

[0151] The three-level indicator weight system in 2023 shows some changes in the weight distribution of economy, livelihood security and environment. Per capita disposable income of residents is still the most important indicator, but the weight has dropped from 2.7% in 2022 to 2.6%. The weights of indicators such as per capita GDP, ecological environment satisfaction, social security and employment expenditure as a proportion of general public budget expenditure, and the emission intensity of major air pollutants from fixed pollution sources have fluctuated slightly, but the overall difference is not large. In the 2023 weight system, the weight of agricultural labor productivity has decreased. The weight of the three indicators in confidence intensity is 0.8% in 2023, which is not significantly different from 2022. This may reflect a more detailed and comprehensive consideration of agricultural production efficiency, as well as a relatively reduced focus on factors such as confidence intensity. The three-level indicator weight system in 2023 has undergone some fine-tuning compared with 2022, but the overall difference is small. In the past two years, Xiamen has maintained a certain stability in its attention to livelihood security, environment and agricultural production while maintaining economic development. This reflects the comprehensive consideration and trade-off of multiple aspects under the framework of high-quality development.

[0152] Through the above steps, a Bayesian-based indicator weight correction framework was established. This framework combined expert experience and previous evaluation results, and used the inverse cumulative distribution function and Sigmoid function to correct the final weight value, providing a more accurate and reliable result for the comprehensive evaluation of Xiamen's high-quality development.

[0153] Based on this, we can further use the indicator data from 2018 to 2022 provided by various departments of the Xiamen Municipal Government as the basis, use the power coefficient method to non-dimensionalize the data, and combine the weights revised in the previous article to synthesize the indicators, comprehensively calculate the comprehensive indicators of high-quality development and the scores of the seven first-level indicators and their affiliated second- and third-level indicators, and describe and analyze them, which will not be repeated here.

[0154] The embodiment of the present invention can not only adapt to the dynamically changing economic and technological environment, but also provide a flexible and efficient mechanism to ensure the flexibility and rationality of weight allocation. Compared with the static weight method, the method adopted in this embodiment can quickly respond to changes in the external environment, such as policy adjustments, economic fluctuations, etc., thereby improving the scientificity and timeliness of decision-making. The method also has broad application prospects in the fields of resource optimization, early warning monitoring and risk assessment.

[0155] Embodiment 2:

[0156] The present invention also provides a terminal device for dynamically correcting indicator weights for comprehensive evaluation, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps in the above-mentioned method embodiment of embodiment 1 of the present invention when executing the computer program.

[0157] Further, as an executable solution, the terminal device for dynamic correction of indicator weights for comprehensive evaluation may be a computing device such as a desktop computer, a notebook, a PDA, and a cloud server. The terminal device for dynamic correction of indicator weights for comprehensive evaluation may include, but not limited to, a processor and a memory. Those skilled in the art may understand that the composition structure of the terminal device for dynamic correction of indicator weights for comprehensive evaluation is merely an example of a terminal device for dynamic correction of indicator weights for comprehensive evaluation, and does not constitute a limitation on the terminal device for dynamic correction of indicator weights for comprehensive evaluation. It may include more or less components than the above, or a combination of certain components, or different components. For example, the terminal device for dynamic correction of indicator weights for comprehensive evaluation may also include input and output devices, network access devices, buses, etc., which are not limited in the embodiments of the present invention.

[0158] Further, as an executable solution, the processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the terminal device for dynamic correction of the weight of the index for comprehensive evaluation, and uses various interfaces and lines to connect the various parts of the terminal device for dynamic correction of the weight of the index for comprehensive evaluation.

[0159] The memory can be used to store the computer program and / or module, and the processor realizes the various functions of the terminal device for dynamic correction of the index weight for comprehensive evaluation by running or executing the computer program and / or module stored in the memory, and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system and at least one application required for a function; the data storage area can store data created according to the use of the mobile phone, etc. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0160] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method in the embodiment of the present invention are implemented.

[0161] The module / unit integrated in the terminal device for dynamic correction of the weight of the index for comprehensive evaluation can be stored in a computer-readable storage medium if it is implemented in the form of a software functional unit and sold or used as an independent product. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory) and software distribution medium, etc.

[0162] Although the present invention has been specifically shown and described in conjunction with the preferred embodiments, it should be understood by those skilled in the art that various changes may be made to the present invention in form and details without departing from the spirit and scope of the present invention as defined by the appended claims, all of which are within the scope of protection of the present invention.

Claims

1. A method for dynamic correction of index weights for comprehensive evaluation, characterized in that: The following steps are involved: S1: Obtain all the indicators required for comprehensive evaluation at the initial moment, as well as the indicator value and weight value of each indicator; S2: Based on the change of the required indicators at the current moment relative to the required indicators at the previous moment, a contingency table is constructed to characterize the degree of change of each indicator; S3: Based on the contingency table, the posterior probability of each indicator is calculated by Bayesian probability, and then the posterior probability matrix is ​​constructed based on the posterior probabilities of all indicators; S4: Correcting the posterior probability matrix by using a correction matrix obtained based on the Probit function to obtain a corrected probability matrix; S5: Perform standard normal correction on the corrected probability matrix; S6: Based on the results of standard normal correction, the weight value of each indicator at the current moment is obtained.

2. The method for dynamic correction of index weights for comprehensive evaluation according to claim 1, characterized in that: All the indicators required at the initial moment in step S1 are obtained by screening all the indicators involved in the comprehensive evaluation, and the screening process is carried out through the rough set theory.

3. The method for dynamic correction of index weights for comprehensive evaluation according to claim 2, characterized in that: All indicators in step S1 include indicators of at least two levels; when screening all indicators involved in the comprehensive evaluation, the first-level indicators are screened first, and then all the second-level indicators contained in the screened first-level indicators are screened, and so on.

4. The method for dynamic correction of index weights for comprehensive evaluation according to claim 1, characterized in that: The weight value of each indicator at the initial moment is obtained by the expert scoring method, that is, after constructing a contingency table to represent the expert evaluation results of each indicator, the influence of each indicator is calculated by a measurement method based on the rank effect value as the standard. After normalizing the rank effect value of each indicator, the weight value of each indicator is obtained.

5. The method for dynamic correction of index weights for comprehensive evaluation according to claim 1, characterized in that: The method for constructing the contingency table in step S2 is: obtaining the scoring results of multiple experts at the current moment for each indicator required at the current moment; when the indicator did not appear at the previous moment, the expert's scoring result for the indicator at the current moment is the value interval to which the indicator value of the indicator belongs; when the previous moment also includes the indicator, the expert's scoring result for the indicator at the current moment is the change interval of the indicator at the current moment relative to the previous moment; constructing a contingency table based on the scoring results of all experts for each indicator required at the current moment; the rows in the contingency table represent indicators, the columns represent value intervals or change intervals, and the values ​​of the elements in the table represent the number of expert scoring results for the corresponding indicators in all expert scoring results that are corresponding value intervals or change intervals.

6. The method for dynamic correction of index weights for comprehensive evaluation according to claim 1, characterized in that: When performing standard normal correction on the corrected probability matrix in step S5, the cumulative distribution function of the standard normal distribution is selected for mapping.

7. A terminal device for dynamically correcting the weight of indicators for comprehensive evaluation, characterized in that: The method comprises a processor, a memory and a computer program stored in the memory and running on the processor, wherein the processor implements the steps of the method according to any one of claims 1 to 6 when executing the computer program.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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