Index weight determination method and device combining analytic hierarchy process and expert weighting

Abstract

The invention relates to the technical field of performance evaluation, and particularly discloses an analytic hierarchy process and expert weighting combined index weight determination method and device, and the method comprises the steps: selecting a plurality of experts, and obtaining the sorting vector of each expert through an analytic hierarchy process; and on the basis of the sorting vectors of the experts, performing expert clustering analysis to obtain expert weights, and weakening the evaluation randomness of the analytic hierarchy process and the difference of subjective cognition of evaluation experts by utilizing the majority principle and logic clearness of expert judgment results. According to the method, feature vectors (sorting vectors) obtained by each expert through analytic hierarchy process can clearly express the judgment of each expert on the importance of the indexes, and then, by adopting an expert empowerment mode, through a clustering algorithm, the majority principle and logic clearness of expert judgment results are combined and considered, so that the judgment accuracy of the indexes is improved. And the evaluation randomness of the analytic hierarchy process and the difference of subjective cognition of evaluation experts are weakened, so that the final index weight is more persuasive.

Description

Technical Field

[0001] This invention relates to the field of performance evaluation technology, specifically to a method and apparatus for determining indicator weights that combines hierarchical analysis with expert weighting. Background Technology

[0002] Weights represent the relative importance of different indicators. Depending on the source of the original data used to calculate the weight coefficients, the calculation methods include:

[0003] (1) Subjective empowerment method

[0004] Subjective weighting methods refer to methods that calculate the weights of indicators based on the decision-maker's subjective experience and judgment using specific rules, such as the Delphi method and the analytic hierarchy process. These methods have relatively mature theoretical foundations and can well reflect the background conditions of the evaluated object and the evaluator's intentions. However, their accuracy depends heavily on the accumulated knowledge and experience of experts, resulting in significant subjectivity and relatively poor objectivity.

[0005] (2) Objective empowerment method

[0006] Objective weighting methods refer to methods that determine weights based on objective information about the evaluation indicators using specific rules, such as the entropy method and the deviation maximization method. These methods rely on objective data, but their biggest drawback is that the assigned weights sometimes do not match reality; that is, important indicators have low weights, while unimportant indicators have high weights.

[0007] (3) Combination method

[0008] The combined weighting method combines the advantages of subjective and objective weighting methods. First, it uses both methods to calculate the subjective and objective weights separately. Then, it determines the ratio of the subjective and objective weights based on the actual situation, thus obtaining the overall weight. This method reflects the decision-maker's subjective information to a certain extent while retaining the objectivity of the original data; however, its accuracy depends on determining the proportion of subjective and objective weights.

[0009] Based on this technical background, the present invention studies a method and apparatus for determining index weights that combines hierarchical analysis and expert weighting. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention provides a method and apparatus for determining indicator weights that combines hierarchical analysis (AHP) with expert weighting. The method first uses the feature vectors (ranking vectors) obtained by each expert through AHP to clearly express their judgments on the importance of the indicators. Then, it employs expert weighting and a clustering algorithm, taking into account the majority principle and logical clarity of expert judgments, thereby reducing the randomness of AHP evaluation and the differences in subjective understanding among evaluation experts, making the final indicator weights more convincing.

[0011] To achieve the above objectives, a first aspect of the present invention provides a method for determining index weights that combines hierarchical analysis and expert weighting, comprising:

[0012] Multiple experts were selected and their ranking vectors were obtained using the analytic hierarchy process (AHP) to represent each expert's judgment on the importance of the indicator.

[0013] Based on the ranking vectors of each expert, expert clustering analysis is used to obtain expert weights. This weights are then used to leverage the majority principle and logical clarity of expert judgments to reduce the randomness of the analytic hierarchy process and the differences in subjective perception among the evaluation experts, making the final indicator weights more convincing.

[0014] A second aspect of the present invention provides an indicator weight determination device combining hierarchical analysis and expert weighting, comprising:

[0015] The analytic hierarchy process module is used to select multiple experts and use the analytic hierarchy process to obtain the ranking vectors of each expert, thereby expressing the judgment of each expert on the importance of the indicator;

[0016] The clustering module is used to obtain expert weights based on the ranking vectors of each expert through expert clustering analysis. It then leverages the majority principle and logical clarity of expert judgments to reduce the randomness of the analytic hierarchy process and the differences in subjective perception among evaluation experts, making the final indicator weights more convincing.

[0017] A third aspect of the present invention provides an electronic device, the electronic device comprising:

[0018] Memory, which stores executable instructions;

[0019] A processor that executes the executable instructions in the memory to implement the method for determining index weights that combines hierarchical analysis and expert weighting as described in the first aspect.

[0020] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for determining index weights that combines hierarchical analysis and expert weighting as described in the first aspect.

[0021] The beneficial effects of this invention include:

[0022] (1) The method for determining index weights by combining hierarchical analysis and expert weighting proposed in this invention first uses the feature vectors (ranking vectors) obtained by each expert through hierarchical analysis to clearly express each expert's judgment on the importance of the index. Then, the method of expert weighting is adopted, and through clustering algorithm, the majority principle and logical clarity of the expert judgment results are taken into account, which reduces the randomness of the evaluation of hierarchical analysis and the difference in subjective understanding of the evaluation experts, making the final index weights more convincing.

[0023] (2) The method for determining indicator weights by combining hierarchical analysis and expert weighting proposed in this invention first obtains the ranking vector of each expert for each indicator through hierarchical analysis, reflecting the individual understanding of the importance of each indicator by each expert; from individual understanding to collective understanding, the expert weights are determined by comprehensively considering the collective opinion of experts (clustering, the more experts in a class, the greater the weight between classes, reflecting the principle of "majority rule") and the logical clarity of each expert's judgment (assigning different expert weights to experts in a class by the consistency ratio coefficient and the degree of deviation from the core judgment within the class, avoiding some experts being assigned large expert weights due to unclear judgment logic) to obtain different expert weights. The indicator weights calculated in this way reflect the scientificity and objectivity to the greatest extent.

[0024] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0025] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings.

[0026] Figure 1 This is a flowchart illustrating the method for determining index weights that combines hierarchical analysis and expert weighting proposed in this invention.

[0027] Figure 2 This is a schematic diagram of the expert analytic hierarchy process in a specific implementation of the method for determining index weights that combines hierarchical analysis and expert weighting proposed in this invention.

[0028] Figure 3 This is a schematic diagram of the expert weight determination process in a specific implementation of the method for determining index weights that combines hierarchical analysis and expert weighting proposed in this invention. Detailed Implementation

[0029] Preferred embodiments of the invention will now be described in more detail. While preferred embodiments of the invention are described below, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0030] This invention provides a method for determining indicator weights that combines hierarchical analysis with expert weighting, such as... Figure 1 As shown, it includes:

[0031] Multiple experts were selected and their ranking vectors were obtained using the analytic hierarchy process (AHP) to represent each expert's judgment on the importance of the indicator.

[0032] Based on the ranking vectors of each expert, expert clustering analysis is used to obtain expert weights. This weights are then used to leverage the majority principle and logical clarity of expert judgments to reduce the randomness of the analytic hierarchy process and the differences in subjective perception among the evaluation experts, making the final indicator weights more convincing.

[0033] This invention first uses the feature vectors (ranking vectors) obtained by each expert through hierarchical analysis to clearly express each expert's judgment on the importance of the indicators. Then, it adopts an expert weighting method and a clustering algorithm, taking into account the majority principle and logical clarity of the expert judgment results, to reduce the randomness of the evaluation of the hierarchical analysis method and the difference in the subjective understanding of the evaluation experts, so as to make the final indicator weights more convincing.

[0034] According to the present invention, the ranking vectors of each expert obtained by multiple experts using the analytic hierarchy process (AHP) include:

[0035] A table comparing the relative importance of each indicator is generated through expert scoring;

[0036] Based on the comparison judgment table, construct the indicator judgment matrix;

[0037] Calculate the eigenvalues ​​and eigenvectors of the index judgment matrix; the eigenvectors are the sorting vectors.

[0038] Consistency is determined by the indicator judgment matrix. If the indicator judgment matrix satisfies the consistency requirement, a sorting vector is output. Otherwise, the comparison judgment table is updated and the indicator judgment matrix is ​​adjusted until the indicator judgment matrix satisfies the consistency requirement.

[0039] According to the present invention, generating a relative importance comparison table through expert scoring includes:

[0040] Experts assign a rating to each indicator based on its relative importance, and the ratio of the rating scores is used to represent the degree of importance of each pair of indicators.

[0041] The importance of the indicators is judged according to the analytic hierarchy process, and the ratios are divided into multiple importance intervals according to their size to form a comparison judgment table;

[0042] Based on the comparison judgment table, the indicator judgment matrix is ​​constructed as follows:

[0043] Based on the comparison and judgment table, fill in the indicator evaluation set table;

[0044] The indicator evaluation set table corresponds to the indicator judgment matrix, where the diagonal elements of the matrix are 1, the product of the elements symmetrical about the diagonal is 1, and the values ​​of the off-diagonal elements are determined according to the comparison judgment table.

[0045] The ratio of each element in the indicator judgment matrix represents the importance of that row's row index relative to its column index.

[0046] According to the present invention, the formula for calculating the consistency index is as follows:

[0047]

[0048] Where CI is the consistency index, n is the number of indices, and λ is the number of indices. max The largest eigenvalue of the indicator judgment matrix;

[0049] Consistency indicator judgment using the indicator judgment matrix includes:

[0050] When the order of the indicator judgment matrix is ​​greater than 2, the judgment is made by the ratio of the consistency index CI to the average random consistency index RI of the same order of the indicator judgment matrix. This ratio is the random consistency ratio coefficient, denoted as CR.

[0051] When CR = CI / RI < 0.1, the indicator judgment matrix satisfies the consistency requirement; otherwise, the indicator judgment matrix does not satisfy the consistency requirement.

[0052] According to the present invention, based on the ranking vectors of each expert, expert weights are obtained by expert clustering analysis, including:

[0053] The compatibility of each expert's ranking vector is calculated to obtain the compatibility matrix;

[0054] Experts are clustered based on their compatibility and a set threshold.

[0055] Calculate the inter-class weights based on the expert clustering results;

[0056] Based on the consistency of the indicator matrix, calculate the intra-class weights;

[0057] The expert weight is obtained by multiplying the inter-class weight and the intra-class weight;

[0058] The weights of various indicators are obtained by multiplying the ranking vector of each expert by its corresponding expert weight and then summing them.

[0059] According to the present invention, the formula for calculating compatibility is:

[0060]

[0061] Where d(i,j) is the compatibility between expert i and expert j, W i =(wi1 ,w i2 …w in ) and W j =(w j1 ,w j2 …w jn ) are the ranking vectors of expert i and expert j, respectively, and n is the number of indicators;

[0062] When d(i,j) satisfies d(i,i)=1, d(i,j)=d(j,i), it means that the smaller the compatibility, the higher the similarity of the judgments of the two experts.

[0063] Based on the compatibility level and a set threshold, experts are clustered, including:

[0064] Set a threshold T. When d(i,j)≤T, the expert E will be... i and E j They cluster into one class, of which E i and E j The judgment matrices constructed for expert i and expert j are given, and the sorting vector and consistency ratio coefficient are obtained.

[0065] According to the present invention, the formula for calculating inter-class weights is as follows:

[0066]

[0067] Where t is the number of expert classifications, m k Let λ be the number of experts in the k-th category. k Inter-class weights;

[0068] The formula for calculating intra-class weight is:

[0069]

[0070] Where, f(CR) i Let be a function representing the consensus ratio of expert i, indicating the logical clarity of the expert's judgment. The smaller the consensus ratio coefficient, the larger the value of this function. Its expression is:

[0071]

[0072] in, Let i be the average ranking vector of experts from class i to class k. European distance, G is the center of the k-th type of expert. k For the k-th type of experts, Let i be the distance function from expert i to the class core. The closer expert i is to the center, the better. The larger the value, the closer the expert's judgment is to the core judgment of the k-th type of expert;

[0073] Average ranking vector from expert i to expert k The expression for the Euclidean distance is:

[0074]

[0075] The expression for the distance function from expert i to the class core is:

[0076]

[0077] This invention first obtains the ranking vectors of each expert for each indicator through hierarchical analysis, reflecting each expert's personal understanding of the importance of each indicator. From individual understanding to collective understanding, expert weights are determined by comprehensively considering the collective opinion of experts (clustering, the more experts in a cluster, the greater the weight between clusters, reflecting the principle of "majority rule") and the logical clarity of each expert's judgment (assigning different expert weights within a cluster to experts within a cluster based on the consistency ratio coefficient and the degree of deviation from the core judgment within the cluster, avoiding assigning large expert weights to some experts whose judgment logic is unclear). The indicator weights calculated in this way reflect the scientificity and objectivity to the greatest extent.

[0078] The present invention will be described in more detail below through embodiments.

[0079] Example 1:

[0080] like Figure 1 As shown, this embodiment proposes a method for determining indicator weights that combines hierarchical analysis with expert weighting. It assumes that experts are invited to score four types of indicators, namely indicators A, B, C, and D, to determine the indicator weights, which serve as the basis for evaluating and selecting multiple options.

[0081] Hierarchical Analysis of Experts (i.e.) Figure 2 (As shown) Step 1: Expert scoring to generate a relative importance comparison table;

[0082] Traditional analytic hierarchy process (AHP) requires experts to compare the importance of indicators pairwise, which can lead to logical errors when there are many indicators. The method in this invention stipulates that experts only need to score the relative importance of each indicator on a five-level scale (1, 3, 5, 7, 9). The ratio of these scores represents the relative importance of each pair of indicators, with all scores falling within the range of 1, 1.29, 1.4, 1.67, 1.8, 2.3, 3, 5, 7, 9. Following the five importance assessment methods of AHP, these ratios are divided into five importance intervals, as shown in Table 1. Therefore, experts do not need to compare the importance of indicators pairwise or fill in a judgment matrix, and this method is more in line with human cognitive processes.

[0083] Table 1. Relative Importance Judgment Table

[0084]

[0085]

[0086] Step 2 of the Hierarchical Analysis of Experts: Constructing the judgment matrix:

[0087] Based on the returned expert scoring sheets, fill out the indicator importance comparison table with reference to the relative importance judgment table, as shown in Table 2; for the four indicators, compare them pairwise, and a total of [number missing] comparisons are required. Second comparison;

[0088] Table 2. Comparison of the Importance of the Four Indicators

[0089]

[0090] Next, fill in the indicator comment set table (as shown in Table 3) and construct the judgment matrix. The comment set table corresponds to a 4*4 matrix. The diagonal elements of the matrix are 1, and the product of the elements symmetrical about the diagonal is 1. The values ​​of the off-diagonal elements are determined according to the importance comparison judgment table. The ratio of each element represents the importance of the "row index" relative to the "column index" of that row. For example, if indicator B is "significantly important" to indicator A, then in the row representing "indicator B", find the column corresponding to "indicator A" and fill in the value 5, which corresponds to the 2nd row and 1st column. Correspondingly, fill in 1 / 5 in the 1st row and 2nd column symmetrical about the diagonal. The process of filling in other elements is similar.

[0091] Table 3. Index Comments Collection

[0092]

[0093] Therefore, the judgment matrix obtained from the indicator evaluation set table is:

[0094]

[0095] Step 3 of the Hierarchical Analysis of Experts (AAMI): Solve for the eigenvalues ​​and eigenvectors of the judgment matrix.

[0096] The largest eigenvalue of the matrix is ​​obtained by using the square root method. max =4.1533, the corresponding eigenvector is:

[0097] w=(0.0587,0.1693,0.3860,0.3860);

[0098] This feature vector is called the sorting vector. The judgment matrix and the sorting vector are the basic parameters for experts to participate in the expert weighting algorithm.

[0099] Step 4 of the Analytic Hierarchy Process (AHP): Consistency Judgment

[0100] The purpose of consistency judgment is to avoid logical errors such as "A is more important than B, B is more important than C, and C is more important than A" in the process of comparing relative importance.

[0101] Consistency index is represented by CI; it is defined as:

[0102]

[0103] Where n is the number of indices. When the order is greater than 2, the ratio of the consistency index CI of the judgment matrix to the average random consistency index RI of the same order is called the random consistency ratio of the judgment matrix, denoted as CR. When CR = CI / RI < 0.1, the judgment matrix has the required consistency. Otherwise, the judgment matrix needs to be adjusted. The average random consistency indices of matrices from order 1 to 9 are shown in Table 4.

[0104] Table 4. Average random consistency index of matrices of order 1 to 9

[0105]

[0106] In this example, CI = 0.0511 and CR = 0.0568 < 0.1, so the consistency of the judgment matrix is ​​acceptable. Generally, experts have a clear understanding of the relative importance of each indicator, and logical errors are less likely to occur when the number of indicators is small. When consistency is not met, it is necessary to go back and modify the comparison judgment table of the importance of the evaluation indicators.

[0107] Therefore, the ranking vectors for the four indicators A, B, C, and D can be obtained as follows:

[0108] w=(0.0587,0.1693,0.3860,0.3860);

[0109] Expert weighting determination (e.g.) Figure 3 (As shown) Step 1: Hierarchical analysis yields the judgment matrix and sorting vector:

[0110] Taking four peer indicators—Indicator A, Indicator B, Indicator C, and Indicator D—as examples, the expert weighting process is illustrated; ten experts are selected for hierarchical analysis, with E... i (i = 1 to 10); let A, B, C, and D represent these four indicators. The judgment matrix constructed by the experts, the ranking vector (W1 to W10), and the consistency ratio coefficient are shown in Table 5:

[0111] Table 5. Sort vectors (W1~W10) and consistency ratio coefficients

[0112]

[0113]

[0114] Analysis of the 10 judgment matrices reveals that different experts have different perceptions of the relative importance of different indicators. This can be seen from the different solutions of the ranking vector. In this embodiment, this difference among experts is amplified for the sake of process explanation. Expert clustering is to classify experts based on the differences in the ranking vector according to a certain algorithm, and assign the same inter-class weight to experts in the same class, thus reflecting the process of "clustering".

[0115] Expert weight determination step two: Calculation of sorting vector compatibility:

[0116] Compatibility represents a measure of the similarity between two expert ranking vectors, where d(i,j) represents the compatibility between expert i and expert j, and W... i =(w i1 ,w i2 …w in ) and W j =(w j1 ,w j2 …w jn Let ) represent the ranking vectors of expert i and expert j, and n be the number of indicators. Then:

[0117]

[0118] The smaller the compatibility, the higher the similarity between the judgments of the two experts.

[0119] Expert weight determination step three: Constructing the compatibility matrix:

[0120] Based on the ranking vectors of the 10 experts, the similarity measure can be calculated pairwise. According to the properties of d(i,j), we need to calculate... The compatibility matrix can be listed as follows:

[0121]

[0122] Expert weight determination step four: Expert clustering:

[0123] Expert clustering classifies experts based on their compatibility, using the metric d(i,j) to represent compatibility. A smaller d(i,j) indicates greater compatibility. Typically, a threshold T is set; when d(i,j) ≤ T, experts can be considered to be... i and E j Clustered into one category, in this embodiment a threshold T = 0.02 is set, and the compatibility matrix is ​​observed. Based on the set threshold, classification can be performed as {E1, E7, E9}, {E2, E4}, {E3, E 10 There are 5 categories in total: {E5, E6} and {E8}, as follows;

[0124]

[0125] Expert weight determination step five: Calculate inter-class weights:

[0126] Suppose that experts can be divided into t classes, and the number of experts in the k-th class is m. k Inter-class weight λ k The calculation formula is:

[0127]

[0128] In this embodiment, the inter-class weights of the five types of experts are:

[0129] λ2=λ3=λ4=0.1818, λ5=0.0455;

[0130] Expert weight determination step six: Calculate the within-class weights:

[0131] The expert set of type k is G k The intra-class weight calculation uses Calculate, where f(CR) i The function denoted by represents the consensus ratio of expert i, indicating the logical clarity of the expert's judgment. The smaller the consensus ratio coefficient, the larger the function value. Therefore:

[0132]

[0133] This represents the average ranking vector from expert i to expert k. European distance, The center of the k-th class of experts is represented; it can be proven that the average sorting vector... The unique solution to this planning problem is: to make the ranking vector of all experts in the k-th class of experts reach... The sum of the Euclidean distances is minimized; therefore This represents the distance function from expert i to the class core; the closer expert i is to the center, the better. The larger the value, the closer the expert's judgment is to the core judgment of the k-th type of expert;

[0134] in:

[0135]

[0136] The calculation results of the consensus function and class core deviation distance for various types of experts are shown in Table 6.

[0137] Table 6. Consistency functions and core deviation distances of various expert groups

[0138]

[0139]

[0140] From the formula The intra-class weights for each class are calculated as shown in Table 7.

[0141] Table 7 Intra-class weights for each category

[0142]

[0143] Step 7 in determining expert weights: Calculate expert weights.

[0144] The expert weight is obtained by multiplying the inter-class weight and the intra-class weight. The multiplication relationship makes the sum of the expert weights equal to 1, which satisfies the requirements of weight allocation.

[0145] λ i =λ k ·ω i (k = 1 ~ 5, i = 1 ~ 10);

[0146] The calculation results are shown in Table 8;

[0147] Table 8 Expert Weights

[0148] 1 ]]> ​ 2 ]]> ​ <![CDATA[λ 3 ]]> <![CDATA[λ 4 ]]> <![CDATA[λ 5 ]]> <![CDATA[λ 6 ]]> <![CDATA[λ 7 ]]> <![CDATA[λ 8 ]]> <![CDATA[λ 9 ]]> <![CDATA[λ 10 ]]> 0.1319 0.0935 0.0909 0.0833 0.0805 0.1013 0.1540 0.0455 0.1232 0.0909

[0149] Obtain the indicator weights:

[0150] The weights of the four categories of indicators A, B, C, and D are obtained by multiplying each expert's ranking vector and its corresponding expert weight, and then summing them up, as shown in Table 9.

[0151] Table 9 Indicator Weights

[0152]

[0153] Therefore, the weights of the four same-level indicators, A, B, C, and D, obtained through analytic hierarchy process and expert weighting are shown in Table 10.

[0154] Table 10 Indicator Weights

[0155]

[0156] Example 2:

[0157] This embodiment provides a method for determining indicator weights that combines hierarchical analysis with expert weighting, such as... Figure 1 As shown, it includes:

[0158] Multiple experts were selected and their ranking vectors were obtained using the analytic hierarchy process (AHP) to represent each expert's judgment on the importance of the indicator.

[0159] Based on the ranking vectors of each expert, expert clustering analysis is used to obtain expert weights. This weights are then used to leverage the majority principle and logical clarity of expert judgments to reduce the randomness of the analytic hierarchy process and the differences in the subjective perceptions of the evaluation experts, making the final indicator weights more convincing.

[0160] In this embodiment, the ranking vectors of each expert, obtained by multiple experts using the analytic hierarchy process (AHP), include:

[0161] A table comparing the relative importance of each indicator is generated through expert scoring;

[0162] Based on the comparison judgment table, construct the indicator judgment matrix;

[0163] Calculate the eigenvalues ​​and eigenvectors of the index judgment matrix; the eigenvectors are the sorting vectors.

[0164] Consistency is determined by the indicator judgment matrix. If the indicator judgment matrix satisfies the consistency requirement, the sorting vector is output. Otherwise, the comparison judgment table is updated and the indicator judgment matrix is ​​adjusted until the indicator judgment matrix satisfies the consistency requirement.

[0165] In this embodiment, a relative importance comparison table is generated through expert scoring, including:

[0166] Experts assign a rating to each indicator based on its relative importance, and the ratio of the rating scores is used to represent the degree of importance of each pair of indicators.

[0167] The importance of the indicators is judged according to the analytic hierarchy process, and the ratios are divided into multiple importance intervals according to their size to form a comparison judgment table;

[0168] Based on the comparison judgment table, the indicator judgment matrix is ​​constructed as follows:

[0169] Based on the comparison and judgment table, fill in the indicator evaluation set table;

[0170] The indicator evaluation set table corresponds to the indicator judgment matrix, where the diagonal elements of the matrix are 1, the product of the elements symmetrical about the diagonal is 1, and the values ​​of the off-diagonal elements are determined according to the comparison judgment table.

[0171] The ratio of each element in the indicator judgment matrix represents the importance of that row's row index relative to its column index;

[0172] In this embodiment, the formula for calculating the consistency index is:

[0173]

[0174] Where CI is the consistency index, n is the number of indices, and λ is the number of indices. max The largest eigenvalue of the indicator judgment matrix;

[0175] Consistency indicator judgment using the indicator judgment matrix includes:

[0176] When the order of the indicator judgment matrix is ​​greater than 2, the judgment is made by the ratio of the consistency index CI to the average random consistency index RI of the same order of the indicator judgment matrix. This ratio is the random consistency ratio coefficient, denoted as CR.

[0177] When CR = CI / RI < 0.1, the indicator judgment matrix satisfies the consistency requirement; otherwise, the indicator judgment matrix does not satisfy the consistency requirement.

[0178] In this embodiment, based on the ranking vectors of each expert, expert clustering analysis is used to obtain expert weights, including:

[0179] The compatibility of each expert's ranking vector is calculated to obtain the compatibility matrix;

[0180] Experts are clustered based on their compatibility and a set threshold.

[0181] Calculate the inter-class weights based on the expert clustering results;

[0182] Based on the consistency of the indicator matrix, calculate the intra-class weights;

[0183] The expert weight is obtained by multiplying the inter-class weight and the intra-class weight;

[0184] The weights of each indicator are obtained by multiplying the ranking vector of each expert by its corresponding expert weight and then summing them up.

[0185] In this embodiment, the formula for calculating compatibility is:

[0186]

[0187] Where d(i,j) is the compatibility between expert i and expert j, W i =(w i1 ,w i2 …w in ) and W j =(w j1 ,w j2 …w jn ) are the ranking vectors of expert i and expert j, respectively, and n is the number of indicators;

[0188] When d(i,j) satisfies d(i,i)=1, d(i,j)=d(j,i), it means that the smaller the compatibility, the higher the similarity of the judgments of the two experts.

[0189] Based on the compatibility level and a set threshold, experts are clustered, including:

[0190] Set a threshold T. When d(i,j)≤T, the expert E will be...i and E j They cluster into one class, of which E i and E j The judgment matrices constructed for expert i and expert j are respectively, and the ranking vector and consistency ratio coefficient are obtained.

[0191] In this embodiment, the formula for calculating inter-class weights is:

[0192]

[0193] Where t is the number of expert classifications, m k Let λ be the number of experts in the k-th category. k Inter-class weights;

[0194] The formula for calculating intra-class weight is:

[0195]

[0196] Where, f(CR) i Let be a function representing the consensus ratio of expert i, indicating the logical clarity of the expert's judgment. The smaller the consensus ratio coefficient, the larger the value of this function. Its expression is:

[0197]

[0198] in, Let i be the average ranking vector of experts from class i to class k. European distance, G is the center of the k-th type of expert. k For the k-th type of experts, Let i be the distance function from expert i to the class core. The closer expert i is to the center, the better. The larger the value, the closer the expert's judgment is to the core judgment of the k-th type of expert;

[0199] Average ranking vector from expert i to expert k The expression for the Euclidean distance is:

[0200]

[0201] The expression for the distance function from expert i to the class core is:

[0202]

[0203] Example 3:

[0204] This embodiment provides a method for determining indicator weights that combines hierarchical analysis with expert weighting, including:

[0205] The analytic hierarchy process module is used to select multiple experts and use the analytic hierarchy process to obtain the ranking vectors of each expert, thereby expressing the judgment of each expert on the importance of the indicator;

[0206] The clustering module is used to obtain expert weights based on the ranking vectors of each expert through expert clustering analysis. Then, by leveraging the majority principle and logical clarity of expert judgments, it reduces the randomness of the analytic hierarchy process and the differences in the subjective perceptions of the evaluation experts, making the final indicator weights more convincing.

[0207] In this embodiment, multiple experts use the analytic hierarchy process (AHP) to obtain the ranking of each expert.

[0208] The quantity includes:

[0209] A table comparing the relative importance of each indicator is generated through expert scoring;

[0210] Based on the comparison judgment table, construct the indicator judgment matrix;

[0211] Calculate the eigenvalues ​​and eigenvectors of the index judgment matrix; the eigenvectors are the sorting vectors.

[0212] Consistency is determined by the indicator judgment matrix. If the indicator judgment matrix satisfies the consistency requirement, the sorting vector is output. Otherwise, the comparison judgment table is updated and the indicator judgment matrix is ​​adjusted until the indicator judgment matrix satisfies the consistency requirement.

[0213] In this embodiment, a relative importance comparison table is generated through expert scoring, including:

[0214] Experts assign a rating to each indicator based on its relative importance, and the ratio of the rating scores is used to represent the degree of importance of each pair of indicators.

[0215] The importance of the indicators is judged according to the analytic hierarchy process, and the ratios are divided into multiple importance intervals according to their size to form a comparison judgment table;

[0216] Based on the comparison judgment table, the indicator judgment matrix is ​​constructed as follows:

[0217] Based on the comparison and judgment table, fill in the indicator evaluation set table;

[0218] The indicator evaluation set table corresponds to the indicator judgment matrix, where the diagonal elements of the matrix are 1, the product of the elements symmetrical about the diagonal is 1, and the values ​​of the off-diagonal elements are determined according to the comparison judgment table.

[0219] The ratio of each element in the indicator judgment matrix represents the importance of that row's row index relative to its column index;

[0220] In this embodiment, the formula for calculating the consistency index is:

[0221]

[0222] Where CI is the consistency index, n is the number of indices, and λ is the number of indices. max The largest eigenvalue of the indicator judgment matrix;

[0223] Consistency indicator judgment using the indicator judgment matrix includes:

[0224] When the order of the indicator judgment matrix is ​​greater than 2, the judgment is made by the ratio of the consistency index CI to the average random consistency index RI of the same order of the indicator judgment matrix. This ratio is the random consistency ratio coefficient, denoted as CR.

[0225] When CR = CI / RI < 0.1, the indicator judgment matrix satisfies the consistency requirement; otherwise, the indicator judgment matrix does not satisfy the consistency requirement.

[0226] In this embodiment, based on the ranking vectors of each expert, expert clustering analysis is used to obtain expert weights, including:

[0227] The compatibility of each expert's ranking vector is calculated to obtain the compatibility matrix;

[0228] Experts are clustered based on their compatibility and a set threshold.

[0229] Calculate the inter-class weights based on the expert clustering results;

[0230] Based on the consistency of the indicator matrix, calculate the intra-class weights;

[0231] The expert weight is obtained by multiplying the inter-class weight and the intra-class weight;

[0232] The weights of each indicator are obtained by multiplying the ranking vector of each expert by its corresponding expert weight and then summing them up.

[0233] In this embodiment, the formula for calculating compatibility is:

[0234]

[0235] Where d(i,j) is the compatibility between expert i and expert j, W i =(w i1 ,w i2 …w in ) and W j =(w j1 ,w j2 …w jn ) are the ranking vectors of expert i and expert j, respectively, and n is the number of indicators;

[0236] When d(i,j) satisfies d(i,i)=1, d(i,j)=d(j,i), it means that the smaller the compatibility, the higher the similarity of the judgments of the two experts.

[0237] Based on the compatibility level and a set threshold, experts are clustered, including:

[0238] Set a threshold T. When d(i,j)≤T, the expert E will be... i and E j They cluster into one class, of which E i and E j The judgment matrices constructed for expert i and expert j are respectively, and the ranking vector and consistency ratio coefficient are obtained.

[0239] In this embodiment, the formula for calculating inter-class weights is:

[0240]

[0241] Where t is the number of expert classifications, m k Let λ be the number of experts in the k-th category. k Inter-class weights;

[0242] The formula for calculating intra-class weight is:

[0243]

[0244] Where, f(CR) i Let be a function representing the consensus ratio of expert i, indicating the logical clarity of the expert's judgment. The smaller the consensus ratio coefficient, the larger the value of this function. Its expression is:

[0245]

[0246] in, Let i be the average ranking vector of experts from class i to class k. European distance, G is the center of the k-th type of expert. k For the k-th type of experts, Let i be the distance function from expert i to the class core. The closer expert i is to the center, the better. The larger the value, the closer the expert's judgment is to the core judgment of the k-th type of expert;

[0247] Average ranking vector from expert i to expert k The expression for the Euclidean distance is:

[0248]

[0249] The expression for the distance function from expert i to the class core is:

[0250]

[0251] Example 4:

[0252] This invention provides an electronic device including a memory and a processor, comprising:

[0253] Memory, which stores executable instructions;

[0254] The processor executes executable instructions in memory to implement a method for determining index weights that combines hierarchical analysis and expert weighting.

[0255] This memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0256] The processor may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the invention, the processor is used to execute computer-readable instructions stored in the memory.

[0257] Those skilled in the art should understand that, in order to solve the technical problem of how to achieve a good user experience, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included within the protection scope of this invention.

[0258] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0259] Example 5:

[0260] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements a method for determining index weights that combines hierarchical analysis and expert weighting.

[0261] A computer-readable storage medium according to embodiments of the present invention stores non-transitory computer-readable instructions. When these non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the methods described in the foregoing embodiments of the present invention are performed.

[0262] The aforementioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or portable hard drive), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).

[0263] The embodiments of this invention propose a method for determining indicator weights that combines hierarchical analysis and expert weighting. First, each expert obtains a feature vector (ranking vector) using hierarchical analysis, which clearly expresses each expert's judgment on the importance of the indicator. Then, an expert weighting method is used, which combines the majority principle and logical clarity of the expert judgment results with clustering algorithm, reducing the randomness of the evaluation of hierarchical analysis and the difference in subjective understanding of the evaluation experts, making the final indicator weights more convincing.

[0264] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for determining indicator weights that combines analytic hierarchy process (AHP) with expert weighting, characterized in that, include: Multiple experts were selected and their ranking vectors were obtained using the analytic hierarchy process (AHP) to represent each expert's judgment on the importance of the indicator. Based on the ranking vectors of each expert, expert clustering analysis is used to obtain expert weights. This weights are then used to leverage the majority principle and logical clarity of expert judgments to reduce the randomness of the analytic hierarchy process and the differences in subjective perception among the evaluation experts, making the final indicator weights more convincing.

2. The method according to claim 1, characterized in that, The ranking vectors of each expert, obtained by using the analytic hierarchy process (AHP) separately, include: A table comparing the relative importance of each indicator is generated through expert scoring; Based on the comparison and judgment table, construct the index judgment matrix; Calculate the eigenvalues ​​and eigenvectors of the index judgment matrix; the eigenvectors are the sorting vectors. Consistency indicators are determined using the indicator judgment matrix. If the indicator judgment matrix satisfies consistency, the sorting vector is output; otherwise, the comparison judgment table is updated, and the indicator judgment matrix is ​​adjusted until the indicator judgment matrix satisfies consistency.

3. The method according to claim 2, characterized in that, A relative importance comparison table is generated based on expert scoring, including: Experts assign a rating to each indicator based on its relative importance, and the ratio of the rating scores is used to represent the degree of importance of each pair of indicators. The importance of the indicators is judged according to the analytic hierarchy process, and the ratios are divided into multiple importance intervals according to their size to form a comparison judgment table; Based on the comparison and judgment table, constructing the index judgment matrix includes: Based on the comparison and judgment table, fill in the indicator comment set table; The index evaluation set table corresponds to the index judgment matrix, wherein the diagonal elements of the matrix are 1, the product of the elements symmetrical about the diagonal is 1, and the values ​​of the off-diagonal elements are determined according to the comparison judgment table. The ratio of each element in the index judgment matrix represents the importance of the row index relative to the column index.

4. The method according to claim 2, characterized in that, The formula for calculating the consistency index is as follows: Where CI is the consistency index, n is the number of indices, and λ is the number of indices. max The largest eigenvalue of the indicator judgment matrix; The consistency index judgment using the aforementioned index judgment matrix includes: When the order of the indicator judgment matrix is ​​greater than 2, the judgment is made by the ratio of the consistency index CI to the average random consistency index RI of the same order of the indicator judgment matrix. This ratio is the random consistency ratio coefficient, denoted as CR. When CR = CI / RI < 0.1, the indicator judgment matrix satisfies the consistency requirement; otherwise, the indicator judgment matrix does not satisfy the consistency requirement.

5. The method according to claim 3, characterized in that, Based on the ranking vectors of each expert, expert weights are obtained through expert clustering analysis, including: The compatibility of each expert's ranking vector is calculated to obtain the compatibility matrix; Experts are clustered based on their compatibility and a set threshold. Calculate the inter-class weights based on the expert clustering results; Based on the consistency of the indicator matrix, calculate the intra-class weights; The expert weight is obtained by multiplying the inter-class weight and the intra-class weight; The weights of various indicators are obtained by multiplying the ranking vector of each expert by its corresponding expert weight and then summing them.

6. The method according to claim 5, characterized in that, The formula for calculating the compatibility is: Where d(i,j) is the compatibility between expert i and expert j, W i =(w i1 ,w i2 …w in ) and W j =(w j1 ,w j2 …w jn ) are the ranking vectors of expert i and expert j, respectively, and n is the number of indicators; When d(i,j) satisfies d(i,i)=1, d(i,j)=d(j,i), it means that the smaller the compatibility, the higher the similarity of the judgments of the two experts. Based on the compatibility level and a set threshold, experts are clustered, including: Set a threshold T. When d(i,j)≤T, the expert E will be... i and E j They cluster into one class, of which E i and E j The judgment matrices constructed for expert i and expert j are given, and the sorting vector and consistency ratio coefficient are obtained.

7. The method according to claim 6, characterized in that, The formula for calculating the inter-class weights is as follows: Where t is the number of expert classifications, m k Let λ be the number of experts in the k-th category. k Inter-class weights; The formula for calculating the intra-class weight is: ω i =0.5f(CR i )+0.5g[d(i,W k* )]; Where, f(CR) i Let be a function representing the consensus ratio of expert i, indicating the logical clarity of the expert's judgment. The smaller the consensus ratio coefficient, the larger the value of this function. Its expression is: Where d(i,W) k* W is the average ranking vector from expert i to expert k. k* The European distance, W k* G is the center of the k-th type of expert. k Let g[d(i,W) be the set of experts of the kth class. k* [)] represents the distance function from expert i to the class core. The closer expert i is to the center, the greater the distance function. k* The larger the value of ], the closer the expert's judgment is to the core judgment of the k-th type of expert; The average ranking vector W from expert i to expert k-th class k* The expression for the Euclidean distance is: The expression for the distance function from expert i to the class core is:

8. A device for determining index weights by combining hierarchical analysis and expert weighting, characterized in that, include: The analytic hierarchy process module is used to select multiple experts and use the analytic hierarchy process to obtain the ranking vectors of each expert, thereby expressing the judgment of each expert on the importance of the indicator; The clustering module is used to obtain expert weights based on the ranking vectors of each expert through expert clustering analysis. It then leverages the majority principle and logical clarity of expert judgments to reduce the randomness of the analytic hierarchy process and the differences in subjective perception among evaluation experts, making the final indicator weights more convincing.

9. An electronic device, characterized in that, The electronic device includes: Memory, which stores executable instructions; A processor that executes the executable instructions in the memory to implement the method for determining index weights that combines hierarchical analysis and expert weighting according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method for determining index weights that combines hierarchical analysis and expert weighting as described in any one of claims 1-7.

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