A DEMATEL-ISM model dynamic threshold calculation method based on centrality characteristics

Abstract

The application discloses a DEMATEL-ISM model dynamic threshold calculation method based on centrality characteristics. The method aims at the subjectivity problem of threshold determination in the construction of the reachable matrix of the traditional DEMATEL-ISM model, introduces the sorting distribution characteristics of factor centrality, establishes a centrality-influence strength correlation model to realize the dynamic optimization of the threshold, determines the initial threshold through an empirical formula, expands the candidate threshold range, calculates the reachable matrix corresponding to each candidate threshold and the factor node degree sorting, introduces the Spearman correlation coefficient to quantify the similarity of the node degree sorting and the centrality sorting, and finally selects the optimal threshold. Compared with the prior art, the application gets rid of the dependence on a single empirical formula, improves the scientificity and objectivity of threshold determination, enhances the robustness of the threshold and the noise resistance of the model, effectively retains the interaction relationship between key factors, makes the reachable matrix more consistent with the actual causal relationship network, and is suitable for complex system factor analysis, risk assessment, hierarchical structure division and other scenes.

Description

Technical Field

[0001] This invention belongs to the fields of systems engineering analysis and multi-criteria decision-making technology. Specifically, it relates to a dynamic threshold calculation method for the DEMATEL-ISM model based on centrality features. It is applicable to scenarios that require analysis using the DEMATEL-ISM model, such as the analysis of interaction between factors in complex systems, risk assessment, hierarchical structure partitioning, and the construction of causal relationship networks. Background Technology

[0002] The DEMATEL-ISM model is a commonly used combinatorial model in complex systems analysis. It analyzes the interrelationships of factors within a system using the DEMATEL model to obtain a comprehensive influence matrix. The ISM model then transforms this comprehensive influence matrix into an reachability matrix, thereby completing the hierarchical structure of factors and clearly presenting the hierarchical causal relationships within the system. In the application of this combinatorial model, the construction of the reachability matrix is ​​the core link between the DEMATEL and ISM models, and determining the threshold is a crucial step in constructing the reachability matrix—by setting a threshold to binarize the elements of the comprehensive influence matrix, significant influence relationships between factors can be filtered out, thus obtaining the reachability matrix.

[0003] In existing technologies, the threshold determination of the DEMATEL-ISM model generally adopts an empirical formula method, that is, by comprehensively considering the mean of all elements of the influence matrix. Added standard deviation Obtain the initial threshold This initial threshold is then directly used as the final threshold for constructing the reachability matrix. However, this method has several limitations: It is highly subjective and lacks objective quantitative basis: it relies entirely on a single empirical formula to determine the threshold without taking into account the distribution characteristics and interaction relationships of the system's own factors, and the rationality of the threshold is not verified by quantitative indicators. The results are too simplistic and easily lead to information loss: fixed thresholds cannot adapt to the characteristics of factors in complex systems. If the threshold is too high, weak influence relationships between key factors may be lost, or if the threshold is too low, invalid interference relationships may be introduced, making it difficult to fully capture the complex interactions between factors. Poor noise resistance and large result bias: The individual differences in data distribution are not considered. When the data distribution of the comprehensive influence matrix is ​​discrete, the threshold obtained by the empirical formula is prone to deviate from the actual situation, which leads to the causal relationship reflected by the reachability matrix not matching the actual system, and thus affects the hierarchical structure analysis results of the subsequent ISM model.

[0004] Currently, existing research has not proposed effective solutions to the above problems, and there is a lack of a threshold calculation method that can combine system characteristics, quantify the rationality of thresholds, and achieve dynamic screening. Therefore, developing a dynamic threshold calculation method based on the characteristics of system factors themselves, and improving the scientificity, objectivity, and robustness of threshold determination in the DEMATEL-ISM model, has significant practical significance and application value. Summary of the Invention

[0005] (a) Purpose of the invention This invention aims to address the problems in traditional Dematel-ISM models, such as reliance on a single empirical formula for threshold determination, high subjectivity, monotonous results, easy loss of key factor relationships, and poor noise resistance, when constructing the reachability matrix. It provides a dynamic threshold calculation method based on centrality features. This method introduces the factor centrality ranking distribution characteristics of the Dematel model, and achieves dynamic optimization and selection of the threshold by quantifying the similarity between node degree ranking and centrality ranking. This eliminates excessive reliance on empirical formulas, making the threshold more closely reflect the actual characteristics of the system, providing a scientific and objective basis for the construction of the reachability matrix, and ultimately improving the accuracy of the analysis results of the Dematel-ISM model.

[0006] (II) Technical Solution To solve the above-mentioned technical problems, the present invention specifically provides the following technical solution: 1. A dynamic threshold calculation method for the DEMATEL-ISM model based on centrality features, characterized in that the method addresses the threshold determination problem when constructing the reachability matrix of the DEMATEL-ISM model, and achieves dynamic threshold optimization by quantifying the similarity between the factor node degree ranking and the centrality ranking, including the following steps: S1. Determine the initial threshold of the comprehensive influence matrix in the DEMATEL model using empirical formulas. ; S2. Based on the initial threshold Select at equal intervals on both sides Number of values, forming a collection A set of candidate thresholds; S3. Using each value in the candidate threshold set as a threshold, calculate the corresponding reachability matrix. ,in ; S4. Calculate the node degree mi of each factor in the reachability matrix under different candidate thresholds, and sort the factors based on the node degree. S5. Introduce the Spearman correlation coefficient to calculate the similarity between the factor node degree ranking and the factor center degree ranking in the DEMATEL model under different candidate thresholds; S6. Compare the Spearman correlation coefficients corresponding to different candidate thresholds, select the candidate threshold with the largest coefficient as the optimal threshold, and construct the final reachability matrix of the DEMATEL-ISM model based on the optimal threshold.

[0007] 2. The method for calculating a dynamic threshold of a DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, in step S1, the initial threshold... The empirical formula is:

[0008] In the formula, To comprehensively influence the mean of all elements in the matrix, The standard deviation of all elements in the matrix is ​​used to comprehensively influence the matrix.

[0009] 3. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, in step S3, the reachability matrix... elements The calculation formula is:

[0010] In the formula, Let be any value in the candidate threshold set. To integrate the elements of the influence matrix, The total number of factors in the system. =1 indicates a factor Factors There is a direct influence relationship. =1 indicates a factor Factors There is no direct impact.

[0011] 4. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, in step S4, the node degree mi is the th node in the reachability matrix. The sum of the row elements reflects the degree of influence of a single factor on the overall system.

[0012] 5. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, in step S5, the formula for calculating the Spearman correlation coefficient is:

[0013] In the formula, The Spearman correlation coefficient. The total number of factors in the system. This represents the difference between the factor's node degree ranking and its centrality ranking. The closer the result is to 1, the higher the consistency between the node degree ranking and the centrality ranking.

[0014] 6. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, in step S6, the selection principle for the optimal threshold is: to select the candidate threshold corresponding to the maximum value of the Spearman correlation coefficient, under which the structural features reflected by the reachable matrix and the influence structure characterized by the comprehensive influence matrix have the highest consistency at the ranking level.

[0015] 7. A method for calculating the dynamic threshold of a DEMATEL-ISM model based on centrality features according to any one of claims 1-6, characterized in that the method is applicable to a large number of factors. For complex systems with arbitrary positive integers, the spacing between candidate thresholds can be flexibly adjusted according to the system data distribution characteristics.

[0016] (III) Beneficial Effects Compared with the prior art, the present invention has the following advantages: Improving the scientific rigor and objectivity of threshold determination: Breaking through the limitations of a single empirical formula, by expanding the range of candidate thresholds and combining them with Spearman's correlation coefficient, the judgment of the reasonableness of the threshold is transformed from subjective experience into objective numerical quantification, reducing interference from human factors and making the determination of the threshold more scientifically based. Enhance the robustness of the threshold and the noise resistance of the model: Dynamically select the optimal threshold based on the factor centrality characteristics and data distribution of the system itself, so that the threshold can be adapted to the individual characteristics of different complex systems, effectively reduce the result bias caused by data dispersion, and improve the noise resistance of the DEMATEL-ISM model. Complete preservation of the interaction relationships between key factors: By filtering with the optimal threshold, the problem of losing key weak influence relationships caused by a fixed threshold being too high is avoided, so that the reachability matrix can more comprehensively and accurately capture the complex interaction of factors in the system and fit the actual causal relationship network. The method is highly versatile and adaptable: it is suitable for complex systems with any number of positive integer factors, and the spacing between candidate thresholds can be flexibly adjusted according to the actual scenario. It can be widely applied to various analysis scenarios of DEMATEL-ISM models such as risk assessment, project management, and system optimization, and has good engineering practicality and promotion value. Attached Figure Description

[0017] Figure 1 The flowchart below shows the steps of the dynamic threshold calculation method for the DEMATEL-ISM model based on centrality features according to the present invention, including: Input layer: Comprehensive influence matrix and factor centrality ranking obtained from the DEMATEL model; Computational layer: overall influence matrix, initial threshold calculation, candidate threshold selection, reachability matrix calculation, node degree sorting, Spearman coefficient calculation; Output layer: Optimal threshold; Detailed Implementation To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description is provided in conjunction with the implementation of the optimal threshold and the final reachability matrix constructed based on the optimal threshold. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0018] The direct inducing factors of the return behavior were analyzed using the DEMATEL-ISM model, and the comprehensive influence matrix constructed using expert scoring is as follows:

[0019] The constructed factor centrality ranking is as follows:

[0020] To solve the above-mentioned technical problems, the present invention specifically provides the following technical solution: 1. A dynamic threshold calculation method for the DEMATEL-ISM model based on centrality features. This method addresses the threshold determination problem when constructing the reachability matrix of the DEMATEL-ISM model. It achieves dynamic threshold optimization by quantifying the similarity between the factor node degree ranking and the centrality ranking, including the following steps: S1. Determine the initial threshold of the comprehensive influence matrix in the DEMATEL model using empirical formulas. ; S2. Based on the initial threshold Select at equal intervals on both sides Number of values, forming a collection A set of candidate thresholds; S3. Using each value in the candidate threshold set as a threshold, calculate the corresponding reachability matrix. ,in ; S4. Calculate the node degree mi of each factor in the reachability matrix under different candidate thresholds, and sort the factors based on the node degree. S5. Introduce the Spearman correlation coefficient to calculate the similarity between the factor node degree ranking and the factor center degree ranking in the DEMATEL model under different candidate thresholds; S6. Compare the Spearman correlation coefficients corresponding to different candidate thresholds, select the candidate threshold with the largest coefficient as the optimal threshold, and construct the final reachability matrix of the DEMATEL-ISM model based on the optimal threshold.

[0021] 2. A method for calculating a dynamic threshold in a Dematel-ISM model based on centrality features, characterized in that, in step S1, the initial threshold... The empirical formula is:

[0022] In the formula, To comprehensively influence the mean of all elements in the matrix, This represents the standard deviation of all elements in the comprehensive influence matrix. Based on the comprehensive influence matrix, the following is calculated: , ,therefore .

[0023] Based on the initial threshold Select at equal intervals on both sides Number of values, forming a collection A set of candidate thresholds; the selected threshold set is: , , , , , , .

[0024] 3. A method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features, characterized in that, in step S3, the reachability matrix... elements The calculation formula is:

[0025] In the formula, Let be any value in the candidate threshold set. To integrate the elements of the influence matrix, The total number of factors in the system. =1 indicates a factor Factors There is a direct influence relationship. =1 indicates a factor Factors There is no direct impact.

[0026] After constructing the overall influence matrix based on the comprehensive influence matrix, reachability matrices are then constructed based on the overall influence matrix data and different threshold values ​​in the threshold set.

[0027] 4. A method for calculating the dynamic threshold of a DEMATEL-ISM model based on centrality features, characterized in that, in step S4, the node degree mi is the th node in the reachability matrix. The sum of the row elements reflects the degree of influence of a single factor on the overall system.

[0028] Based on the reachability matrix data at different thresholds, the node degree of the reachability matrix at different thresholds is calculated. The factors are then ranked based on their node degree data. The results are as follows:

[0029] 5. A method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features, characterized in that, in step S5, the formula for calculating the Spearman correlation coefficient is:

[0030] In the formula, The Spearman correlation coefficient. The total number of factors in the system. This represents the difference between the factor's node degree ranking and its centrality ranking. The closer the result is to 1, the higher the consistency between the node degree ranking and the centrality ranking.

[0031] By calculating the reachability matrix under different thresholds, the node degree and ranking of each factor in the reachability matrix are determined. The Spearman coefficients for different thresholds are shown in the table below:

[0032] 6. A dynamic threshold calculation method for the DEMATEL-ISM model based on centrality features, characterized in that, in step S6, the selection principle for the optimal threshold is: selecting the candidate threshold corresponding to the maximum value of the Spearman correlation coefficient, under which the structural features reflected by the reachable matrix and the influence structure characterized by the comprehensive influence matrix have the highest consistency at the ranking level.

[0033] In summary, the reachability matrix constructed with a threshold of 0.105 has the highest similarity between the factor node degree ranking and the center degree ranking, which is more consistent with the previous data, rather than the 0.11 calculated by the empirical formula.

Claims

1. A method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features, characterized in that, This method addresses the threshold determination problem when constructing the reachability matrix in the DEMATEL-ISM model. It achieves dynamic threshold optimization by quantifying the similarity between the factor node degree ranking and the center degree ranking, and includes the following steps: S1. Determine the initial threshold of the comprehensive influence matrix in the DEMATEL model using empirical formulas. ; S2. Based on the initial threshold Select at equal intervals on both sides Number of values, forming a collection A set of candidate thresholds; S3. Using each value in the candidate threshold set as a threshold, calculate the corresponding reachability matrix. ,in ; S4. Calculate the node degree of each factor in the reachability matrix under different candidate thresholds. m i And sort the factors based on the degree of the nodes; S5. Introduce the Spearman correlation coefficient to calculate the similarity between the factor node degree ranking and the factor center degree ranking in the DEMATEL model under different candidate thresholds; S6. Compare the Spearman correlation coefficients corresponding to different candidate thresholds, select the candidate threshold with the largest coefficient as the optimal threshold, and construct the final reachability matrix of the DEMATEL-ISM model based on the optimal threshold.

2. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, In step S1, the initial threshold The empirical formula is: In the formula, To comprehensively influence the mean of all elements in the matrix, The standard deviation of all elements in the matrix is ​​used to comprehensively influence the matrix.

3. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, In step S3, the reachable matrix elements The calculation formula is: In the formula, Let be any value in the candidate threshold set. To integrate the elements of the influence matrix, The total number of factors in the system. =1 indicates a factor Factors There is a direct influence relationship. =1 indicates a factor Factors There is no direct impact.

4. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, In step S4, node degree m i The th in the reachability matrix The sum of the row elements reflects the degree of influence of a single factor on the overall system.

5. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, In step S5, the formula for calculating the Spearman correlation coefficient is as follows: In the formula, The Spearman correlation coefficient. The total number of factors in the system. This represents the difference between the factor's node degree ranking and its centrality ranking. The closer the result is to 1, the higher the consistency between the node degree ranking and the centrality ranking.

6. The method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to claim 1, characterized in that, In step S6, the selection principle for the optimal threshold is as follows: select the candidate threshold corresponding to the maximum value of the Spearman correlation coefficient. Under this threshold, the structural features reflected by the reachable matrix and the influence structure characterized by the comprehensive influence matrix have the highest consistency at the ranking level. A method for calculating the dynamic threshold of the DEMATEL-ISM model based on centrality features according to any one of claims 1-6, characterized in that, This method is applicable to the number of factors For complex systems with arbitrary positive integers, the spacing between candidate thresholds can be flexibly adjusted according to the system data distribution characteristics.

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