Network elasticity multi-index fusion quantitative analysis method

Abstract

The invention relates to the technical field of computers, in particular to a network elasticity multi-index fusion quantitative analysis method, which comprises the following steps of: acquiring index values of a plurality of indexes corresponding to a to-be-evaluated system under the condition of being attacked for a plurality of times, and establishing an initial decision matrix based on the index values; processing the initial decision matrix by using an entropy weight method, and determining the weight of each index; according to the weight of each index, using the correlation coefficient between the indexes to replace the interaction degree, and determining the fuzzy measure of different index sets; and determining the elasticity score of the to-be-evaluated system according to the fuzzy measure of each index set. According to the method, the influence of subjective factors on a multi-index fusion result is overcome to a certain extent through the weight of the index determined by the entropy weight method and the fuzzy measure calculated by replacing the interaction degree with the correlation coefficient, and the accuracy and comparability of a network elasticity evaluation result can be improved.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a network elasticity multi-index fusion quantitative analysis method. Background Art

[0002] Network resilience usually refers to the ability of a network to predict, withstand, recover and adapt when facing adverse conditions, pressure, attacks or damage. A highly resilient network can withstand external shocks to a certain extent and quickly restore services after a problem occurs. When evaluating network resilience, a single indicator often cannot fully reflect the actual performance of the network. The use of a multi-indicator fusion method can comprehensively consider the relationship between different performance indicators, thereby more accurately evaluating the resilience of the network. Therefore, the network resilience multi-indicator fusion technology continues to develop with the expansion of network scale and the increase of complexity, and gradually becomes an important direction for network management and optimization.

[0003] The current network resilience multi-index fusion method mainly adopts qualitative analysis and relies on expert scoring to determine the weight and importance of each indicator. Although qualitative analysis is relatively simple to implement and does not require complex measurement tools, it has some significant limitations, such as strong subjectivity, which makes the evaluation results easily affected by the subjective opinions of experts; at the same time, due to the lack of a standardized evaluation system, the indicator values ​​in different environments or time may be different, which reduces the comparability and credibility of the evaluation results. Summary of the invention

[0004] In order to solve the technical problem that the network resilience assessment results of the above-mentioned existing network resilience multi-index fusion method are of low accuracy, the purpose of the present invention is to provide a network resilience multi-index fusion quantitative analysis method, and the technical solution adopted is as follows:

[0005] An embodiment of the present invention provides a method for quantitative analysis of network resilience multi-indicator fusion, the method comprising the following steps:

[0006] Obtaining the index values ​​of several indicators corresponding to the system to be evaluated when it is subjected to several attacks, and establishing an initial decision matrix based on the index values; wherein the system to be evaluated is a system that needs to be evaluated for network resilience;

[0007] Use the entropy weight method to process the initial decision matrix and determine the weight of each indicator;

[0008] According to the weight of each indicator, the correlation coefficient between indicators is used instead of the interaction degree to determine the fuzzy measurement of different indicator sets;

[0009] According to the fuzzy measure of each indicator set, the resilience score of the system to be evaluated is determined.

[0010] Furthermore, the entropy weight method is used to process the initial decision matrix to determine the weight of each indicator, including:

[0011] The initial decision matrix is ​​standardized to obtain a standardized matrix;

[0012] According to the size of each element in the standardized matrix, the entropy value of each indicator is determined;

[0013] According to the entropy value of each indicator, the entropy weight of each indicator is determined, and the entropy weight is used as the weight of the corresponding indicator.

[0014] Furthermore, the initial decision matrix is ​​normalized to obtain a normalized matrix, including:

[0015] If the index value of the jth index of the i-th test object is a positive index, the expression for standardization is:

[0016] In the formula, r ij The data obtained after the index value of the jth index of the i-th test object is standardized. Represents the smallest index value among the index values ​​of the jth index of all test objects, Represents the maximum index value among the index values ​​of the jth index of all test objects;

[0017] If the index value of the jth index of the i-th test object is a reverse index, the expression for standardization is:

[0018]

[0019] Among them, the test object is the system to be evaluated under different attack conditions.

[0020] Furthermore, determining the entropy value of each indicator according to the size of each element in the standardized matrix includes:

[0021] Normalize each element in the standardized matrix to obtain the normalized index value of each index of each test object;

[0022] For any indicator, the entropy value of the indicator is calculated according to the normalized indicator value of the indicator for each test object.

[0023] Furthermore, the step of calculating the entropy value of the indicator according to the normalized indicator value of each test object includes:

[0024] The calculation formula for the entropy value of the jth indicator is:

[0025] In the formula, Q jrepresents the entropy value of the jth indicator, ln represents the logarithmic function with the natural constant e as the base, f ij represents the normalized index value of the jth index of the ith test object, and d represents the number of test objects.

[0026] Furthermore, determining the entropy weight of each indicator according to the entropy value of each indicator includes:

[0027] In the formula, w j represents the entropy weight of the jth indicator, Q j represents the entropy value of the jth indicator, and J represents the number of indicators.

[0028] Furthermore, the fuzzy measures of different indicator sets are determined based on the weights of the indicators and using the correlation coefficients between the indicators instead of the interaction degree, including:

[0029] According to the indicator values ​​of each indicator of each test object, the correlation coefficient between every two indicators is determined, and then the correlation coefficient is determined as the degree of interaction;

[0030] According to the weight of each indicator and the interaction degree between every two indicators, the fuzzy measure of different indicator sets is determined.

[0031] Furthermore, the step of determining the correlation coefficient between every two indicators according to the indicator values ​​of each indicator of each test object includes:

[0032] For any two indicators, all indicator values ​​of each test object are sorted according to a preset order, and the rank of the indicator values ​​of the two indicators in each sorted sequence is determined;

[0033] Determine the rank difference value of each data pair according to the ranks of the index values ​​of the two indices in each sorted sequence, wherein the data pair is composed of the ranks of the index values ​​of the two indices in the same sorted sequence;

[0034] According to the rank difference value of each data pair, the correlation coefficient of the two indicators is determined.

[0035] Furthermore, determining the correlation coefficient of the two indicators according to the rank difference value of each data pair and the number of all test objects includes:

[0036] In the formula, ρ j′j represents the correlation coefficient between the j′th indicator and the jth indicator, n represents the number of all test objects, Represents the square of the rank difference value of the I-th data pair.

[0037] Furthermore, determining the resilience score of the system to be evaluated according to the fuzzy measure of each indicator set includes:

[0038] Using Choquet fuzzy integral, the fuzzy measure of each indicator set is calculated and analyzed to obtain the resilience score of the system to be evaluated.

[0039] The present invention has the following beneficial effects:

[0040] The present invention provides a network resilience multi-index fusion quantitative analysis method, which first obtains the index values ​​of several indicators corresponding to the system to be evaluated when it is attacked several times, and establishes an initial decision matrix based on the index values; uses the entropy weight method to process the initial decision matrix to determine the weight of each indicator; according to the weight of each indicator, the correlation coefficient between the indicators is used instead of the interaction degree to determine the fuzzy measurement of different indicator sets; and according to the fuzzy measurement of each indicator set, determines the resilience score of the system to be evaluated.

[0041] The present invention adopts objective quantitative analysis and relies entirely on measured data for evaluation, which has the advantages of objectivity, accuracy and comparability. Compared with the traditional qualitative analysis method, this method is more scientific and objective, can reduce the influence of subjective factors on the evaluation results, improve the accuracy and credibility of the evaluation, and can further ensure the scientificity, accuracy and practicality of the multi-index fusion results, providing more effective tools and support for the evaluation and optimization of network resilience. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1 This is a flow chart of a method for quantitative analysis of network elasticity multi-index fusion according to an embodiment of the present invention;

[0044] Figure 2 Schematic diagram of a coal mine safety investment evaluation index system in an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of the numerical values ​​of various indicators of a coal mine from 2009 to 2019;

[0046] Figure 4 This is a schematic diagram of the dimensionless values ​​of various indicators of a coal mine from 2009 to 2019. DETAILED DESCRIPTION

[0047] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation methods, structures, features and effects of the technical solutions proposed by the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0048] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0049] In order to enhance the comparability and credibility of network resilience assessment results, the present invention aims to provide a quantitative analysis method. First, the weight of each indicator can be obtained by the entropy method. Secondly, considering that different indicators are not independent of each other, but have a certain correlation, in order to improve the reliability of network resilience assessment, it is necessary to analyze the overall assessment of different indicator sets under fuzzy and uncertain conditions. However, if the opinions of different assessors are simply linearly weighted, it will lose objectivity and may even cause distortion of the assessment results. Fuzzy measure and Choquet fuzzy integral are effective tools to solve the above problems. The present invention introduces 2-additive fuzzy measure, and uses correlation coefficient instead of the interaction degree affected by subjectivity in the process of calculating fuzzy measure, and further uses Choquet fuzzy integral to calculate the resilience score of the system.

[0050] Specifically, an embodiment of the present invention provides a network resilience multi-index fusion quantitative analysis method, such as Figure 1 As shown, the following steps are included:

[0051] S1, obtain the index values ​​of several indicators corresponding to the system to be evaluated when it is attacked several times, and establish an initial decision matrix based on the index values.

[0052] First, obtain the index values ​​of several indicators corresponding to the system to be evaluated when it is subjected to several attacks.

[0053] In this embodiment, the system to be evaluated refers to a system that needs to be evaluated for network resilience. In order to evaluate the network resilience of the system to be evaluated, the index values ​​of several indicators of the system to be evaluated when it is attacked several times are obtained. Among them, different systems have different properties, and the corresponding number and type of indicators are also different, so this embodiment does not specifically limit the number and type of indicators of the system to be evaluated; in addition, in order to analyze the resilience recovery ability of the system to be evaluated when it is attacked by different types of attacks, the system to be evaluated is attacked several times, and the index values ​​of each attack on the system to be evaluated may be the same or different, and the attack type and number are not specifically limited here.

[0054] Secondly, based on the indicator values ​​of each indicator corresponding to different test objects, an initial decision matrix is ​​constructed.

[0055] In this embodiment, the elements in the initial decision matrix are the index values ​​of each index of each test object, the number of rows in the initial decision matrix is ​​the number of indicators, and the number of columns in the matrix is ​​the number of test objects. The index value of the jth (jth column) index of the i-th (i-th row) test object in the initial decision matrix can be recorded as a ij , i can be equal to 1, 2, 3..., d, d represents the number of test objects, j can be equal to 1, 2, 3..., J, J represents the number of indicators. Among them, the initial decision matrix is ​​used to organize the indicator values ​​of all indicators corresponding to all test objects, which is helpful for the subsequent analysis of the weights of different indicators. The weights can be used to characterize the important calculation factors of the corresponding indicators when calculating the fuzzy measure.

[0056] So far, this embodiment has obtained an initial decision matrix corresponding to the indicator values ​​of several indicators corresponding to the system to be evaluated when it is attacked several times.

[0057] S2, use the entropy weight method to process the initial decision matrix and determine the weight of each indicator.

[0058] In this embodiment, in order to analyze the correlation between the various indicators of the system to be evaluated and quantify the importance of different indicators in the quantitative fuzzy measurement, it can also characterize the importance of each indicator in the quantitative analysis process of the fusion of multiple indicators of network resilience, and it is necessary to determine the weight of each indicator based on the initial decision matrix. Among them, through the system to be evaluated that suffers from different types of attacks, multiple test objects of the system to be evaluated are obtained, that is, the system to be evaluated that suffers from different types of attacks is used as the test object.

[0059] As a specific implementation, the above step S2 can be implemented through steps S201 to S203 (not shown in the figure):

[0060] S201, normalizing the initial decision matrix to obtain a standardized matrix.

[0061] In this embodiment, the numerical ranges of the indicator values ​​of different indicators are different. In order to uniformly analyze different indicators, it is necessary to unify the dimensions of different indicators. This is achieved by standardizing the initial decision matrix in this embodiment.

[0062] Specifically, all indicator values ​​are classified into two categories: positive indicators and negative indicators. Positive indicators refer to the increase of indicator values, which indicates that the network resilience of the system is stronger, while negative indicators refer to the decrease of indicator values, which indicates that the network resilience of the system is stronger.

[0063] Then, the index value of the jth index of the i-th test object is standardized. If the index value of the jth index of the i-th test object is a positive index, the expression for the standardized processing is:

[0064] In the formula, r ij The data obtained after the index value of the jth index of the i-th test object is standardized. Represents the smallest index value among the index values ​​of the jth index of all test objects, Indicates the maximum index value among the index values ​​of the j-th index of all test objects.

[0065] If the index value of the jth index of the i-th test object is a reverse index, the expression for standardization is:

[0066]

[0067] It should be noted that indicators with different attributes have different impacts on the network resilience assessment results. Therefore, when normalizing them, it is necessary to perform differentiated normalization according to the indicator attributes, which helps to improve the accuracy of the indicator value analysis results of different indicators, and thus improve the reliability of the fusion results when multiple indicators are fused later.

[0068] S202, determining the entropy value of each indicator according to the size of each element in the standardized matrix.

[0069] In this embodiment, before determining the weight of the indicator, the data distribution of the indicator in the entire standardized matrix is ​​analyzed first, that is, the entropy value of each indicator is determined.

[0070] Specifically, each element in the standardized matrix is ​​normalized to obtain the normalized index value of each index of each test object; for any index, the entropy value of the index is calculated according to the normalized index value of the index of each test object. Among them, the process of normalization and entropy value calculation are both prior arts, which are not within the protection scope of the present invention and will not be elaborated in detail here.

[0071] As an example, the calculation formula for the normalized index value of the jth index of the i-th test object may be:

[0072] In the formula, f ij represents the normalized index value of the jth index of the i-th test object, r ij represents the index value of the jth index of the ith test object, and d represents the number of test objects.

[0073] The calculation formula for the entropy value of the jth indicator can be:

[0074] In the formula, Q j It represents the entropy value of the j-th indicator, and ln represents the logarithmic function with the natural constant e as the base.

[0075] S203, determining the entropy weight of each indicator according to the entropy value of each indicator, and using the entropy weight as the weight of the corresponding indicator.

[0076] As an example, the calculation formula for the entropy weight of the jth indicator can be:

[0077] In the formula, w j represents the entropy weight of the jth indicator, Q j represents the entropy value of the jth indicator, and J represents the number of indicators.

[0078] It should be noted that in the process of multi-indicator fusion, using the entropy weight of each indicator as the weight of the corresponding indicator can significantly affect the effectiveness and rationality of the fusion result. The reason is that the entropy weight method is based on the concept of information entropy. By analyzing the variability of the indicator values ​​of each indicator, the importance of each indicator is objectively determined. The entropy weight method can objectively reflect the contribution of each indicator, thereby making the weight distribution more scientific; in the fusion of multiple indicators, the indicator values ​​of each indicator may have uncertainty and noise. Calculating the weights by the entropy weight method can effectively reduce the impact of data uncertainty on the fusion results, making the fusion results more stable; the traditional subjective weighting method is easily affected by the subjective judgment of the decision maker, while the entropy weight method distributes weights according to the characteristics of the data itself, thereby effectively eliminating subjective bias and making the fusion results more fair.

[0079] So far, this embodiment has obtained the weights of various indicators.

[0080] S3, according to the weight of each indicator, the correlation coefficient between indicators is used instead of the interaction degree to determine the fuzzy measurement of different indicator sets.

[0081] In order to overcome the defect that the indicator values ​​of the same indicator in different environments or at different times may be different due to the lack of a standardized evaluation system, it is necessary to determine the fuzzy measurement of different indicator sets.

[0082] The above step S3 can be implemented through steps S301 to S302 (not shown in the figure):

[0083] S301, determining the correlation coefficient between every two indicators according to the indicator value of each indicator of each test object, and then determining the correlation coefficient as the interaction degree.

[0084] Taking any two indicators as an example, the above step S301 can be implemented through steps S311 to S313 (not shown in the figure):

[0085] S311, sorting all indicator values ​​of each test object according to a preset order, and determining a new data set corresponding to the two indicators.

[0086] Specifically, the indicator values ​​of the same indicator of all test objects are taken as input objects, the indicator values ​​of the same indicator are sorted in ascending order, and the sorting position (i.e., rank) of each indicator value is taken as a new data set to obtain a new data set corresponding to each indicator.

[0087] It should be noted that if there are repeated index values ​​in the sorted index value sequence, the repeated index values ​​are assigned the same rank and the average rank is taken. As an example, a sorted index value sequence is {1, 2, 3, 3, 3, 4, 5}, and the ranks of index value 3 are 3, 4 and 5. The average of all ranks corresponding to index value 3 is calculated, that is, (3+4+4) / 3=4, and a new data set corresponding to the sorted index value sequence is obtained, that is, {1, 2, 4, 4, 4, 6, 7}.

[0088] S312: Determine the rank difference value of each data pair according to the new data set corresponding to the two indicators.

[0089] Specifically, the ranks of the same position in the new data set corresponding to the two indicators are combined into data pairs, and the difference between the two ranks in each data pair is calculated, and the difference is used as the rank difference value.

[0090] As an example, the calculation formula for the rank difference value of the Ith data pair can be:

[0091] Where, d I represents the rank difference value of the I-th data pair, represents the rank of the j′th index in the Ith data pair, Represents the rank of the jth indicator in the Ith data pair.

[0092] S313: Determine the correlation coefficient of the two indicators according to the rank difference value of each data pair.

[0093] As an example, the calculation formula of the Spearman correlation coefficient between the j′th indicator and the jth indicator can be:

[0094] In the formula, ρ j′j represents the correlation coefficient between the j′th indicator and the jth indicator, n represents the number of all test objects, Represents the square of the rank difference value of the I-th data pair.

[0095] It should be noted that by referring to the calculation process of the correlation coefficient between the j′th indicator and the jth indicator, the correlation coefficient between every two indicators can be obtained; the interaction degree in the existing fuzzy measurement is greatly affected by subjectivity, and the obtained fuzzy measurement lacks objectivity, so it is necessary to use the correlation coefficient to replace the interaction degree affected by subjectivity, so as to further enhance the accuracy of the multi-indicator fusion results of network resilience.

[0096] S302: Determine fuzzy measures of different indicator sets according to the weights of the indicators and the degree of interaction between every two indicators.

[0097] Firstly, according to the weight of each indicator and the interaction degree between every two indicators, the Mobius transformation coefficient of each indicator and every two indicators is calculated.

[0098] P=∑ j w j +∑ {j′,j} ρ j′j w j′ w j ; In the formula, w j represents the weight of the jth indicator, ρ j′j represents the correlation coefficient between the j′th indicator and the jth indicator, w j′ Represents the weight of the j′th indicator.

[0099] In the formula, m j represents the Mobius transformation coefficient of the jth index, m j′j Represents the Möbius transformation coefficients of the j-th index and the j′-th index.

[0100] Secondly, the fuzzy measures of different indicator sets are calculated based on the Mobius transformation coefficients of each indicator and every two indicators using 2-additive fuzzy measures.

[0101] In this embodiment, among all the indicators, the indicators are combined and divided to obtain indicator sets with different combinations. As an example, the calculation formula of the fuzzy measure of the indicator set K can be:

[0102] u(K)=∑ j∈K m j +∑ {j′,j}∈K m j′j ;

[0103] It should be noted that, by referring to the calculation process of the fuzzy measure of the reference indicator set K, the fuzzy measure of the indicator set of each combination can be obtained.

[0104] Using the correlation coefficient between indicators instead of the interaction degree to determine the fuzzy measurement of different indicator sets can bring a series of beneficial effects, especially in the scenario of multi-indicator decision-making and evaluation. Specifically, the correlation coefficient can quantify the monotonic relationship between different indicators, reflecting the dependence and synergy between them. This quantification helps to understand the mutual influence between indicators more clearly, so as to better consider these relationships in the fuzzy measurement; using the correlation coefficient instead of the traditional interaction degree can more accurately describe the relationship between indicator sets. The correlation coefficient can reflect the real correlation between data, making the fuzzy measurement more accurate and avoiding the deviation caused by improper interaction; by establishing a fuzzy measurement based on the correlation coefficient, more reliable information support can be provided to decision makers, who can more clearly identify which indicators have a significant impact on the results, thereby optimizing resource allocation and strategy formulation.

[0105] So far, this embodiment has obtained fuzzy measures of different indicator sets.

[0106] S4, determine the resilience score of the system to be evaluated based on the fuzzy measurement of each indicator set.

[0107] Specifically, for the system to be evaluated under any type of attack, the Choquet fuzzy integral is used to calculate and analyze the fuzzy measure of each indicator set to obtain the resilience score of the system to be evaluated.

[0108] As an example, the calculation formula for the resilience score of the system to be evaluated can be:

[0109] In the formula, ∫fdu represents the elasticity score of the system to be evaluated. The indicators of the system to be evaluated are sorted according to the normalized indicator values. The sorting result is f(x1)≤f(x2)≤f(x3)≤……≤f(x n ), f(x i ) represents the performance of the i-th indicator after ranking of the system to be evaluated, that is, the standardized indicator value, f(x0)=0, u(A i ) is to consider x i ,x i+1 ,…,x n The importance of A i ={x i ,x i+1 ,…,x n}, that is, the fuzzy measure of the set consisting of the ith to nth indicators after all indicators of the system to be evaluated are sorted.

[0110] It should be noted that by introducing Choquet fuzzy integral, the network resilience assessment results of the system to be evaluated under different attack conditions can be quantified. Compared with the traditional fuzzy measurement determined by the correlation of subjective factors, the fuzzy measurement determined by the correlation between actual indicators in the present invention can effectively improve the reference value and reliability of the resilience score of the system to be evaluated.

[0111] So far, this embodiment has obtained the elasticity score of the system to be evaluated.

[0112] The present invention provides a quantitative analysis method for network resilience using multiple indicators. This method uses objective quantitative analysis and relies entirely on measured data for evaluation, which has the advantages of being objective, accurate, and comparable. Compared with traditional qualitative analysis methods, this method is more scientific and objective, can reduce the impact of subjective factors on the evaluation results, and improve the accuracy and credibility of the evaluation. Through this method, the scientificity, accuracy, and practicality of the results can be further ensured, providing more effective tools and support for the evaluation and optimization of network resilience.

[0113] In order to verify the effectiveness of the present invention, the interaction degree of the economic benefit evaluation of coal mine safety investment based on Choquet fuzzy integral in the existing method is replaced by the correlation coefficient, and the verification process is as follows:

[0114] First, determine several indicators of coal mine safety investment. The schematic diagram of the coal mine safety investment evaluation indicator system is as follows: Figure 2 shown.

[0115] Second, determine the numerical values ​​of various indicators of a coal mine from 2009 to 2019, such as Figure 3 shown.

[0116] Third, in order to unify the dimensions of different indicators, the values ​​of all indicators are standardized to obtain the dimensionless values ​​of various indicators of a coal mine from 2009 to 2019, such as Figure 4 shown.

[0117] Fourth, by calculating the entropy values ​​of different indicators, we can get the entropy values ​​of 8 different indicators, specifically: w1=0.145, w2=0.115, w3=0.0883, w4=0.1022, w5=0.1002, w6=0.1075, w7=0.1922, w8=0.1487.

[0118] Fifth, the Mobius transformation coefficient is determined according to the entropy values ​​of different indicators, as shown in Table 1:

[0119] Table 1

[0120]

[0121] Sixth, the 2-additive fuzzy measure is calculated by the Mobius transform coefficient, as shown in Table 2:

[0122] Table 2

[0123]

[0124] Seventh, compare the evaluation scores of different years, as shown in Table 3:

[0125] Table 3

[0126]

[0127] It can be seen from Table 3 that the Choquet integral value obtained by replacing the correlation degree with the correlation coefficient is more objective, which helps to improve the comparability and credibility of the evaluation results, so as to overcome the fact that the evaluation results are easily affected by the subjective opinions of experts.

[0128] The embodiments described above are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A network resilience multi-index fusion quantitative analysis method, characterized in that: The following steps are involved: Obtaining the index values ​​of several indicators corresponding to the system to be evaluated when it is subjected to several attacks, and establishing an initial decision matrix based on the index values; wherein the system to be evaluated is a system that needs to be evaluated for network resilience; Use the entropy weight method to process the initial decision matrix and determine the weight of each indicator; According to the weight of each indicator, the correlation coefficient between indicators is used instead of the interaction degree to determine the fuzzy measurement of different indicator sets; According to the fuzzy measure of each indicator set, the resilience score of the system to be evaluated is determined.

2. The network resilience multi-index fusion quantitative analysis method according to claim 1 is characterized in that: The entropy weight method is used to process the initial decision matrix and determine the weight of each indicator, including: The initial decision matrix is ​​standardized to obtain a standardized matrix; According to the size of each element in the standardized matrix, the entropy value of each indicator is determined; According to the entropy value of each indicator, the entropy weight of each indicator is determined, and the entropy weight is used as the weight of the corresponding indicator.

3. The network elasticity multi-index fusion quantitative analysis method according to claim 2 is characterized in that: The initial decision matrix is ​​standardized to obtain a standardized matrix, including: If the index value of the jth index of the i-th test object is a positive index, the expression for standardization is: In the formula, r ij The data obtained after the index value of the jth index of the i-th test object is standardized. Represents the smallest index value among the index values ​​of the jth index of all test objects, Represents the maximum index value among the index values ​​of the jth index of all test objects; If the index value of the jth index of the i-th test object is a reverse index, the expression for standardization is: Among them, the test object is the system to be evaluated under different attack conditions.

4. The network elasticity multi-index fusion quantitative analysis method according to claim 3 is characterized in that: Determining the entropy value of each indicator according to the size of each element in the standardized matrix includes: Normalize each element in the standardized matrix to obtain the normalized index value of each index of each test object; For any indicator, the entropy value of the indicator is calculated according to the normalized indicator value of the indicator for each test object.

5. The network elasticity multi-index fusion quantitative analysis method according to claim 4 is characterized in that: The step of calculating the entropy value of the indicator according to the normalized indicator value of each test object includes: The calculation formula for the entropy value of the jth indicator is: In the formula, Q j represents the entropy value of the jth indicator, ln represents the logarithmic function with the natural constant e as the base, and f ij represents the normalized index value of the jth index of the ith test object, and d represents the number of test objects.

6. The network resilience multi-index fusion quantitative analysis method according to claim 4 is characterized in that: Determining the entropy weight of each indicator according to the entropy value of each indicator includes: In the formula, w j represents the entropy weight of the jth indicator, Q j represents the entropy value of the jth indicator, and J represents the number of indicators.

7. The network resilience multi-index fusion quantitative analysis method according to claim 1 is characterized in that: According to the weight of each indicator, the correlation coefficient between indicators is used instead of the interaction degree to determine the fuzzy measure of different indicator sets, including: According to the indicator values ​​of each indicator of each test object, the correlation coefficient between every two indicators is determined, and then the correlation coefficient is determined as the degree of interaction; According to the weight of each indicator and the interaction degree between every two indicators, the fuzzy measure of different indicator sets is determined.

8. The network resilience multi-index fusion quantitative analysis method according to claim 7 is characterized in that: Determining the correlation coefficient between every two indicators according to the indicator values ​​of each indicator of each test object includes: For any two indicators, all indicator values ​​of each test object are sorted according to a preset order to determine a new data set corresponding to the two indicators, where the data in the new data set is the rank of the indicator values; Determine, according to a new data set corresponding to the two indices, a rank difference value of each data pair, wherein the data pair is composed of the ranks of the index values ​​of the two indices; According to the rank difference value of each data pair, the correlation coefficient of the two indicators is determined.

9. The network resilience multi-index fusion quantitative analysis method according to claim 8 is characterized in that: Determining the correlation coefficient of the two indicators according to the rank difference value of each data pair and the number of all test objects includes: In the formula, ρ j′j represents the correlation coefficient between the j′th indicator and the jth indicator, n represents the number of all test objects, Represents the square of the rank difference value of the I-th data pair.

10. The network resilience multi-index fusion quantitative analysis method according to claim 1 is characterized in that: Determining the resilience score of the system to be evaluated based on the fuzzy measure of each indicator set includes: Using Choquet fuzzy integral, the fuzzy measure of each indicator set is calculated and analyzed to obtain the resilience score of the system to be evaluated.

Images