Industrial software resource evaluation method and system based on improved FAHP-TOPSIS method

Abstract

The invention discloses an industrial software resource evaluation method and system based on an improved FAHP-TOPSIS method, and belongs to the technical field of industrial software resource evaluation. The method comprises the following steps: determining an evaluation index system of industrial software resources by using an AHP method; according to score comparison of a plurality of experts for the evaluation index system, obtaining a weight cognitive matrix of each expert for each industrial software resource evaluation index; and analyzing and determining the relative importance of the weight cognitive matrix endowed by each expert in the overall index system through a grey correlation analysis method, and forming a comprehensive weight value of each evaluation index. According to the method, the TOPSIS method is utilized, the industrial software resources are subjected to efficiency sorting and optimization according to the comprehensive weight values, judgment errors caused by professional background differences of experts are effectively avoided, the accuracy and reliability of evaluation are remarkably improved, complex evaluation indexes and interrelations are effectively processed, and the decision making process is made to be more reasonable.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial software resource evaluation, and particularly relates to an industrial software resource evaluation method and system based on an improved FAHP-TOPSIS method. Background Art

[0002] In modern industrial production and management, industrial software plays a crucial role. With the rapid development of technology and the diversification of industrial demands, the evaluation of industrial software resources has become a key link in enterprise informatization construction. The evaluation of industrial software resources refers to the systematic analysis and evaluation of various industrial software using multiple performance indicators, with the aim of screening out the software solutions most suitable for the specific needs of enterprises. However, in the actual evaluation process, due to differences in the professional backgrounds and preferences of evaluation experts, there are different cognitions and understandings of the same indicator, which are prone to large deviations.

[0003] The evaluation objectives of industrial software resources include software compatibility, reliability, usability, technical support, cost-effectiveness, security, and scalability, etc. The evaluation process requires scientific weighing and synthesis of indicators in different dimensions. However, due to the subjectivity of expert scoring, different experts may have different cognitions of the importance and advantages and disadvantages of indicators. For example, some experts may value the powerfulness of functions more and consider high costs reasonable, while others may be more inclined to choose software with high economy, even if it has some deficiencies in certain functions. Such subjective deviations may affect the objectivity and rationality of the final selection during the weighing process. Therefore, in order to reduce the subjective influence of expert scoring and ensure the objective evaluation of optimization objectives, a method combining subjective and objective methods is needed to evaluate industrial software resources. Summary of the Invention

[0004] The purpose of the present invention is to provide an industrial software resource evaluation method and system based on an improved FAHP-TOPSIS method to solve the technical problem that the existing subjective evaluation method affects the evaluation rationality.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions:

[0006] The present invention discloses an industrial software resource evaluation method based on an improved FAHP-TOPSIS method, including the following steps:

[0007] Use the AHP method to determine the evaluation index system of industrial software resources; obtain the weight cognition matrix of each expert for each industrial software resource evaluation index according to the scoring comparison of several experts for the evaluation index system;

[0008] By using the grey relational analysis method, analyze and determine the relative importance of the weight perception matrix given by each expert in the overall index system, and form the comprehensive weight values of each evaluation index;

[0009] Use the TOPSIS method to rank and optimize the efficiency of industrial software resources according to the comprehensive weight values.

[0010] Furthermore, the steps to determine the evaluation index system of industrial software resources are as follows: analyze the relationships between various indicators in industrial software resources, and divide each indicator into a hierarchical structure, including the target layer, the scheme layer, and the criterion layer, and establish the evaluation index system of industrial software resources.

[0011] Furthermore, the specific steps to obtain the weight perception of each expert for each evaluation index of industrial software resources include: construct a judgment matrix based on the scoring comparison of several experts for the evaluation index system, and then obtain the weight perception matrix of each expert for each evaluation index of industrial software resources according to the constructed judgment matrix.

[0012] Furthermore, the process of constructing the judgment matrix includes: invite multiple experts to use the scale method of 0.1 - 0.9 to compare different indicators in the same layer of the evaluation index system of industrial software resources pairwise, and obtain A=(r ij ) n×n ;

[0013] where: A is the judgment matrix, r ij represents the importance scale of indicator i relative to indicator j, n is the number of evaluation indicators, i and j are the i-th and j-th evaluation indicators of n evaluation indicators respectively, i≠j;

[0014] The process of obtaining the weight perception of each expert for each evaluation index of industrial software resources according to the constructed judgment matrix includes:

[0015] Respectively use the arithmetic mean method and the eigenvalue method to calculate the first-level index weights and the corresponding second-level index weights of A k , then multiply the first-level index weights by the corresponding second-level index weight values to obtain the comprehensive weight values corresponding to each second-level index, and after averaging the two, obtain the weight perception matrix of each expert for each evaluation index of industrial software resources.

[0016] Furthermore, the weight perception matrix of the K-th expert is W k =(w k1 , w k2 ,…, w kn ); then the weight perception matrix of m experts for each evaluation index of industrial software resources is W=(W1, W2,..., W k ,..., W m )T ;

[0017] The W k is calculated through ;

[0018] where k represents the k-th expert, and are the comprehensive weight values corresponding to each secondary index obtained by multiplying the weight of the first-level index calculated by the arithmetic mean method and the eigenvalue method by the corresponding weight value of the secondary index, respectively.

[0019] Furthermore, after obtaining the weight recognition matrix, consistency test is also included; the steps of the consistency test are as follows:

[0020] According to the test index, conduct a consistency test on the weight recognition matrix to judge whether the evaluation indexes of the experts for the evaluation index system conform to consistency. If so, proceed to the steps of the grey relational analysis method; if not, reconstruct the judgment matrix;

[0021] The test index is C I and C R , C I is the consistency test index, and C R is the consistency ratio

[0022] The calculation formula is as follows:

[0023]

[0024] where n is the order of the judgment matrix; when C R < 0.1, it indicates that the expert evaluation indexes conform to consistency;

[0025] λ kmax is the maximum eigenvalue λ k obtained by the eigenvalue decomposition method for calculating the judgment matrix A kmax , and A k is the judgment matrix of the k-th expert.

[0026] Furthermore, through the grey relational analysis method, the specific process of analyzing and determining the relative importance of the weight recognition matrix given by each expert in the overall index system includes:

[0027] Construct a correlation matrix for the weight recognition matrix according to the grey relational analysis method, and the grey correlation matrix is B;

[0028]

[0029] where W ki = B ki, where \(k = [1, 2, \ldots, m]\), \(m\) is the number of experts; \(i = [1, 2, \ldots, n]\), \(n\) is the number of evaluation indicators.

[0030] Subsequently, the matrix \(B\) is standardized to obtain the matrix \(C\). The maximum value of each row is selected from the matrix \(C\) to obtain the matrix \(C\). ※ ; Matrix \(C\) ※ is the reference sequence;

[0031] According to the matrix \(C\) ※ Calculate the correlation coefficient between the evaluation information of the \(k\)-th expert on the \(i\)-th indicator and the reference value of the \(i\)-th indicator. The calculation formula is as follows:

[0032]

[0033] where \(\xi\) ik is the correlation coefficient, \(\rho\) is the resolution coefficient, \(\rho\in[0, 1]\), is the \(k\)-th reference value of the reference sequence of matrix \(C\), \(c\) * is the evaluation information of the \(k\)-th expert on the \(i\)-th indicator; ik is the evaluation information of the \(k\)-th expert on the \(i\)-th indicator;

[0034] Subsequently, the average value of the correlation coefficients of each expert is calculated to obtain the correlation degree. The calculation formula is as follows:

[0035]

[0036] where \(\alpha\) k is the correlation coefficient of the weight of the industrial software evaluation indicator of the \(k\)-th expert;

[0037] Finally, the correlation degrees of \(m\) experts \(\alpha = [\alpha_1, \alpha_2, \ldots, \alpha\) k , \ldots, \alpha\) m ;

[0038] Finally, according to the correlation degrees of \(m\) experts, calculate the relative importance of the weight cognitive matrix given by each expert in the overall index system, and form the comprehensive weight value of each evaluation indicator. The calculation formula is as follows:

[0039] \(W\) * =\(\beta\times W\);

[0040] where \(W\) is the weight cognitive matrix of \(m\) experts for each industrial software resource evaluation indicator, \(\beta\) is the relative importance of the weight cognitive matrix given by each expert in the overall index system; \(W\) * is the comprehensive weight value of each evaluation indicator formed by calculating the relative importance of the weight cognitive matrix given by each expert in the overall index system according to the correlation degrees of \(m\) experts.

[0041] Further, β = (β1, β2,..., β k ,..., β m ); It is calculated from β k .

[0042] Among them, β k is the relative importance of the weight cognitive matrix given by the k-th expert in the overall index system, and the calculation formula is:

[0043]

[0044] Further, using the TOPSIS method, the specific steps for sorting and optimizing the efficiency of industrial software resources according to the comprehensive weight value are as follows:

[0045] Use the TOPSIS method to transform the quantitative and qualitative indicators in the evaluation index system of industrial software resources into a single-objective evaluation for analysis, and construct a fuzzy decision matrix D containing qualitative and quantitative data; normalize the fuzzy decision matrix D to obtain a normalized decision matrix E; find the optimal and worst solutions of the minimum, most likely value, and maximum value corresponding to each quantitative and qualitative indicator respectively, and form the optimal solution set E + and the worst solution set E - , and calculate the positive ideal distance d + and the negative ideal distance d - respectively. The adopted formulas are as follows:

[0046]

[0047] Among them, is the distance between the i-th industrial software resource evaluation object and the positive ideal solution, is the distance between the i-th industrial software resource evaluation object and the negative ideal solution, W i * is the comprehensive weight value of each evaluation index, is the optimal value of the j-th index among all evaluation objects, e ij is the actual value of the j-th index of the i-th evaluation object;

[0048] Subsequently, use the formula i = 1, 2,..., m; 0 ≤ C i ≤ 1 to calculate the closeness C i between each industrial software and the optimal and worst solutions. Calculate the defuzzified C through the formula i , and sort C i from large to small to obtain the comprehensive evaluation ranking result of industrial software resources;

[0049] The fuzzy decision matrix D is

[0050] where x ij =(a ij , b ij , c ij ), a ij , b ij , c ij are respectively the minimum value, the most likely value and the maximum value of the evaluation of the i-th index by the evaluation experts.

[0051] The present invention discloses an evaluation system for implementing the above evaluation method.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention discloses an industrial software resource evaluation method based on an improved FAHP-TOPSIS method. This method uses the analytic hierarchy process to determine the weights of each evaluation index of the evaluation experts for industrial software resources, ensuring the comprehensiveness and professionalism of the evaluation; first, the analytic hierarchy process (AHP) is used to determine the weight cognition of each evaluation expert for each industrial software resource evaluation index, and through grey relational analysis, the relative importance of the weights of each expert is analyzed and determined, thereby improving the objectivity of the evaluation. Finally, considering the scores and weight ratios of each expert comprehensively, the comprehensive weights of each evaluation index are formed, and the fuzzy ideal solution method (TOPSIS) is used to construct a fuzzy decision matrix based on the maximum value, the minimum value and the most likely value, improving the flexibility and adaptability of the decision-making process. This method combines the advantages of multiple scoring and quantitative analysis, effectively avoids the judgment errors caused by the differences in the professional backgrounds of experts, significantly enhances the accuracy and reliability of the evaluation, effectively processes complex evaluation indexes and their relationships, and makes the decision-making process more reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flowchart of the industrial software resource evaluation method based on the improved FAHP-TOPSIS method of the present invention;

[0055] Figure 2 is a hierarchical structure diagram of industrial software resource evaluation indexes. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0057] It should be noted that the terms "first", "second", etc. in the description, claims and above-mentioned drawings of the present invention are used to distinguish similar objects, and do not necessarily describe a specific order or sequence. It should be understood that such data used can be interchanged under appropriate circumstances, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily limit to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0058] As shown in Figure 1, the present invention discloses an industrial software resource evaluation method based on an improved FAHP-TOPSIS method, including the following steps:

[0059] Step 1: Establish an evaluation index system

[0060] Before using the AHP method to determine the index weights of the evaluation indexes of industrial software resources, it is necessary to analyze the relationships between various indexes, divide each index into a hierarchical structure, including the target layer, the scheme layer and the criterion layer, and establish an industrial software resource evaluation index system;

[0061] Step 2: Construct a judgment matrix

[0062] Invite m experts to use a scale method of 0.1 - 0.9 to make pairwise comparisons of different indexes in the same layer of the industrial software resource evaluation index system established in Step 1. Suppose there are n evaluation indexes, then the scoring judgment matrix A=(r ij ) n×n of each expert is obtained, where r ij represents the importance scale of index i relative to index j;

[0063] Step 3: Calculate the index weights

[0064] Use the arithmetic mean method and the eigenvalue method to calculate the weights respectively, and average the weights of the two as the final weight value. For the scoring of the kth expert, the arithmetic mean method normalizes the judgment matrix A k column by column, divides each element by the sum of its column, then sums the normalized columns row by row, and finally divides the sum of each row by the corresponding number of elements to obtain the corresponding weights; the eigenvalue decomposition method calculates the maximum eigenvalue λ k of the judgment matrix A kmax , and the eigenvector υ kmax corresponding to λ kmax , and normalizes the eigenvector υ kmaxThe normalization process yields the corresponding weights. Based on the weights of the first-level and second-level indicators obtained by the arithmetic mean method and the eigenvalue method, the weight of each first-level indicator is multiplied by the corresponding weight value of the second-level indicator to obtain the comprehensive weight value corresponding to each second-level indicator and According to the formula Calculate the weight value \(W_{k}\) of each secondary evaluation index of industrial software resources scored by the \(k\)th expert k =(w k1 ,w k2 ,…,w kn ); The weight values \(W=(W_{1},W_{2},...,W k ,...,W m ) T ;

[0065] Step 4: Consistency test

[0066] Perform a consistency test on the weight matrix \(W k in Step 3. The test indicators are the consistency test indicator \(C I and the consistency ratio \(C R . The calculation formulas are as follows:

[0067]

[0068] where \(n\) is the order of the judgment matrix \(A k ;

[0069] When the consistency ratio \(C R <0.1, it indicates that the expert evaluation indicators meet the consistency;

[0070] Step 5: Construct the grey correlation matrix

[0071] Based on the weight matrix \(W\) of each expert for each industrial software evaluation indicator obtained in Step 3, construct the grey correlation matrix

[0072] where \(W ki =B ki , \(k = [1,2,\ldots,m]\), \(m\) is the number of experts; \(i = [1,2,\ldots,n]\), \(n\) is the number of evaluation indicators;

[0073] Step 6: Select the reference sequence

[0074] Perform standardization processing on the grey correlation matrix \(B\) in Step 5 to eliminate the influence between the dimensions and magnitudes of each indicator, obtaining the processed matrix \(C\). Select the maximum value in each row from the matrix \(C\), that is, the maximum value of the weight values scored by each expert for each indicator as the reference sequence \(m\) is the number of experts;

[0075] Step Seven: Calculate the correlation degree α

[0076] Based on the reference sequence c obtained in Step Six * , calculate the correlation coefficient ξ between the evaluation information of the k-th expert on the i-th index and the reference value of the i-th index ik , and the calculation formula is as follows:

[0077]

[0078] In the formula: ρ is the resolution coefficient, ρ ∈ [0, 1], and generally ρ = 0.5;

[0079] Take the average of the correlation coefficients of the industrial software evaluation index weights of each expert to obtain the correlation degree α k , and the calculation formula is as follows:

[0080]

[0081] The correlation degree α of m experts = [α1, α2, …, α k , …, α m ;

[0082] Step Eight: Calculate the comprehensive index weight

[0083] Based on the correlation degree α calculated in Step Seven, calculate the importance β of the judgment information provided in the industrial software resource evaluation scheme by m experts, and combine with the index weight W of m experts obtained in Step Three to obtain the comprehensive weight W * = β × W;

[0084] Step Nine: Construct a fuzzy decision matrix

[0085] In the industrial software evaluation index system, there are both quantitative indexes and qualitative indexes. The TOPSIS method is used to transform the multi-objective problem into a single-objective evaluation for analysis, and a fuzzy decision matrix D containing qualitative data and quantitative data is constructed;

[0086] Step Ten: Solve the positive and negative ideal solutions

[0087] To eliminate the influence of the dimension of the industrial software fuzzy decision matrix, the matrix is normalized to obtain the normalized decision matrix E; respectively find the optimal solution and the worst solution of the minimum value, the most likely value, and the maximum value corresponding to each index, and form the optimal solution set E + and the worst solution set E - , and respectively solve the distances d + and d - from the decision-making goal to the positive and negative ideal solutions; the formula is as follows:

[0088]

[0089] Step Eleven: Sorting of Comprehensive Evaluation Results

[0090] Use i = 1, 2,..., m; 0 ≤ C i ≤ 1 to calculate the closeness C of each industrial software to the optimal solution and the worst solution i , and through calculate the defuzzified C i , and sort C i from large to small to obtain the comprehensive evaluation ranking result of industrial software resources

[0091] Preferably, the target layer of the evaluation index system of industrial software resources in Step One is to select the industrial software resource with the best comprehensive performance from the scheme layer, and the evaluation criterion layer includes function adaptability, service level, user experience, and software quality; function adaptability includes: customization ability, scalability, compatibility, and integration ability; service level includes: security, efficiency, reliability, and flexibility; user experience includes: user support, cost-effectiveness, sustainability, ease of use, rating, and sales volume; software quality includes: stability, response time, throughput, and maintainability

[0092] Preferably, in Step Eight, the importance degree β of the judgment information provided in the evaluation scheme of industrial software resources by the k-th expert is calculated through the grey relational algorithm k , and the formula is as follows

[0093]

[0094] Then the importance degree β of the judgment information of m experts is β = (β1, β2,..., β k ,..., β m )

[0095] Preferably, the judgment weight information W = (W1, W2,..., W k ,..., W m ) T provided by the expert for the secondary evaluation index of industrial software resources obtained through the analytic hierarchy process in Step Three, combined with the importance degree β = (β1, β2,..., β k ,..., β m ) of the judgment information of the expert calculated by the grey relational method in Step Eight, to obtain the final comprehensive weight value W * of the secondary evaluation index, and the calculation formula is: W * = β × W

[0096] Preferably, the fuzzy decision matrix constructed in step nine includes quantitative data and qualitative data, where the quantitative data is obtained from the industrial software platform: including the scores and sales volumes of industrial software; the qualitative data is obtained by the method of expert scoring: experts evaluate each industrial software from sixteen aspects including customization ability, scalability, compatibility, integration ability, security, efficiency, reliability, flexibility, user support, cost-effectiveness, sustainability, ease of use, stability, response time, throughput, and maintainability, and the evaluation indicators are: extremely poor, very poor, poor, relatively poor, average, relatively good, good, very good, excellent, corresponding scales are: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. There are m industrial softwares, and the industrial software resources with a total of n evaluation indicators of quantitative data and qualitative data are evaluated. The finally constructed decision matrix D is:

[0097]

[0098] In the formula: x ij =(a ij , b ij , c ij ), a ij , b ij , c ij are respectively the minimum value, the most likely value, and the maximum value of the evaluation of the i-th indicator by the evaluation expert.

[0099] Preferably, the scores of the quantitative data in the above steps are determined by the method of the 95% confidence interval of the normal distribution; when calculating the confidence interval of the score, the sample mean x is the current score, the standard deviation σ is the square root of the average of the sum of the squares of the differences between each user score and the mean, and the sample size n is the sales volume; the 95% confidence interval CI calculation formula is: In the formula, z = 1.96;

[0100] The sales volume determines the maximum and minimum values by the 95% confidence interval of the t-distribution. The mean x is the average of the sales volumes of the currently participating software for evaluation, and the standard deviation s calculation formula is;

[0101]

[0102] In the formula, n is the number of industrial softwares participating in the evaluation; according to the 95% confidence level and degrees of freedom, the corresponding t value is found from the t-distribution table. The t value changes with the change of the sample size; the confidence interval calculation formula is:

[0103]

[0104] Example 1

[0105] Step 1: As Figure 1As shown, the target layer of the evaluation index system of industrial software resources in the first step is to select the industrial software resource with the optimal comprehensive performance from the scheme layer. The criterion layer includes function adaptability, service level, user experience, and software quality. Function adaptability includes: customization ability, scalability, compatibility, and integration ability. Service level includes: security, efficiency, reliability, and flexibility. User experience includes: user support, cost-effectiveness, sustainability, ease of use, ratings, and sales volume. Software quality includes: stability, response time, throughput, and maintainability.

[0106] According to the determined evaluation index system (such as Figure 2 shown), establish an expert judgment matrix. Invite three experts to compare each pair of indicators at each layer using a scale method of 0.1 - 0.9. The scale meanings are shown in Table 1:

[0107] Table 1 Scale Meanings of Pairwise Comparisons of Each Layer of Indicators by Three Experts

[0108]

[0109] Step 2: Invite multiple experts to use a scale method of 0.1 - 0.9 to make pairwise comparisons of different indicators at the same level in the industrial software resource evaluation index system established in the first step. Suppose there are n evaluation indicators, then the scoring judgment matrix A = (r ij ) n×n is obtained, where r ij represents the importance scale of indicator i relative to indicator j. The five judgment matrices of the first expert are shown in Tables 2 - 6:

[0110] Table 2 Judgment Matrix 1

[0111]

[0112]

[0113] Table 3 Judgment Matrix 2

[0114]

[0115] Table 4 Judgment Matrix 3

[0116]

[0117] Table 5 Judgment Matrix 4

[0118]

[0119]

[0120]

[0121]

[0122] Step 3: Calculate the index weights. Use the arithmetic mean method and the eigenvalue method to calculate the judgment matrix respectively to obtain the relative weights of each index. The arithmetic mean method normalizes the judgment matrix by column, divides each element by the sum of its column, then sums the normalized columns by row, and finally divides each element after summation by n to obtain the corresponding weight vector. According to the obtained weights of the first-level and second-level indicators, multiply the weight of the first-level indicator by the corresponding weight value of the second-level indicator to obtain the weight value corresponding to each second-level indicator. Calculate the weight value W of the first expert for the first second-level evaluation indicator customization ability 11 =W B1 ×W B11 , then the weights given by the first expert for all indicators are

[0123] The calculation results of the arithmetic mean method for the first expert's evaluation are shown in Table 6 as follows:

[0124] Table 6 Calculation results of the arithmetic mean method for the first expert's evaluation

[0125]

[0126] Use the eigenvalue decomposition method to calculate the largest eigenvalue λ of the evaluation judgment matrix A1 of the first expert 1max , and λ 1max The corresponding eigenvector υ 1max , normalize the eigenvector υ 1max to obtain the weight of each evaluation index of industrial software resources considered by the first expert The calculation results of the eigenvalue method are shown in Table 7 as follows:

[0127] Table 7 Calculation results of the eigenvalue method

[0128]

[0129] According to the formula calculate the weight W of each evaluation index of industrial software resources given by the kth expert k =(w k1 , w k2 , …, w kn ); the weight values W of the m experts for the secondary evaluation indicators of industrial software resources = (W1, W2, ..., W k , ..., W m ) T ;

[0130] Sum and calculate the average of the comprehensive weight values calculated by the arithmetic mean method and the eigenvalue method to obtain the weight of the first expert, as shown in Table 8:

[0131] Table 8 Weights of the First Expert

[0132]

[0133]

[0134] Step 4: Conduct a consistency test on the weights and calculate C using the formula R Both are less than 0.1;

[0135] Step 5: Obtain the weight values of the evaluations of each indicator by the three experts according to the above calculation method, and construct the grey correlation matrix B as follows:

[0136]

[0137] Step 6: Since the values in the grey correlation matrix B are all in the range of 0 - 1 and the larger the value, the better, there is no need for standardization; select the largest weight value among all evaluation indicators of each industrial software to form the reference sequence c * =[0.0955, 0.1251, 0.0896];

[0138] Step 7: Through the formula: Calculate the correlation coefficient ξ between the evaluation information of each expert on each indicator and its corresponding reference value as shown in Table 9:

[0139] Table 9 Correlation Coefficient between the Evaluation Information of Each Expert on Each Indicator and Its Corresponding Reference Value

[0140]

[0141] According to the formula Take the mean of the correlation coefficients ξ of each expert to obtain the correlation degree α = [0.5935, 0.4511, 0.6183];

[0142] Step 8: From the correlation degrees obtained in the above steps, through the formula Calculate the importance degree β = [0.3569, 0.2713, 0.3718] of the evaluation information provided in the industrial software resource evaluation scheme by each expert, and perform matrix multiplication of the importance degree of each expert's evaluation information with the grey correlation matrix, i.e., W * =β×W, and the final weight value W of each evaluation indicator can be obtained * As shown in Table 10:

[0143] Table 10 Final Weight Value W *

[0144]

[0145] Step 9: The constructed fuzzy decision matrix for industrial software resource evaluation includes quantitative data and qualitative data. The quantitative data is obtained from the industrial software platform, including the scores and sales volumes of industrial software. The qualitative data is obtained by the method of expert scoring. Experts evaluate each industrial software from sixteen aspects: customization ability, scalability, compatibility, integration ability, security, efficiency, reliability, flexibility, user support, cost-effectiveness, sustainability, ease of use, stability, response time, throughput, and maintainability.

[0146] The scores of quantitative data are determined by the method of the 95% confidence interval of the normal distribution. When calculating the confidence interval of the scores, the sample mean x is the current score, the standard deviation σ is the square root of the average of the sum of the squares of the differences between each user score and the mean, and the sample size n is the sales volume. The formula for the 95% confidence interval CI is: where z = 1.96;

[0147] The sales volume determines the maximum and minimum values by the 95% confidence interval of the t-distribution. The mean x is the average of the current software sales volumes participating in the evaluation, and the formula for the standard deviation s is;

[0148]

[0149] where m is the number of industrial software participating in the evaluation;

[0150] According to the 95% confidence level and degrees of freedom, the corresponding t-value is found from the t-distribution table. The t-value changes with the sample size, and the confidence interval formula is:

[0151]

[0152] The calculated score and sales volume data are shown in Table 11:

[0153] Table 11 Score and sales volume data

[0154]

[0155] The qualitative attributes are obtained by expert scoring, as shown in Table 12:

[0156]

[0157]

[0158] Step 10: Due to the existence of evaluation and sales volume data, etc., which leads to inconsistent dimensions, all the above quantitative and qualitative data are normalized to obtain the normalized decision matrix E. The optimal solution and the worst solution corresponding to the minimum value a are as follows:

[0159]

[0160] The optimal and worst solutions corresponding to the most likely value b are as follows:

[0161]

[0162] The optimal and worst solutions corresponding to the maximum value c are as follows:

[0163]

[0164] Define the distance of each industrial software to the positive ideal solution E + as d + , and the distance to the negative ideal solution E - as d - . The calculation formula is as follows:

[0165]

[0166] The distances of each industrial software to the optimal and worst solutions are obtained as shown in Table 13:

[0167] Table 13 Distances of Industrial Software to the Optimal and Worst Solutions

[0168]

[0169] Step Eleven: Use to calculate the closeness C of each industrial software to the optimal and worst solutions i , and calculate the defuzzified C through i , as shown in Table 14:

[0170] Table 14 Closeness of Each Industrial Software to the Optimal and Worst Solutions

[0171]

[0172] Sort the defuzzified C i from largest to smallest, and the comprehensive evaluation ranking result of industrial software resources is A > B > C.

[0173] The above content is only to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. An industrial software resource evaluation method based on an improved FAHP-TOPSIS method, characterized in that The steps include: Using the AHP method to determine the evaluation index system of industrial software resources; obtaining the weight perception matrix of each expert for each evaluation index of industrial software resources based on the scoring comparison of several experts for the evaluation index system; Through the grey relational analysis method, analyzing and determining the relative importance of the weight perception matrix given by each expert in the overall index system to form the comprehensive weight value of each evaluation index; Using the TOPSIS method to perform efficiency ranking and optimization of industrial software resources according to the comprehensive weight value.

2. The industrial software resource evaluation method based on the improved FAHP-TOPSIS method according to claim 1, wherein The steps to determine the evaluation index system of industrial software resources are: analyzing the relationships between various indicators in industrial software resources, dividing each indicator into a hierarchical structure, including the target layer, the scheme layer, and the criterion layer, and establishing the evaluation index system of industrial software resources.

3. The industrial software resource evaluation method based on the improved FAHP-TOPSIS method according to claim 1, characterized in that The specific steps to obtain the weight perception of each expert for each evaluation index of industrial software resources include: constructing a judgment matrix based on the scoring comparison of several experts for the evaluation index system, and then obtaining the weight perception matrix of each expert for each evaluation index of industrial software resources according to the constructed judgment matrix.

4. The industrial software resource evaluation method based on the improved FAHP-TOPSIS method according to claim 3, wherein, The process of constructing the judgment matrix includes: inviting multiple experts to use the scale method of 0.1-0.9 to make pairwise comparisons of different indicators in the same level of the evaluation index system of industrial software resources, and obtaining A=(r ij ) n×n ; Where: A is the judgment matrix, and r ij represents the importance scale of index i relative to index j, n is the number of evaluation indexes, i and j are the ith and jth evaluation indexes among the n evaluation indexes respectively, and i ≠ j; The process of obtaining the weight perception matrix of each expert for each evaluation index of industrial software resources based on the constructed judgment matrix includes: The arithmetic mean method and the eigenvalue method are respectively used to calculate A k The weights of the first-level indicators and the corresponding second-level indicators are obtained, and then the weight of the first-level indicator is multiplied by the corresponding second-level indicator weight value to obtain the comprehensive weight value corresponding to each second-level indicator. After averaging the two, the weight recognition matrix of each expert for the evaluation indicators of each industrial software resource is obtained.

5. The industrial software resource evaluation method based on the improved FAHP-TOPSIS method according to claim 4, wherein, The weight recognition matrix of the K-th expert is W k =(w k1 , w k2 , …, w kn ); then the weight recognition matrix of m experts for each industrial software resource evaluation index is W = (W1, W2, ..., W k , ..., W m ) T ; The said W k is obtained by calculation; Among them, k represents the k-th expert, and are the comprehensive weight values corresponding to each secondary index obtained by multiplying the weight of the primary index calculated by the arithmetic mean method and the eigenvalue method by the corresponding weight value of the secondary index, respectively.

6. The industrial software resource evaluation method based on the improved FAHP-TOPSIS method according to claim 5, wherein After obtaining the weight perception matrix, consistency check is also included; the steps of the consistency check are: According to the test index, performing consistency check on the weight perception matrix to judge whether the evaluation indexes of the experts for the evaluation index system meet the consistency. If so, proceed to the steps of the grey relational analysis method; if not, reconstruct the judgment matrix; The test index is C I and C R , C I is the consistency test index, and C R is the consistency ratio The calculation formula is as follows: where n is the order of the judgment matrix; C R When <0.1, it indicates that the expert evaluation index meets the consistency; λ kmax Calculate the judgment matrix A by the eigenvalue decomposition method k The maximum eigenvalue λ kmax of which A k is the judgment matrix of the k-th expert 7. A method for evaluating industrial software resources based on the improved FAHP-TOPSIS method according to claim 5, characterized in that The specific process of analyzing and determining the relative importance of the weight perception matrix given by each expert in the overall index system through the grey relational analysis method includes: Constructing a relational matrix for the weight perception matrix according to the grey relational analysis method, and the grey relational matrix is B; Among them, W ki = B ki , k = [1, 2, …, m], where m is the number of experts; i = [1, 2, …, n], where n is the number of evaluation indicators; Subsequently, matrix B is standardized to obtain matrix C, and the maximum value of each row is selected from matrix C to obtain matrix C ※ ; Matrix C ※ is the reference sequence; According to matrix C ※ Calculate the correlation coefficient between the evaluation information of the k-th expert on the i-th index and the reference value of the i-th index. The calculation formula is as follows: Among them, ξ ik is the correlation coefficient, ρ is the resolution coefficient, ρ ∈ [0, 1], is the matrix C * the k-th reference value of the reference sequence, c ik is the evaluation information of the k-th expert on the i-th index; Subsequently, calculating the average value of the correlation coefficients of each expert to obtain the correlation degree, and the calculation formula is as follows: Among them, α k is the correlation coefficient of the weight of the industrial software evaluation index of the k-th expert; Finally, the relevance degrees of m experts are obtained as α = [α1, α2, …, α k , …, α m ; Finally, calculating the relative importance of the weight perception matrix given by each expert in the overall index system according to the correlation degrees of m experts to form the comprehensive weight value of each evaluation index, and the calculation formula is as follows: W * = β × W; Among them, \(W\) is the weight perception matrix of \(m\) experts for each evaluation index of industrial software resources, and \(\beta\) is the relative importance of the weight perception matrix given by each expert in the overall index system; \(W\) * is the comprehensive weight value of each evaluation index formed according to the relative importance of the weight perception matrix given by each expert calculated based on the correlation degree of \(m\) experts in the overall index system.

8. The industrial software resource evaluation method based on the improved FAHP-TOPSIS method according to claim 7, characterized in that The β = (β1, β2,..., β k ,..., β m ); is calculated from β k ; where β k is the relative importance of the weight recognition matrix assigned by the k-th expert in the overall index system, and the calculation formula is:

9. The industrial software resource evaluation method based on the improved FAHP-TOPSIS method according to claim 7, wherein The specific steps of using the TOPSIS method to perform efficiency ranking and optimization of industrial software resources according to the comprehensive weight value are: Using the TOPSIS method, the quantitative and qualitative indicators in the evaluation index system of industrial software resources are transformed into single-objective evaluation for analysis, and a fuzzy decision matrix D containing qualitative and quantitative data is constructed; the fuzzy decision matrix D is normalized to obtain the normalized decision matrix E; the optimal and worst solutions of the minimum value, the most likely value, and the maximum value corresponding to each quantitative and qualitative indicator are found respectively, and the optimal solution set E + and the worst solution set E - are obtained, and the distances d + from the decision-making objective to the positive ideal solution and the negative ideal solution d - are calculated respectively using the following formulas: Among them, is the distance between the i-th industrial software resource evaluation object and the positive ideal solution, is the distance between the i-th industrial software resource evaluation object and the negative ideal solution, W i * is the comprehensive weight value of each evaluation index, is the optimal value of the j-th index among all evaluation objects, e ij is the actual value of the j-th index of the i-th evaluation object; Subsequently, the formula 0 ≤ C i ≤ 1 is used to calculate the closeness C between each industrial software and the optimal solution and the worst solution i , and the defuzzified C is calculated through the formula i , and C i is sorted from large to small to obtain the comprehensive evaluation ranking result of industrial software resources; The fuzzy decision matrix D is where x ij =(a ij , b ij , c ij ), a ij , b ij , c ij are the minimum value, the most likely value, and the maximum value of the evaluation by the evaluation expert for the i-th index, respectively.

10. An industrial software resource evaluation system based on the improved FAHP-TOPSIS method, characterized in that, Used to implement the evaluation method described in any one of claims 1 to 9.

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