An Improved TOPSIS Material Selection Method and System Based on Information Entropy

Abstract

This invention belongs to the field of material selection technology, and specifically discloses an improved TOPSIS material selection method and system based on information entropy. It includes: calculating the information entropy of each material attribute to obtain the weight coefficients of each attribute; using the TOPSIS method, determining positive and negative ideal solutions based on the weight coefficients, and calculating the distance between each candidate material scheme and the fuzzy positive and negative ideal solutions to obtain the relative proximity; and determining the optimal material scheme based on the relative proximity. The calculation method for positive and negative ideal solutions is as follows: constructing a weighted standardized matrix based on the weight coefficients, then calculating the standard deviation of each attribute based on the weighted standardized matrix, and introducing triangular fuzzy numbers to construct the fuzzy positive and negative ideal solutions. This invention effectively improves the scientificity and reliability of material selection, is applicable to the optimal decision-making of multi-attribute materials under complex working conditions, and has significant advantages, especially in lightweight design in fields such as automotive engineering.

Description

Technical Field

[0001] This invention belongs to the field of material selection technology, and more specifically, relates to an improved TOPSIS material selection method and system based on information entropy. Background Technology

[0002] In mechanical engineering design, material selection is crucial, as its decisions directly impact the mechanical properties, manufacturing economy, and lightweighting level of the structure. With the continuous development of mechanical engineering, single materials often fail to meet the diverse needs of mechanical structures under complex working conditions, making multi-material selection a key step in optimizing and improving the performance of mechanical structures. However, given the various working conditions and numerous material properties faced by mechanical structures in actual operation, how to scientifically and rationally select multiple materials has become an important issue.

[0003] Currently, existing material selection methods in engineering practice face several key problems. On the one hand, the subjective weighting of attributes suffers from significant bias. Traditional subjective weighting methods (such as expert scoring) struggle to eliminate human error and fail to objectively reflect the contribution of material attributes to decision-making. On the other hand, the quantification of multidimensional attribute coupling relationships is insufficient. For example, the traditional TOPSIS method uses Euclidean distance to calculate the distance between the proposed solution and the ideal solution, completely ignoring the correlation between material attributes. Furthermore, it is highly susceptible to the influence of data dimensions and is very sensitive to outliers, leading to deviations in distance calculations and consequently affecting the accuracy of material selection. Therefore, a more scientific and accurate material selection method is urgently needed to address these issues. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides an improved TOPSIS material selection method and system based on information entropy, the purpose of which is to effectively improve the scientificity and reliability of material selection.

[0005] To achieve the above objectives, according to one aspect of the present invention, an improved TOPSIS material selection method based on information entropy is proposed, comprising the following steps:

[0006] S1. Calculate the information entropy of each property of the material, and then obtain the weight coefficient of each property.

[0007] S2. Using the TOPSIS method, positive and negative ideal solutions are determined based on weight coefficients, and the distance between each candidate material scheme and the fuzzy positive and negative ideal solutions is calculated to obtain the relative closeness. The optimal material scheme is determined based on the relative closeness.

[0008] The calculation method for positive and negative ideal solutions is as follows: construct a weighted standardization matrix based on the weight coefficients, then calculate the standard deviation of each attribute based on the weighted standardization matrix, and introduce triangular fuzzy numbers to construct fuzzy positive and negative ideal solutions.

[0009] As a further optimization, a weighted standardized matrix is ​​constructed based on the weighting coefficients, specifically as follows:

[0010] V = (v ij ) m×n

[0011] v ij =w j z ij

[0012] Among them, w j The weight coefficient of the j-th attribute is represented by m; m is the number of material types, and n is the number of material attributes; V represents the weighted normalization matrix, Z represents the normalization matrix, and v ij z ij These represent the corresponding values ​​of the i-th material in matrices V and Z for the j-th attribute, respectively.

[0013] As a further optimization, triangular fuzzy numbers are introduced to construct fuzzy positive and negative ideal solutions, specifically:

[0014] For benefit-type attributes where a larger value is better:

[0015] The most likely value of the ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy positive ideal solution Most likely value of negative ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy negative ideal solution L represents the preset fuzzy interval width parameter, σ j This represents the standard deviation of the j-th attribute;

[0016] For cost-type attributes where smaller values ​​are preferred:

[0017] The most likely value of the ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy positive ideal solution Most likely value of negative ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy negative ideal solution

[0018] Fuzzy positive ideal solution for all attributes Fuzzy Negative Ideal Solution By combining them separately, we obtain the overall fuzzy positive ideal solution and fuzzy negative ideal solution.

[0019] As a further preferred option, the width of the fuzzy interval is set to 1.5 times the standard deviation, i.e., L = 1.5.

[0020] As a further optimization, the distance between each candidate material scheme and the fuzzy positive and negative ideal solution is calculated using Mahalanobis distance.

[0021] As a further preferred method, the distance between each candidate material scheme and the fuzzy positive and negative ideal solutions is calculated using Mahalanobis distance, including:

[0022] For fuzzy positive ideal solutions:

[0023]

[0024] Among them, a + b + c + Let represent the lower bound, most likely value, and upper bound vector of the fuzzy positive ideal solution, respectively; They represent v respectively i With a + b + c + Mahalanobis distance, v i Let S represent the i-th candidate material scheme, and let S represent the covariance matrix.

[0025] For fuzzy negative ideal solutions:

[0026]

[0027] Among them, a - b - c - Let represent the lower bound, most likely value, and upper bound vector of the fuzzy negative ideal solution, respectively; They represent v respectively i With a - b - c - Mahalanobis distance;

[0028] Then, by weighting, we obtain the final distance to the fuzzy positive and negative ideal solutions:

[0029]

[0030] in, They represent v respectively i Distance to the fuzzy positive ideal solution and the fuzzy negative ideal solution; ω a ω b ω c The weights ω represent the lower bound, the most likely value, and the upper bound, respectively. a +ω b +ω c =1.

[0031] As a further preferred option, the covariance matrix S is calculated as follows:

[0032]

[0033] in, Let λ be the mean vector of the weighted normalized matrix, λ be the regularization parameter, and I be the identity matrix.

[0034] As a further preferred embodiment, step S1 includes the following steps:

[0035] S11. Construct the original decision matrix X = (x ij ) m×n Where m is the number of material types, n is the number of material properties, and x ij This represents the value of the i-th material in X on the j-th attribute;

[0036] S12. The original decision matrix is ​​standardized using a linear transformation method to obtain the standardized matrix Z = (z ij ) m×n , z ij This represents the value of the i-th material in Z on the j-th attribute;

[0037] S13. Based on the normalized matrix Z, calculate the proportion of the i-th material under the j-th attribute. Where ε is a very small positive number;

[0038] S14, According to specific gravity p ij Calculate the information entropy of the j-th attribute. And the difference coefficient g was obtained. j =1-e j ;

[0039] S15. Calculate the weight coefficient of the j-th attribute. And satisfy

[0040] As a further preferred option, when determining the normalization matrix in step S12:

[0041] For benefit-type attributes where a larger value is better:

[0042]

[0043] For cost-type attributes where smaller values ​​are preferred:

[0044]

[0045] According to another aspect of the present invention, an improved TOPSIS material selection system based on information entropy is provided, including a processor for executing the above-described improved TOPSIS material selection method based on information entropy.

[0046] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0047] 1. This invention determines the weights of each material attribute based on the information entropy method, overcoming the shortcomings of traditional methods that rely on experience and subjective judgment, and objectively reflects the importance of material attributes. Furthermore, it introduces triangular fuzzy numbers that combine attribute standard deviations into the TOPSIS method to construct positive and negative ideal solutions, fully considering the uncertainties in actual decision-making, making the decision results more consistent with the actual situation. Compared with the traditional TOPSIS method, it can more comprehensively and systematically select multi-attribute materials, effectively improving the scientificity and reliability of material selection.

[0048] 2. Using Mahalanobis distance for similarity measurement effectively eliminates the influence of material property correlation, dimensions, and outliers, significantly improving the accuracy and reliability of material selection decisions. Attached Figure Description

[0049] Figure 1 This is a flowchart of the improved TOPSIS material selection method based on information entropy, as described in an embodiment of the present invention.

[0050] Figure 2 This is a flowchart of the method for determining material property weights based on information entropy in an embodiment of the present invention;

[0051] Figure 3 This is a flowchart of the improved TOPSIS material selection method according to an embodiment of the present invention;

[0052] Figure 4 This is a schematic diagram of a 100% frontal collision scenario for the anti-collision beam according to an embodiment of the present invention;

[0053] Figure 5 This is a probe diagram showing the deformation of the floor beam before a 100% frontal collision under the comparative example of the all-steel structure anti-collision beam of the present invention.

[0054] Figure 6 This is a probe diagram of the deformation of the floor beam before a 100% frontal collision under the condition of the anti-collision beam after material selection in an embodiment of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0056] This invention provides an improved TOPSIS material selection method based on information entropy, such as... Figure 1 As shown, it includes the following steps:

[0057] S1. Construct a material selection decision matrix, including material schemes and the values ​​of each material attribute, standardize them, calculate the information entropy of each material attribute, and calculate the weight coefficient of each attribute.

[0058] like Figure 2 As shown, the specific steps include the following:

[0059] S11. Constructing the initial decision matrix: Based on material performance parameters and operating condition requirements, construct the initial decision matrix X = (x ij ) m×n Where m is the number of material types, n is the number of material properties, and x ij Let be the value of the i-th material on the j-th attribute.

[0060] S12. Standardization Process: The original decision matrix is ​​standardized using a linear transformation method to obtain the standardized matrix Z = (z... ij ) m×n Among them, the benefit-type attribute is classified as follows: Processing, cost-type attributes by The process yields a standardized matrix table; benefit-type attributes are those with larger values, while cost-type attributes are those with smaller values.

[0061] S13. Calculate the proportion: For the standardized matrix Z, calculate the proportion of the i-th material under the j-th attribute. Where ε = 10 -6 It is a very small positive number.

[0062] S14. Calculate information entropy and difference coefficient: Based on p ij Calculate the information entropy of the j-th attribute. Obtain the information entropy table and the difference coefficient g. j =1-e j .

[0063] S15. Determine attribute weights: Calculate attribute weights satisfy

[0064] S2. Substitute the weighting coefficients into the TOPSIS method, introduce triangular fuzzy numbers to construct fuzzy representations of positive and negative ideal solutions, calculate the Mahalanobis distance between each material scheme and the positive and negative ideal solutions, then calculate the relative proximity, and select the scheme with the closest relative proximity to 1 as the optimal material scheme.

[0065] like Figure 3 As shown, the specific steps include the following:

[0066] S21. Construct the weighted normalization matrix: Based on the normalization matrix Z and the attribute weights w j Calculate the weighted standardized matrix V = (v ij ) m×n This yields a weighted standardized matrix table, where v ij =w j z ij .

[0067] S22. Constructing the triangular fuzzy positive and negative ideal solutions: Introduce the triangular fuzzy number A = (a, b, c), and calculate the standard deviation σ of each attribute based on the weighted standardization matrix. j Constructing fuzzy positive ideal solutions and negative ideal solution Then, the fuzzy positive ideal solution for all attributes By combining these, we obtain the overall fuzzy positive ideal solution V. + fuzzy negative ideal solution for all attributes Combining these, we obtain the overall fuzzy negative ideal solution V. - .

[0068] Furthermore, for benefit-type attributes, the most likely value of the positive ideal solution is the attribute's maximum value. Thus, the lower limit is obtained. upper limit Then the fuzzy positive ideal solution

[0069] The most likely value of a negative ideal solution is the minimum value of the attribute. Thus, the lower limit is obtained. upper limit Then the fuzzy negative ideal solution

[0070] For cost-type attributes, the most likely value of the positive ideal solution is the minimum value of the attribute. Thus, the lower limit is obtained. upper limit Then the fuzzy positive ideal solution

[0071] The most likely value of a negative ideal solution is the maximum value of the attribute. Thus, the lower limit is obtained. upper limit Then the fuzzy negative ideal solution

[0072] Where L represents the preset fuzzy interval width parameter, and in this embodiment, the fuzzy interval width is set to 1.5 times the standard deviation σ. j Therefore, we take L = 1.5.

[0073] S23. Mahalanobis distance calculation: Calculate the data covariance matrix S and add a regularization term, then use Mahalanobis distance. Calculate the fuzzy positive ideal solution V for each material scheme. + and negative ideal solution V - The distances at the lower bound (a), the most likely value (b), and the upper bound (c) are then weighted to obtain the Mahalanobis distances of the final positive and negative ideal solutions. and

[0074] Specifically, for fuzzy positive ideal solutions:

[0075]

[0076] Among them, a + b + c + Let represent the lower bound, most likely value, and upper bound vector of the fuzzy positive ideal solution, respectively; They represent v respectively i With a + b + c + Mahalanobis distance, v i Let S represent the i-th candidate material scheme, and let S represent the covariance matrix.

[0077] For fuzzy negative ideal solutions:

[0078]

[0079] Among them, a - b - c - Let represent the lower bound, most likely value, and upper bound vector of the fuzzy negative ideal solution, respectively; They represent v respectively i With a - b - c - Mahalanobis distance;

[0080] Then, by weighting, we obtain the final distance to the fuzzy positive and negative ideal solutions:

[0081]

[0082] Where, ω a ω b ω c The weights ω represent the lower bound, the most likely value, and the upper bound, respectively. a +ω b +ω c =1; In this embodiment, we take...

[0083] Furthermore, the covariance matrix S is calculated as follows:

[0084]

[0085] in The mean vector of the weighted standardized matrix, λ = 10 -5 Here, I is the regularization parameter, and I is the identity matrix.

[0086] S24. Relative Proximity Ranking: Based on... Calculate the relative similarity, rank the candidate materials, and select the optimal material.

[0087] This invention effectively improves the scientific nature and reliability of material selection, and is applicable to the optimal decision-making of multi-attribute materials under complex working conditions. It has significant advantages, especially in lightweight design in fields such as automotive engineering, and provides an efficient solution for multi-material collaborative optimization.

[0088] The following are specific examples:

[0089] A frontal collision test was conducted on the front bumper beam structure of the car, such as... Figure 4 As shown, the initial material is structural steel, and a finite element mesh is used. The front floor beam is fixed on both sides. A rigid wall with a mass of 150 kg is set to impact the anti-collision beam with an initial velocity of 50 km / h. The X-direction deformation at the front floor beam is as follows. Figure 5 As shown, this represents the intrusion of the cab under this collision condition, with a maximum deformation of 63.866 mm.

[0090] Using the method of this invention for specific material selection:

[0091] S11. Constructing the Initial Decision Matrix: Based on material performance parameters and operating condition requirements, an initial decision matrix is ​​constructed. Taking the material selection of a car's front bumper beam as an example, eight common metallic materials are listed, and typical grades of each material are selected: carbon steel (Q235), duplex steel (DP600), hot-formed steel (22MnB5), martensitic steel (MS1500), aluminum alloy 5 series (5052-H32), aluminum alloy 6 series (6061-T6), magnesium alloy (AZ31B), and titanium alloy (Ti-6Al-4V). The initial decision matrix for material selection is shown in Table 1.

[0092] Table 1 Initial Decision Matrix for Material Selection

[0093]

[0094]

[0095] Where u1 represents density (g / cm³) 3u2 represents Young's modulus (GPa), u3 represents yield strength (MPa), u4 represents tensile strength (MPa), u5 represents elongation (%), u6 represents impact toughness (J, Charpy V), u7 represents machinability, and u8 represents specific energy absorption (kJ / kg). Density is defined as a cost-related attribute, while the others are benefit-related attributes.

[0096] S12. Standardization process: The original decision matrix is ​​standardized using the linear transformation method to obtain the standardized matrix; the generated material property standardized matrix is ​​shown in Table 2.

[0097] Table 2 Standardization Matrix

[0098]

[0099] S13. Calculate the specific gravity: The specific gravity of the material is calculated for the standardized matrix Z, as shown in Table 3.

[0100] Table 3 Material Specific Gravity Table

[0101]

[0102]

[0103] S14. Calculate information entropy and difference coefficient: The information entropy results are shown in Table 4.

[0104] Table 4. Entropy Table of Material Properties

[0105]

[0106] S15. Determine attribute weights: Calculate attribute weight coefficients based on the difference coefficients to obtain the material attribute weight table as shown in Table 5.

[0107] Table 5 Material Property Weighting Table

[0108]

[0109] S21. Construct the weighted normalization matrix: Based on the normalization matrix Z and the attribute weights w j The weighted standardized matrix is ​​calculated as shown in Table 6.

[0110] Table 6 Weighted Standardization Matrix (10) -2 )

[0111]

[0112]

[0113] S22. Constructing fuzzy positive and negative ideal solutions: Introduce triangular fuzzy numbers A = (a, b, c), and calculate the standard deviation σ of each attribute based on the weighted standardization matrix. j Constructing fuzzy positive ideal solutions and negative ideal solution The width of the fuzzy interval is 1.5 times the standard deviation of the attribute value. The fuzzy positive and negative ideal solutions are shown in Table 7.

[0114] Table 7 Fuzzy Positive and Negative Ideal Solutions

[0115]

[0116] S23. Mahalanobis distance calculation: Calculate the data covariance matrix S and add a regularization term. Use Mahalanobis distance to calculate the distance between the material scheme and the fuzzy positive and negative ideal solutions, and then consider the weights. The final positive and negative ideal solutions and their Mahalanobis distances are obtained. and The calculation results are shown in Table 8.

[0117] Table 8. Calculation of Mahalanobis Distance for Positive and Negative Ideal Solutions

[0118]

[0119] S24. Relative Proximity Ranking: The calculated relative proximity is shown in Table 9. The candidate materials were ranked, and the optimal material was selected. The best material for the front bumper beam of the automobile was found to be 6061-T6.

[0120] Table 9 Relative Proximity Calculation Table

[0121]

[0122] To demonstrate the superiority of the method of this invention, a comparative verification was conducted with the traditional TOPSIS method. Without introducing the triangular fuzzy ideal solution and Mahalanobis distance metric, the relative proximity results calculated based on Euclidean distance are shown in Table 10. The optimal material for the traditional TOPSIS method is 22MnB5.

[0123] Table 10. Results of Relative Proximity Calculation Using Traditional TOPSIS Method

[0124]

[0125] Compared to 22MnB5 hot-formed steel, 6061-T6 aluminum alloy offers significant advantages as a material for automotive front bumper beams in terms of lightweighting, energy absorption performance, processing adaptability, and overall performance under various conditions: its density is only 2.7 g / cm³. 3 It is approximately 22MnB5 (7.85g / cm³). 3The weight reduction of the anti-collision beam component by approximately 65.5% (one-third of the weight of the original material) effectively lowers the overall vehicle weight and improves the driving range and handling performance of new energy vehicles. During a collision, the 6061-T6, with its excellent plastic deformation capacity and a specific energy absorption value of 60kJ / kg (higher than 30kJ / kg for 22MnB5), effectively absorbs collision energy through plastic deformation, reducing intrusion into the passenger compartment. Furthermore, with a yield strength of 276MPa and a tensile strength of 310MPa, it achieves a safety factor of 11, meeting high-strength safety requirements. In addition, the 6061-T6 supports mature processes such as hydroforming and friction stir welding, making it suitable for complex cross-section designs. It requires no additional anti-corrosion treatment, reducing manufacturing difficulty and maintenance costs. Its overall performance is comparable to that of the Tesla Model 1. The effectiveness of this invention has been validated in practical applications of models such as the S / X, NIO ES8, Xiaomi SU7, and BYD Han / Yuan PLUS. It particularly meets the dual requirements of lightweighting and high crashworthiness for new energy vehicles. In contrast, the high density and processing limitations of 22MnB5 make it more suitable for secondary structures, while 6061-T6 demonstrates a better balance of comprehensive performance in anti-collision beam design, showcasing the effectiveness of the method of this invention.

[0126] The same method was used to select materials for the front longitudinal beam, the rear longitudinal beam, and the front floor crossbeam. The selected materials were 6061-T6, 22MnB5, and 22MnB5, respectively. Based on the above material selection results, the same working condition simulation was performed again. The deformation in the X direction at the front floor crossbeam was as follows: Figure 6 As shown, the maximum deformation is 9.736 mm; under the all-steel structure before material selection, the deformation in the X direction of the inner side of the front floor crossbeam is 63.866 mm. Compared with the all-steel baseline structure, the maximum deformation of the optimized anti-collision beam remains stable, and the deformation of the inner side of the front floor crossbeam, i.e., the amount of cab intrusion under collision conditions, is significantly reduced by 84.8%, achieving a weight reduction of 5.27 kg, which further verifies the effectiveness of the material selection method proposed in this invention.

[0127] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An improved TOPSIS material selection method based on information entropy, characterized in that, Includes the following steps: S1. Calculate the information entropy of each property of the material, and then obtain the weight coefficient of each property. S2. Using the TOPSIS method, positive and negative ideal solutions are determined based on weight coefficients, and the distance between each candidate material scheme and the fuzzy positive and negative ideal solutions is calculated to obtain the relative closeness. The optimal material scheme is determined based on the relative closeness. The calculation method for positive and negative ideal solutions is as follows: construct a weighted standardization matrix based on the weight coefficients, then calculate the standard deviation of each attribute based on the weighted standardization matrix, and introduce triangular fuzzy numbers to construct fuzzy positive and negative ideal solutions; Construct a weighted standardized matrix based on the weighting coefficients, specifically as follows: wherein, represents a weight coefficient of the j th attribute; is the number of material types, is the number of material attributes; V represents a weighted standardization matrix, and Z represents a standardization matrix, , respectively represent the corresponding value of the th material in the th attribute in the matrix V and Z. By introducing triangular fuzzy numbers, we construct fuzzy positive and negative ideal solutions, specifically as follows: For benefit-type attributes where a larger value is better: The most likely value of the ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy positive ideal solution The most likely value of the negative ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy negative ideal solution L represents the preset fuzzy interval width parameter. Indicates the first Standard deviation of each attribute; For cost-type attributes where smaller values ​​are preferred: The most likely value of the ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy positive ideal solution The most likely value of the negative ideal solution Thus, the lower limit is obtained. upper limit Then the fuzzy negative ideal solution ; Fuzzy positive ideal solution for all attributes Fuzzy negative ideal solution By combining them separately, we obtain the overall fuzzy positive ideal solution and fuzzy negative ideal solution.

2. The improved TOPSIS material selection method based on information entropy as described in claim 1, characterized in that, The width of the fuzzy interval is set to 1.5 times the standard deviation, i.e., L=1.

5.

3. The improved TOPSIS material selection method based on information entropy as described in claim 1, characterized in that, The distance between each candidate material scheme and the fuzzy positive and negative ideal solution is calculated using Mahalanobis distance.

4. The improved TOPSIS material selection method based on information entropy as described in claim 3, characterized in that, The distance between each candidate material scheme and the fuzzy positive and negative ideal solutions of the structure is calculated using Mahalanobis distance, including: For fuzzy positive ideal solutions: in, , , Let represent the lower bound, most likely value, and upper bound vector of the fuzzy positive ideal solution, respectively; , , They represent and , , Mahalanobis distance, Indicates the first i There are 1 candidate material schemes, where S represents the covariance matrix; For fuzzy negative ideal solutions: in, , , Let represent the lower bound, most likely value, and upper bound vector of the fuzzy negative ideal solution, respectively; , , They represent and , , Mahalanobis distance; Then, by weighting, we obtain the final distance to the fuzzy positive and negative ideal solutions: in, , They represent Distance to fuzzy positive ideal solution and fuzzy negative ideal solution; , , These are the weights for the lower bound, the most likely value, and the upper bound, respectively. .

5. The improved TOPSIS material selection method based on information entropy as described in claim 4, characterized in that, The formula for calculating the covariance matrix S is: in, The mean vector of the weighted standardized matrix. For regularization parameters, It is an identity matrix.

6. The improved TOPSIS material selection method based on information entropy as described in any one of claims 1-5, characterized in that, Step S1 includes the following steps: S11. Construct the original decision matrix ,in For the number of material types, For the quantity of material properties, Indicates the first in X The material in the first The possible values ​​for each attribute; S12. The original decision matrix is ​​standardized using a linear transformation method to obtain the standardized matrix. , Indicates the first of Z The material in the first The possible values ​​for each attribute; S13, Based on Standardized Matrix Calculate the first The first attribute The specific gravity of the material ,in It is a very small positive number; S14. According to specific gravity Calculate the first j Information entropy of each attribute And obtain the difference coefficient. ; S15, Calculate the... j The weight coefficients of each attribute And satisfy .

7. The improved TOPSIS material selection method based on information entropy as described in claim 6, characterized in that, When determining the normalization matrix in step S12: For benefit-type attributes where a larger value is better: ； For cost-type attributes where smaller values ​​are preferred: 。 8. An improved TOPSIS material selection system based on information entropy, characterized in that, Includes a processor for executing the improved TOPSIS material selection method based on information entropy as described in any one of claims 1-7.

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