Railway engineering low-carbon construction evaluation method based on improved G2-AEW-UMT model

Abstract

The invention discloses a railway engineering low-carbon construction evaluation method based on an improved G2-AEW-UMT model, and relates to the technical field of railway low-carbon construction, and the method comprises the steps: constructing a railway engineering low-carbon construction evaluation index system; collecting index system sample data, and performing dimensionless preprocessing on the index system sample data by using an extreme value standardization method to obtain an index set; constructing a subjective and objective fusion dynamic weight distribution mechanism based on the index set; and evaluating the low-carbon construction grade of the railway engineering in combination with an unascertained measurement theory and a confidence identification criterion. According to the method, accurate rating of the low-carbon level in the construction stage is achieved, an innovative methodological tool is provided for improving the standardization level of railway engineering green construction, and the core problem that an existing evaluation system is insufficient in operability is effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of railway low-carbon construction, and in particular to a railway engineering low-carbon construction evaluation method based on an improved G2-AEW-UMT model. Background Art

[0002] As a key component of human production, transportation projects consume nearly one-third of the world's energy during their construction and operation. Railway transportation, the core of my country's transportation system, consumes vast quantities of resources and energy during construction and releases CO2 into the environment, posing significant challenges to environmental sustainability.

[0003] Numerous scholars have conducted low-carbon evaluation research focusing on energy consumption and CO2 emissions within green construction evaluation standards, and have proposed a series of carbon emission evaluation indicators. However, multidimensional evaluation standards for low-carbon construction in railway projects still face significant systematization challenges, particularly in determining indicator weights and constructing evaluation models. Current evaluation methods primarily rely on traditional weighting models, such as the Analytic Hierarchy Process (AHP) and the Entropy Weight Method (EWM), which suffer from significant subjective weighting bias, insufficient quantitative evaluation accuracy, and a lack of diagnostic accuracy for key influencing factors. my country's railway construction sector is rapidly developing, characterized by both large project volumes and significant energy and material consumption. This sector is a significant resource consumer and a key sector for achieving the "dual carbon" goals. Therefore, strengthening construction management, promoting low-carbon construction, and exploring its development direction are crucial for achieving sustainable development within the context of the "dual carbon" goals. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention provides a low-carbon construction evaluation method for railway projects based on the improved G2-AEW-UMT model, which solves the problems of insufficient operability, insufficient systematization, and insufficient evaluation accuracy of the existing evaluation system.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model, comprising: Establish an evaluation index system for low-carbon construction of railway projects; Collect the sample data of the indicator system, and use the extreme value standardization method to perform dimensionless preprocessing on the sample data of the indicator system to obtain the indicator set; Based on the improved G2 method of indicator set + anti-entropy weight method AEW, a dynamic weight allocation mechanism integrating subjective and objective factors is constructed; The low-carbon construction level of railway projects is evaluated by combining the Unascertained Measurement Theory (UMT) and the confidence identification criterion. Among them, the improved G2 method + anti-entropy weight method AEW + unascertained measure theory UMT constitutes the improved G2-AEW-UMT model.

[0006] Furthermore, the specific method for constructing a low-carbon construction evaluation index system for railway projects is as follows: Identify direct and indirect carbon emission sources during railway construction by combining bibliometric analysis with engineering field research; According to the identification results, a hierarchical evaluation index system was constructed with construction machinery, construction materials, two zones and three sites, organization and management, and ecological environment as the criterion layers; Clarify the measurement method of each indicator, determine the evaluation value of each indicator based on the internationally accepted grading model and industry practice, and form a low-carbon construction level grading standard.

[0007] Furthermore, the specific method of constructing a dynamic weight allocation mechanism for subjective and objective fusion based on the indicator set through the improved G2 method + anti-entropy weight method AEW is as follows: The improved G2 method is used to determine the subjective weight; the anti-entropy weight method is used to determine the objective weight; and the Lagrange optimal multiplier method is used to determine the subjective and objective comprehensive weight.

[0008] Furthermore, the specific method of determining the subjective weight using the improved G2 method is as follows: Sort the indicators in the indicator set and calculate the Gini coefficient value of each indicator. The calculation expression is:

[0009] in, For indicators The Gini coefficient value, is the number of sample data, For indicators The sum of the sample data, 、 Indicators The corresponding p 、 q Sample values, p 、 q Indicates the index of the sample to be evaluated; Identify the least important indicator among the indicators in the set , calculate each indicator pair The ratio of the coefficient of variation of is expressed as:

[0010] in, For indicators right The ratio of the coefficient of variation of for The Gini coefficient value; Calculate the subjective weight of each indicator , whose expression is:

[0011] Indicates the number of indicators.

[0012] Furthermore, the specific method of determining the objective weight using the anti-entropy weight method is as follows: Constructing an evaluation index matrix :

[0013] in, Standardize data for indicators; Calculate the anti-entropy value of each indicator, the expression is:

[0014]

[0015] in, Indicator The anti-entropy value, Indicates the Among the evaluation indicators The proportion of samples, ln is the natural logarithm, Calculate the objective weight of each indicator , whose expression is: .

[0016] Furthermore, the specific method for determining the subjective and objective comprehensive weights by the Lagrange optimal multiplier method is as follows: According to the minimum information entropy theory, the constraints are established:

[0017] in, represents the constraints, represents the comprehensive weight; The Lagrange optimal multiplier method is used to optimize the calculation of the comprehensive weight, and its expression is: .

[0018] Furthermore, the specific method for evaluating the low-carbon construction level of railway projects by combining the Unascertained Measurement Theory (UMT) and the confidence identification criterion is as follows: The graded space is divided according to the low-carbon construction level classification standard :

[0019] The linear measurement function is selected and combined with the low-carbon construction level grading standard to calculate the single index measurement, and the unascertained measurement matrix is ​​obtained, which is expressed as follows:

[0020] in, Indicates the i Among the evaluation indicators j The samples for t The unknown measurement function value of a single indicator of an evaluation level; make ( ) represents an evaluation object Belong to t The degree of evaluation level, Indicates the t Rating level; The expression is:

[0021] Calculate the multi-index comprehensive measurement evaluation matrix, which is expressed as:

[0022] in, Indicates the i The evaluation index for t The multi-index comprehensive measurement function value of the evaluation level, Indicates the number of evaluation indicators; Determine confidence level , if the hierarchical space is ordered, and satisfy , it can be determined that the construction stage to be evaluated belongs to Rating .

[0023] The beneficial effects of the present invention are: By integrating improved G2 order relationship analysis with an anti-entropy weight optimization algorithm, a dynamic equilibrium configuration of subjective and objective weights is achieved, significantly enhancing the scientific representation capabilities of the indicator system and significantly reducing human influence in the evaluation process. Furthermore, the introduction of unascertained measurement theory to construct a hierarchical assessment model uses a confidence threshold method to accurately quantify the low-carbon performance of the construction phase. This not only reduces the interference of human subjective factors on the evaluation results, but also provides construction companies with an actionable decision-making support tool for developing carbon emission reduction optimization plans. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 The present invention provides a flow chart of a low-carbon construction evaluation method for railway projects based on the improved G2-AEW-UMT model. DETAILED DESCRIPTION

[0025] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0026] like Figure 1 As shown, in one embodiment of the present invention, a low-carbon construction evaluation method for railway engineering based on the improved G2-AEW-UMT model includes the following steps: S1. Establish an evaluation index system for low-carbon construction of railway projects; The specific method is to identify the direct and indirect carbon emission sources generated during railway construction by combining bibliometric analysis with engineering field research; According to the identification results, a hierarchical evaluation index system was constructed with construction machinery, construction materials, two zones and three sites, organization and management, and ecological environment as the criterion layers; Clarify the calculation methods for each indicator, determine the evaluation values ​​for each indicator based on internationally accepted grading models and industry practices, and develop a low-carbon construction level grading standard. In this example, based on the overall construction deployment, railway construction projects are divided into three construction phases: foundation construction, main construction, and installation construction. Given the large-scale nature of construction projects and the significant differences in carbon emission intensity between phases, to more effectively conduct low-carbon construction analysis and research on the project, a phased evaluation will be conducted for the three construction phases (labeled A, B, and C) and the overall project (D). By processing and analyzing indicator data from on-site graphic materials such as construction groups and master plan layouts, and conducting statistical analysis of specific data for each railway construction indicator at different stages, a railway project low-carbon construction evaluation indicator system and evaluation levels covering 15 evaluation indicators were established, as shown in Tables 1 and 2. In response to the defect of incomplete coverage of indicators in existing evaluation systems, the present invention comprehensively identifies the carbon emission sources during the railway construction stage based on the construction principles of the indicator system, and establishes an evaluation indicator system for the criterion layer from multiple aspects, which includes 15 evaluation indicators. It evaluates the low-carbon construction level of railway projects from multiple dimensions. Through the differentiated design of the indicator system, it more accurately reflects the dynamic characteristics of carbon emissions and resource and energy consumption in railway construction. For example, indicators such as the "localization rate of construction materials" are directly related to low-carbon goals and accurately reflect the actual level of low-carbon construction of railway projects.

[0027] Table 1

[0028] Table 2

[0029] The calculation methods of each indicator are as follows: Construction machinery layer: ① New energy machinery share: Assume the number of new energy machinery The total number of construction machinery is , new energy machinery market share I 11, ; ② Carbon emission level of construction machinery: Calculate the carbon emissions of major construction machinery based on the carbon emission calculation method.

[0030] Construction material layer: ①Material localization rate:

[0031] Where, The mass of local materials used in each stage of construction, in kg; It is the total amount of construction materials in each stage, in kg.

[0032] ② Recycled material utilization rate:

[0033] Where, The mass of recycled materials used in each stage of construction, in kg; The total mass of construction materials imported, in kg.

[0034] ③Recyclable material turnover rate:

[0035] The amount of recyclable materials reused at each stage, in kg; It is the inventory of recyclable materials in kg.

[0036] ④Proportion of on-site structural components:

[0037] The mass of sand, gravel and other materials used for on-site production of components, in kg; The amount of concrete used, in kg.

[0038] ⑤ Application rate of green building materials: refer to the "Carbon Neutral Building Evaluation Guidelines" for calculation and scoring.

[0039] Two zones and three fields: ①Solid waste recycling rate:

[0040] S The total amount of solid waste estimated for each stage of the project, in kg; S 1′ is the amount of solid waste recovered at each stage of the project, in kg.

[0041] ②Wastewater treatment and discharge rate meeting standards:

[0042] U is the total amount of wastewater generated at each stage, in kg; U 1′ is the discharge rate of construction wastewater that meets the treatment standards, in kg.

[0043] ③ Waste gas emission compliance rate:

[0044] G The total amount of waste gas estimated for each stage of the project, in kg; G 1′ is the waste gas emission that meets the standards at each stage of the project, in kg.

[0045] Organization and Management: The three indicators of ① green supply chain management application level, ② low-carbon process and method application level, and ③ energy-saving and carbon reduction technology application level all adopt an expert scoring system.

[0046] Ecological environment layer: ① Vegetation recovery rate:

[0047] The vegetation restoration area is The area that can be restored to vegetation is The vegetation recovery rate is I 52.

[0048] ②Annual vegetation carbon exchange rate:

[0049]

[0050] Where, S is the site area, m 2 ; is the annual carbon sequestration amount, For the i the amount of carbon sinks; for i Carbon sink factor of a carbon sink.

[0051] S2. Collect the sample data of the indicator system and use the extreme value standardization method to perform dimensionless preprocessing on the sample data of the indicator system to obtain the indicator set. ; S3, based on the indicator set, a dynamic weight allocation mechanism of subjective and objective fusion is constructed by improving the G2 method + anti-entropy weight method AEW; S3-1. Determine subjective weights using the improved G2 method: Sort the indicators in the indicator set and calculate the Gini coefficient value of each indicator. The calculation expression is:

[0052] in, For indicators The Gini coefficient value, is the number of sample data, For indicators The sum of the sample data, 、 Indicators The corresponding p 、 q Sample values, p 、 q Indicates the index of the sample to be evaluated; Statisticians from the indicator set Identify one indicator that is least important relative to the others (In this embodiment, the exhaust gas emission compliance rate is selected I 33 As the least important reference indicator), calculate the effect of each indicator on The ratio of the coefficient of variation of is expressed as:

[0053] in, For indicators right The ratio of the coefficient of variation of for The Gini coefficient value; Calculate the subjective weight of each indicator , whose expression is:

[0054] Indicates the number of indicators.

[0055] The calculation results are shown in Table 3.

[0056] Table 3

[0057] S3-2. Use the anti-entropy weight method to determine the objective weight: Constructing an evaluation index matrix :

[0058] in, Standardize data for indicators; Calculate the anti-entropy value of each indicator, the expression is:

[0059]

[0060] in, Indicator The anti-entropy value, Indicates the Among the evaluation indicators The proportion of samples, ln is the natural logarithm, Calculate the objective weight of each indicator , whose expression is: .

[0061] The calculation results are shown in Table 4.

[0062] Table 4

[0063] S3-3. Determine the subjective and objective comprehensive weights by using the Lagrange optimal multiplier method: According to the minimum information entropy theory, the constraints are established:

[0064] in, represents the constraints, represents the comprehensive weight; The Lagrange optimal multiplier method is used to optimize the calculation of the comprehensive weight, and its expression is: .

[0065] The calculation results are shown in Table 5.

[0066] Table 5

[0067] The subjective weighting method of the prior art is easily subject to excessive interference from expert experience, and the objective weighting method is difficult to fully consider the differences between indicators. The present invention adopts an improved G2 method to convert expert experience into a quantifiable indicator dispersion ratio by introducing the Gini coefficient difference ratio, which not only retains the value of domain knowledge but also reduces subjective cognitive bias; the anti-entropy weight method is used to determine the objective weight, and its utility in low-carbon construction evaluation is reflected based on the difference of the indicator; finally, the Lagrange optimal multiplier method is used to fuse the subjective and objective weights. The weight calculation method of the present invention obtains a weight value that can more reasonably reflect the importance of each indicator in the low-carbon construction evaluation, making the evaluation results more in line with the actual situation, and significantly improving the accuracy and reliability of the evaluation results. The size of the comprehensive weight value can reflect the size of the impact of the evaluation indicator railway construction. As can be seen from the table, indicators such as the utilization rate of recyclable materials and the annual carbon exchange rate of vegetation have a larger weight, while indicators such as the share of new energy machinery have a smaller weight.

[0068] S4. Combine the unascertained measure theory (UMT) and the confidence identification criterion to evaluate the low-carbon construction level of railway projects.

[0069] The graded space is divided according to the low-carbon construction level classification standard :

[0070] The grading matrix is:

[0071] A linear measurement function is selected and combined with the low-carbon construction level grading standard to calculate the single indicator measurement and obtain the unascertained measurement matrix.

[0072] The specific steps for drawing a linear measurement function equation are shown in Table 6 ( is the grading standard value, r =3; Indicates the i Under the evaluation index j The measurement value of each evaluation object; Indicates the i Under the evaluation index j The membership degree of each evaluation object to different evaluation levels; and are all membership functions, used to calculate the i Under the evaluation index j The evaluation object belongs to l and l +1 rating level of membership, l is the evaluation level index; r is the total number of evaluation levels; x is the value of the evaluation object on a certain evaluation indicator).

[0073] Table 6

[0074] The expression of the unascertained measure matrix is:

[0075] in, Indicates the i Among the evaluation indicators j The samples for t The unknown measurement function value of a single indicator of an evaluation level; make ( ) represents an evaluation object Belong to t The degree of evaluation level, Indicates the t Rating level; The expression is:

[0076] Calculate the multi-index comprehensive measurement evaluation matrix, which is expressed as:

[0077] in, Indicates the i The evaluation index for t The multi-index comprehensive measurement function value of the evaluation level, Indicates the number of evaluation indicators; In this example, the multi-index unascertained measure vectors for each of the four different construction phases (foundation construction phase, main construction phase, installation construction phase, and overall railway passenger station) are calculated. The calculation results are: =(0.1971,0.2929,0.3682,0.1428) =(0.2645,0.3420,0.3270,0.0665) =(0.1371,0.3903,0.2672,0.2683) =(0.2160,0.4391,0.3449,0.0000) Determine confidence level In this embodiment, the confidence =0.5, if the level space is ordered, and satisfy , it can be determined that the construction stage to be evaluated belongs to Rating .

[0078] The calculated ratings for each construction stage are: A. Foundation construction phase: =min{0.1971+0.2929+0.368=0.8572>0.5}=3 B Main construction phase: =min{0.2645+0.3420=0.60065>0.5}=2 C Installation and construction phase: =min{0.1371+0.3903=0.5274>0.5}=2 D Railway Passenger Station Overall: =min{0.2160+0.4391=0.6551>0.5}=2 According to the results of the confidence identification criterion, the low-carbon construction evaluation levels of the four different construction stages can be obtained. In the low-carbon construction evaluation study of railway projects, the low-carbon construction level of the foundation construction stage is qualified; the low-carbon level of the main construction stage and the installation construction stage is good; the overall evaluation of the low-carbon construction level of the railway project is good. In order to enhance the reliability of the comprehensive evaluation model, the TOPSIS model was selected for comparative analysis, as shown in Table 7. Empirical analysis shows that the evaluation model constructed by the present invention shows significant adaptability in all aspects of the entire construction cycle. The evaluation results of the present invention in the main construction stage are consistent with the on-site evaluation results, while the comparison model evaluation shows systematic deviations, which also verifies that the model adopted by the present invention has certain rationality and applicability.

[0079] Table 7

[0080] Combined with the actual situation of the project, the reasons for the low-carbon construction degree in each stage are analyzed as follows: (1) The foundation construction stage includes pre-construction preparation, foundation pit engineering, pile foundation engineering, and foundation piles. A large amount of earthwork excavation operations require frequent use of high-energy-consuming power equipment; secondly, the organizational management mechanism in the early stage of the project is not yet perfect, and the effective utilization level of construction machinery is not high. During the foundation construction stage, due to the excavation of the site, the ecological environment and carbon sink indicators such as green space and vegetation failed to play a role, and some energy-saving and emission reduction related systems and measures have not yet been established. Therefore, the carbon emission level is relatively high, and the low-carbon construction degree barely reaches the qualified level. (2) During the main construction stage and the installation stage, the project management system has become mature, and the construction process has been standardized and upgraded. At the same time, the concrete, steel structure and other materials used in the main structure construction are all high-strength materials, which greatly reduces material loss, thereby achieving the effect of saving resources.

[0081] In summary, the evaluation results are consistent with the actual engineering situation, indicating that the railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model provided by the present invention is scientific and reasonable.

[0082] In summary, based on the characteristics of low-carbon construction of railway projects and taking into account the overall construction capabilities of current construction companies, the present invention supplements traditional evaluation methods from the perspective of quantitative analysis and carbon emissions, and creatively constructs a set of multi-dimensional railway project low-carbon construction evaluation index systems, which makes up for the incomplete defects of traditional construction evaluation index systems as much as possible. Through "domain adaptability improvement", "algorithm optimization" and "engineering verification and expansion", the applicability and practical value of the model are significantly improved, responding to the "dual carbon" goals, providing a quantifiable low-carbon evaluation tool for railway projects, and providing technical support for green railway construction. The present invention constructs a low-carbon construction evaluation model for railway projects, and innovatively proposes a combined weighting model that integrates the improved G2 method, anti-entropy weight (AEW), and Lagrange optimal multiplier method, which effectively solves the technical defects of traditional weighting methods in the rationality of weight distribution. In view of the multi-source heterogeneous data characteristics unique to railway passenger station construction, the Uncertainty Measurement Theory (UMT) is introduced to construct a hierarchical assessment model. Through the confidence threshold quantification method, accurate rating of the low-carbon level during the construction phase is achieved. This provides an innovative methodological tool for improving the standardization level of green construction in railway projects, and effectively solves the core pain point of the existing evaluation system's lack of operability.

Claims

1. A railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model, characterized by: include: Establish an evaluation index system for low-carbon construction of railway projects; Collect the sample data of the indicator system, and use the extreme value standardization method to perform dimensionless preprocessing on the sample data of the indicator system to obtain the indicator set; Based on the indicator set, a dynamic weight allocation mechanism integrating subjective and objective factors is constructed by improving the G2 method and anti-entropy weight method AEW. The low-carbon construction level of railway projects is evaluated by combining the Unascertained Measurement Theory (UMT) and the confidence identification criterion. Among them, the improved G2 method + anti-entropy weight method AEW + unascertained measure theory UMT constitutes the improved G2-AEW-UMT model.

2. A railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model according to claim 1, characterized in that: The specific methods for constructing a low-carbon construction evaluation index system for railway projects are as follows: Identify direct and indirect carbon emission sources during railway construction by combining bibliometric analysis with engineering field research; According to the identification results, a hierarchical evaluation index system was constructed with construction machinery, construction materials, two zones and three sites, organization and management, and ecological environment as the criterion layers; Clarify the measurement method of each indicator, determine the evaluation value of each indicator based on the internationally accepted grading model and industry practice, and form a low-carbon construction level grading standard.

3. The railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model according to claim 1 is characterized in that: The specific method of constructing a dynamic weight allocation mechanism integrating subjective and objective factors based on the indicator set by improving the G2 method + anti-entropy weight method AEW is as follows: The improved G2 method is used to determine the subjective weight; the anti-entropy weight method AEW is used to determine the objective weight; and the Lagrange optimal multiplier method is used to determine the subjective and objective comprehensive weight.

4. A railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model according to claim 3, characterized in that: The specific method of determining subjective weight using the improved G2 method is as follows: Sort the indicators in the indicator set and calculate the Gini coefficient value of each indicator. The calculation expression is: in, For indicators The Gini coefficient value, is the number of sample data, For indicators The sum of the sample data, 、 Indicators The corresponding p 、 q Sample values, p 、 q Indicates the index of the sample to be evaluated; Identify the least important indicator among the indicators in the set , calculate each indicator pair The ratio of the coefficient of variation of is expressed as: in, For indicators right The ratio of the coefficient of variation of for The Gini coefficient value; Calculate the subjective weight of each indicator , whose expression is: Indicates the number of indicators.

5. The railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model according to claim 4 is characterized in that: The specific method of determining the objective weight using the anti-entropy weight method is: Constructing an evaluation index matrix : in, Standardize data for indicators; Calculate the anti-entropy value of each indicator, the expression is: in, Indicator The anti-entropy value, Indicates the Among the evaluation indicators The proportion of samples, ln is the natural logarithm, Calculate the objective weight of each indicator , whose expression is: 。 6. A railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model according to claim 5, characterized in that: The specific method for determining the subjective and objective comprehensive weights by the Lagrange optimal multiplier method is as follows: According to the minimum information entropy theory, the constraints are established: in, represents the constraints, represents the comprehensive weight; The Lagrange optimal multiplier method is used to optimize the calculation of the comprehensive weight, and its expression is: 。 7. The railway engineering low-carbon construction evaluation method based on the improved G2-AEW-UMT model according to claim 4 is characterized in that: The specific method of evaluating the low-carbon construction level of railway projects by combining the Unascertained Measurement Theory (UMT) and the confidence identification criterion is as follows: The graded space is divided according to the low-carbon construction level classification standard : The linear measurement function is selected and combined with the low-carbon construction level grading standard to calculate the single index measurement, and the unascertained measurement matrix is ​​obtained, which is expressed as follows: in, Indicates the i Among the evaluation indicators j The samples for t The unknown measurement function value of a single indicator of an evaluation level; make ( ) represents an evaluation object Belong to t The degree of evaluation level, Indicates the t Rating level; The expression is: Calculate the multi-index comprehensive measurement evaluation matrix, which is expressed as: in, Indicates the i The evaluation index for t The multi-index comprehensive measurement function value of the evaluation level, Indicates the number of evaluation indicators; Determine confidence level , if the hierarchical space is ordered, and satisfy , it can be determined that the construction stage to be evaluated belongs to Rating .

Images