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CN113408908A - Multi-dimensional credit evaluation model construction method based on performance ability and behaviors - Google Patents

Multi-dimensional credit evaluation model construction method based on performance ability and behaviors
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CN113408908A
CN113408908ACN202110693446.7ACN202110693446ACN113408908ACN 113408908 ACN113408908 ACN 113408908ACN 202110693446 ACN202110693446 ACN 202110693446ACN 113408908 ACN113408908 ACN 113408908A
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evaluation
criterion
principal component
index
credit
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周莉
赵燕
朱李红
刘碧松
江洲
李元沉
郑勇跃
刘珏
鲜涛
李向华
孟翠竹
刘栋栋
李华
孙良泉
孙莹
张旻旻
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China National Institute of Standardization
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China National Institute of Standardization
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Abstract

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本发明公开了一种基于履约能力和行为的多维信用评价模型构建方法,获取商贸流通企业信用水平构建构建目标层,通过商贸流通企业信用水平的履约行为和履约能力构建准则层以及指标层,建立多维信用评价模型的主成分,对所述主成分构建指标层和准则层;利用主成分析法对所述指标层进行评价;利用熵值法对准则层进行评价;利用标准化处理后的指标层综合评价值数据进行加权后可得模式的最终评价值。本发明通过基于履约能力和履约行为的多维企业信用评价模型,利用主成分法分析和熵值法进行评价,能够较好的得出企业信用水平的差异,同时能够识别出信用评价的主要影响要素。

Figure 202110693446

The invention discloses a method for constructing a multi-dimensional credit evaluation model based on contract performance capability and behavior, obtaining the credit level of a commercial and trade circulation enterprise to construct a construction target layer, and constructing a criterion layer and an index layer based on the contract performance behavior and contract performance capability of the commercial and trade circulation enterprise's credit level. The principal component of the multi-dimensional credit evaluation model, the index layer and the criterion layer are constructed for the principal component; the principal component analysis method is used to evaluate the index layer; the entropy value method is used to evaluate the criterion layer; the standardized index layer is used The final evaluation value of the mode can be obtained by weighting the comprehensive evaluation value data. Through the multi-dimensional enterprise credit evaluation model based on contract performance ability and contract performance behavior, the present invention uses principal component method analysis and entropy value method for evaluation, can better obtain the difference of enterprise credit level, and can identify the main influencing factors of credit evaluation at the same time .

Figure 202110693446

Description

Multi-dimensional credit evaluation model construction method based on performance ability and behaviors
Technical Field
The invention belongs to the technical field of model construction, and particularly relates to a multi-dimensional credit evaluation model construction method based on performance capability and behaviors.
Background
Quality credits are the willingness and ability of an enterprise to fulfill quality commitments, and quality credits are essentially the manifestation of contractual relationships between the enterprise and consumers regarding product quality. The fact proves that the product has good image of high quality and high credit, and has the function of improving the consumption confidence of people and pulling economic growth which is difficult to replace. Due to imperfect economic order of the market, part of enterprises lack quality credit consciousness, and quality loss behaviors such as fake-making and selling, poor-quality buildings, toxic food, service default and the like still occur in various fields.
As a main body of quality credit, enterprises may go to risk in advance of huge profits brought by low cost and sacrifice the quality credit of the enterprises. Therefore, the construction of a quality credit system is strengthened, the relation between enterprise quality credit and consumers needs to be objectively analyzed, and effective progress can be achieved only by adopting targeted measures and guiding, so that a multi-dimensional credit evaluation model construction method based on performance capability and behavior is provided.
Disclosure of Invention
The invention aims to provide a multi-dimensional credit evaluation model construction method based on performance capability and behaviors, which aims to solve the problems in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention comprises the following steps:
a, acquiring credit level of the commercial and trade circulation enterprises to construct a target layer, constructing a criterion layer and an index layer through the performance behavior and performance capability of the credit level of the commercial and trade circulation enterprises,
b, establishing a principal component of a multi-dimensional credit evaluation model, and establishing an index layer and a criterion layer for the principal component;
c, evaluating the index layer by using a principal component analysis method;
evaluating the criterion layer by using an entropy method;
and E, weighting the index layer comprehensive evaluation value data after the standardization processing to obtain the final evaluation value of the mode.
Further, the performance includes operational capability and transaction capability, the performance includes financial status and social behavior, the operational capability, the transaction capability, the financial status and the social behavior are constructed into a criterion layer, the operational capability includes human resource management, business management and intangible asset management, the transaction capability includes main products, sales income and sales objects, the financial status includes financial quality, financial statement and debt repayment, and the social behavior includes public credit information and market credit information.
Further, the method for evaluating the index layer by the principal component analysis method comprises the following steps:
setting m evaluation objects, using n evaluation indexes x1,x2,L xnEvaluation was carried out. The index value can form an m × n order matrix x ═ xij)m×nLet xk=(x1k,x2k,L xnk)TThe kth column vector of x. Obtaining expected mu-mu of n indexes12,Lμn]TLet v beij=cov(xi,xj)(i,j∈[1,n]Wherein cov (x)i,xj) Denotes xiAnd xjThe covariance between. Thereby obtaining an nxn order covariance matrix V ═ Vij]。
Establishing a mathematical model:
Figure BDA0003127528080000031
in the formula: a ═ α1,α,Lα1]T A=[α12,Lαn]T;α12,LαnIs a coefficient of n indices; d (y) is the variance of y; y is a linear function of the configuration of A and x.
The solution by using the Lagrange multiplier method comprises the following steps:
D(y)=ATVA=λATA=λ (2)
wherein λ ═ λ12,Lλn]The characteristic value of V is from large to small.
Let λiCorresponding feature vector is gammai=(γi1i2,Lγin)TThen the ith principal component is
Figure BDA0003127528080000032
The contribution rate of the ith principal component is
Figure BDA0003127528080000033
βiThe contribution rate used to measure the ith principal component is greater, indicating a greater contribution. The cumulative contribution rate of the first q principal components is
Figure BDA0003127528080000034
In general, if the cumulative contribution rate exceeds 85%, the q principal components may be used. In order to fully utilize the original information without discarding any component, the contribution rate of each principal component is used as its weight. Then, using the obtained principal component and its weight, the overall score of each mode can be obtained as
Figure BDA0003127528080000041
In the formula, P is an m-dimensional column vector.
Standardizing data, calculating the comprehensive evaluation values of different criteria of different evaluation objects according to the divided levels, firstly obtaining an evaluation matrix formed by the criteria associated with one of the criteria, further obtaining a covariance matrix V of the evaluation matrix, and further obtaining the corresponding eigenvalue lambda of each principal componentiAnd a feature vector gammaiThe principal component y is obtained by using the equations (3) and (4), respectivelyiAnd its contribution ratio betaiFinally, the overall evaluation value P of each mode under this criterion is obtained by using the formula (6).
Further, the method for normalizing data includes:
Figure BDA0003127528080000042
in the formula:
Figure BDA0003127528080000043
the maximum value of the j index of the m evaluation objects is shown;
Figure BDA0003127528080000044
the minimum value of the j index of the m evaluation objects is shown; b represents a benefit type index set; c represents a cost index set.
Further, the method for evaluating the criterion layer by using the entropy method comprises the step of forming an evaluation matrix e-e (e) by assuming that m evaluation objects exist and q evaluation criteria are applied to the criterion layerij)m×qFor one evaluation criterion, if the difference between the m values is larger, the function of the index in evaluation is larger.
Entropy of defining the ith evaluation criterion is
Figure BDA0003127528080000051
In the formula:
Figure BDA0003127528080000052
k is 1/ln m; and, assume fijWhen equal to 0, fijlnfij=0。
An entropy weight of the ith evaluation criterion may be defined as
Figure BDA0003127528080000053
In the formula, 0 is not more than omegaiLess than or equal to 1 and
Figure BDA0003127528080000054
and (4) obtaining the comprehensive evaluation value of each criterion, and if the cost index and the benefit index are distinguished during standardization processing, the subsequent standardization processing is regarded as the benefit index, and the standardized comprehensive evaluation value of the index layer is obtained by the formula (9).
Therefore, the entropy value of each criterion can be obtained by using the formula (7), the weight vector omega of each criterion can be obtained by using the formula (8), and the final evaluation values of different evaluation objects can be obtained by simply weighting the overall evaluation value data of the index layers after standardization processing, so that the score ranking of the evaluation objects can be obtained. When the evaluation values obtained by other methods are subjected to ranking comparison, the sensitivity analysis of the evaluation values can be carried out, and the sensitivity analysis formula is as follows:
Figure BDA0003127528080000055
in the formula (I), the compound is shown in the specification,
Figure BDA0003127528080000056
represents the maximum value of the evaluation value;
Figure BDA0003127528080000057
the second largest value of the evaluation value is indicated. Sensitivity contains: the higher the sensitivity is, the better the evaluation value discrimination obtained by the used evaluation algorithm is, and the better the evaluation effect is.
Compared with the prior art, the invention has the beneficial effects that:
according to the method, the evaluation is carried out by utilizing principal component analysis and an entropy method through a multi-dimensional enterprise credit evaluation model based on the performance capability and the performance behavior, so that the difference of the credit level of the enterprise can be obtained well, and the main influence elements of the credit evaluation can be identified.
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FIG. 1 is a schematic diagram of a multi-dimensional credit evaluation model construction method based on performance and behavior according to the present invention;
FIG. 2 is a schematic diagram of credit evaluation indexes of commercial and trade negotiable enterprises;
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments.
As shown in fig. 1, in the present embodiment,
a, acquiring credit level of a commercial and trade circulation enterprise to construct a construction target layer, and constructing a criterion layer and an index layer through a performance behavior and performance capability of the credit level of the commercial and trade circulation enterprise;
10 typical enterprises in the trade and trade circulation industry are selected as research samples. Because the enterprises in the same industry are adopted, the interference of different industry factors is avoided, and the credit evaluation of the enterprises is more scientific and reasonable. The data obtained by calculating the scores using the relevant data indexes disclosed in the fourth quarter of 2020 each enterprise is shown in table 1.
TABLE 1 Enterprise index score data sheet
Figure BDA0003127528080000061
Figure BDA0003127528080000071
B, establishing a principal component of a multi-dimensional credit evaluation model, and establishing an index layer and a criterion layer for the principal component;
referring to fig. 2, the credit evaluation index of the business circulation enterprise is established according to the requirements of the credit evaluation index of the business circulation enterprise in the national standard GB/T39450-:
c, evaluating the index layer by using a principal component analysis method;
the method for evaluating the index layer by the principal component analysis method comprises the following steps:
setting m evaluation objects, using n evaluation indexes x1,x2,L xnEvaluation was carried out. The index value can form an m × n order matrix x ═ xij)m×nLet xk=(x1k,x2k,L xnk)TThe kth column vector of x. Obtaining expected mu-mu of n indexes12,Lμn]TLet v beij=cov(xi,xj)(i,j∈[1,n]Wherein cov (x)i,xj) Denotes xiAnd xjThe covariance between. Thereby obtaining an nxn order covariance matrix V ═ Vij]。
Establishing a mathematical model:
Figure BDA0003127528080000081
in the formula: a ═ α1,α,Lα1]T A=[α12,Lαn]T;α12,LαnIs a coefficient of n indices; d (y) is the variance of y; y is a linear function of the configuration of A and x.
The solution by using the Lagrange multiplier method comprises the following steps:
D(y)=ATVA=λATA=λ (2)
wherein λ ═ λ12,Lλn]The characteristic value of V is from large to small.
Let λiCorresponding feature vector is gammai=(γi1i2,Lγin)TThen the ith principal component is
Figure BDA0003127528080000082
The contribution rate of the ith principal component is
Figure BDA0003127528080000083
βiThe contribution rate used for measuring the ith principal component is larger, the larger the contribution rate is, the larger the cumulative contribution rate of the first q principal components is
Figure BDA0003127528080000084
If the cumulative contribution rate exceeds 85%, the q principal components may be used. In order to fully utilize the original information without discarding any component, the contribution rate of each principal component is used as its weight. Then, using the obtained principal component and its weight, the overall score of each mode can be obtained as
Figure BDA0003127528080000091
In the formula, P is an m-dimensional column vector.
Standardizing data, calculating the comprehensive evaluation values of different criteria of different evaluation objects according to the divided levels, firstly obtaining an evaluation matrix formed by the criteria associated with one of the criteria, further obtaining a covariance matrix V of the evaluation matrix, and further obtaining the corresponding eigenvalue lambda of each principal componentiAnd a feature vector gammaiThe principal component y is obtained by using the equations (3) and (4), respectivelyiAnd its contribution ratio betaiFinally, the overall evaluation value P of each mode under this criterion is obtained by using the formula (6).
The data are first normalized using equation (9). And then, calculating the comprehensive evaluation values of all the criteria of different evaluation objects according to the levels divided in the graph. For one criterion, an evaluation matrix formed by indexes related to the criterion is firstly obtained, a covariance matrix V of the evaluation matrix is further obtained, and corresponding eigenvalues lambda of each principal component are further obtainediAnd a feature vector gammaiThe principal component y is obtained by using the equations (3) and (4), respectivelyiAnd its contribution ratio betaiFinally, the overall evaluation value P of each mode under this criterion is obtained by using equation (6).
Figure BDA0003127528080000092
Figure BDA0003127528080000101
TABLE 2 comprehensive evaluation value of index layer
Evaluating the criterion layer by using an entropy method;
6. in the method for evaluating the criterion layer by using the entropy method, m evaluation objects are assumed in the application of the criterion layer, q evaluation criteria are assumed, and an evaluation matrix e is formed as (e)ij)m×qFor a certain evaluation criterion, if the difference between m values is larger, the action of the index in evaluation is larger.
Entropy of defining the ith evaluation criterion is
Figure BDA0003127528080000102
In the formula:
Figure BDA0003127528080000111
k is 1/ln m; and, assume fijWhen equal to 0, fij ln fij=0。
An entropy weight of the ith evaluation criterion may be defined as
Figure BDA0003127528080000112
In the formula, 0 is not more than omegaiLess than or equal to 1 and
Figure BDA0003127528080000113
and obtaining the comprehensive evaluation value of each criterion, and if the cost index and the benefit index are distinguished during standardization, the subsequent standardization is considered as the benefit index, and the index layer comprehensive evaluation value after standardization is obtained. Therefore, the entropy value of each criterion can be obtained by using the formula (7), the weight vector omega of each criterion can be obtained by using the formula (8), and the final evaluation values of different evaluation objects can be obtained by simply weighting the overall evaluation value data of the index layers after standardization processing, so that the score ranking of the evaluation objects can be obtained. When the evaluation values obtained by other methods are compared in a ranking mode, sensitivity analysis of the evaluation values can be carried out, and a sensitivity analysis formula is as follows:
Figure BDA0003127528080000114
in the formula (I), the compound is shown in the specification,
Figure BDA0003127528080000115
represents the maximum value of the evaluation value;
Figure BDA0003127528080000116
the second largest value of the evaluation value is indicated. Sensitivity contains: the higher the sensitivity is, the better the evaluation value discrimination obtained by the used evaluation algorithm is, and the better the evaluation effect is.
The above-described comprehensive evaluation value of each criterion can be obtained, and the normalized overall evaluation value of the index layer can be obtained from expression (9). The entropy values for each criterion obtained using equation (7) are (0.7321,0.2734,0.3253,0.7683), respectively.
And E, weighting the index layer comprehensive evaluation value data after the standardization processing to obtain the final evaluation value of the mode.
Using equation (8), the weight vector ω is obtained (0.1324,0.6148,0.1486,0.1042),
therefore, the final evaluation values of the modes obtained after simple weighting by using the normalized index layer comprehensive evaluation value data are sequentially (0.6002, 0.5306, 0.3180, 0.3877, 0.7103, 0.5622, 0.4928, 0.3254, 0.3048 and 0.4873), so that the enterprise credit level ranking is obtained, wherein the credit level of enterprise 5 is the highest, enterprise 1 and enterprise 6 are the second, and enterprise 9 is the last.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and equivalent alternatives or modifications according to the technical solution and the inventive concept of the present invention should be covered by the scope of the present invention.

Claims (5)

Translated fromChinese
1.一种基于履约能力和行为的多维信用评价模型构建方法,其特征在于:1. A method for constructing a multi-dimensional credit evaluation model based on performance capability and behavior, characterized in that:包括以下步骤:Include the following steps:A获取商贸流通企业信用水平构建构建目标层,通过商贸流通企业信用水平的履约行为和履约能力构建准则层以及指标层,A. Obtain the credit level of the commercial and trade circulation enterprises to build the target layer, and build the criterion layer and the index layer through the performance behavior and performance ability of the credit level of the commercial and trade circulation enterprises.B建立多维信用评价模型的主成分,对所述主成分构建指标层和准则层;B establishes the principal component of the multi-dimensional credit evaluation model, and constructs the index layer and the criterion layer for the principal component;C利用主成分析法对所述指标层进行评价;C uses the principal component analysis method to evaluate the index layer;D利用熵值法对准则层进行评价;D uses the entropy method to evaluate the criterion layer;E利用标准化处理后的指标层综合评价值数据进行加权后可得模式的最终评价值。E. The final evaluation value of the model can be obtained by weighting the standardized comprehensive evaluation value data of the index layer.2.如权利要求1所述的基于履约能力和行为的多维信用评价模型构建方法,其特征在于:所述履约行为包括经营能力和交易能力,所述履约能力包括财务状况和社会行为,将所述经营能力、交易能力、财务状况和社会行为构建准则层,所述经营能力包括人力资源管理、业务管理和无形资产管理、交易能力包括主营产品、销售收入和销售对象,财务状况包括财务质量、财务报表和债务偿还,所述社会行为包括公共信用信息和市场信用信息。2. The method for constructing a multi-dimensional credit evaluation model based on contract performance capabilities and behaviors as claimed in claim 1, wherein the contract performance behaviors include operating capabilities and transaction capabilities, and the contract performance capabilities include financial status and social behaviors. The management capability, transaction capability, financial status and social behavior construction criteria layer, the management capability includes human resource management, business management and intangible asset management, transaction capability includes main products, sales revenue and sales targets, and financial status includes financial quality. , financial statements and debt repayment, the social behavior includes public credit information and market credit information.3.如权利要求1所述的基于履约能力和行为的多维信用评价模型构建方法,其特征在于:所述主成分析法对所述指标层进行评价的方法为:3. The multi-dimensional credit evaluation model construction method based on contract performance capability and behavior as claimed in claim 1, characterized in that: the method for evaluating the index layer by the principal component analysis method is:设有m个评价对象,需要用n个评价指标x1,x2,L xn进行评价。其指标值可以构成一个m×n阶矩阵x=(xij)m×n,令xk=(x1k,x2k,L xnk)T表示x的第k个列向量。求取n个指标的期望μ=[μ12,L μn]T,令νij=cov(xi,xj)(i,j∈[1,n],其中cov(xi,xj)表示xi和xj之间的协方差。从而求出n×n阶协方差矩阵V=[νij]。There are m evaluation objects, and n evaluation indexes x1 , x2 , and L xn need to be used for evaluation. Its index value can form an m×n-order matrix x=(xij )m×n , let xk =(x1k , x2k , L xnk )T represent the kth column vector of x. Find the expectation μ=[μ1 , μ2 , L μn ]T of n indicators, let νij =cov(xi ,xj )(i,j∈[1,n], where cov(xi , xj ) represents the covariance between xi and xj . Thus, the n×n-order covariance matrix V=[νij ] is obtained.建立数学模型:Build a mathematical model:
Figure FDA0003127528070000021
Figure FDA0003127528070000021
式中:A=[α1,α,L α1]TA=[α12,L αn]T;α12,Lαn为n个指标的系数;D(y)为y的方差;y为A与x构造的线性函数。In the formula: A=[α1 ,α,L α1 ]T A=[α12 ,L αn ]T ; α12 ,Lαn are coefficients of n indicators; D(y) is the variance of y; y is the linear function constructed by A and x.利用拉格朗日乘子法求解有:Using the Lagrange multiplier method to solve:D(y)=ATVA=λATA=λ (2)D(y)=AT VA=λAT A=λ (2)式中,λ=[λ12,L λn]为V的特征值(由大到小)。In the formula, λ=[λ1 , λ2 , L λn ] is the eigenvalue of V (from large to small).设λi对应特征向量为γi=(γi1i2,L γin)T,则第i个主成分分量为Let the eigenvector corresponding to λi be γi =(γi1i2 ,L γin )T , then the i-th principal component is
Figure FDA0003127528070000022
Figure FDA0003127528070000022
第i个主成分分量的贡献率为The contribution rate of the i-th principal component component is
Figure FDA0003127528070000023
Figure FDA0003127528070000023
βi用来度量第i个主成分的贡献率,越大表明其贡献越大,前q个主成分的累积贡献率为βi is used to measure the contribution rate of the i-th principal component. The larger the value, the greater the contribution. The cumulative contribution rate of the first q principal components is
Figure FDA0003127528070000024
Figure FDA0003127528070000024
若累积贡献率超过85%,则只要采用这q个主成分即可。为充分利用原始信息,不丢弃任何成分,采用各个主成分分量的贡献率作为其权重。则利用求得的主成分分量及及其权重,可得各种模式综合得分为If the cumulative contribution rate exceeds 85%, it is only necessary to use the q principal components. In order to make full use of the original information, without discarding any components, the contribution rate of each principal component component is used as its weight. Then using the obtained principal component components and their weights, the comprehensive scores of various modes can be obtained as
Figure FDA0003127528070000031
Figure FDA0003127528070000031
式中,P为一个m维列向量。where P is an m-dimensional column vector.对数据进行标准化处理,按划分的层次分别计算不同评价对象各个准则的综合评价值,对其中某个准则,首先得出与此准则关联的指标形成的评价矩阵,进而得出其协方差矩阵V,进一步求得各个主成分分量的对应的特征值λi和特征向量γi,利用式(3)和式(4)分别得出主成分分量yi及其贡献率βi,最后利用式(6)得出在此准则下各种模式的综合评价值P。Standardize the data, and calculate the comprehensive evaluation value of each criterion of different evaluation objects according to the level of division. For one criterion, first obtain the evaluation matrix formed by the index associated with this criterion, and then obtain its covariance matrix V , and further obtain the corresponding eigenvalue λi and eigenvector γi of each principal component component, use formula (3) and formula (4) to obtain the principal component component yi and its contribution rate βi respectively, and finally use formula ( 6) Obtain the comprehensive evaluation value P of various modes under this criterion.4.如权利要求3所述的基于履约能力和行为的多维信用评价模型构建方法,其特征在于:所述对数据进行标准化处理方法包括:4. The method for constructing a multi-dimensional credit evaluation model based on contract performance capability and behavior as claimed in claim 3, wherein the method for standardizing the data comprises:
Figure FDA0003127528070000032
Figure FDA0003127528070000032
式中:
Figure FDA0003127528070000033
表示m个评价对象在第j个指标的最大值;
Figure FDA0003127528070000034
表示m个评价对象在第j个指标的最小值;B表示效益型指标集合;C表示成本性指标集合。
where:
Figure FDA0003127528070000033
Represents the maximum value of m evaluation objects in the jth index;
Figure FDA0003127528070000034
Represents the minimum value of m evaluation objects in the jth index; B represents the set of benefit indicators; C represents the set of cost indicators.
5.如权利要求1所述的基于履约能力和行为的多维信用评价模型构建方法,其特征在于:在利用熵值法对准则层进行评价方法包括在准则层运用中,假设有m个评价对象,q项评价准则,形成评价矩阵e=(eij)m×q,对其中某个评价准则,若m个取值之间差距越大,则该指标在评价中的作用越大。5. The multi-dimensional credit evaluation model construction method based on contract performance capability and behavior as claimed in claim 1, characterized in that: in utilizing the entropy method to evaluate the criterion layer, the evaluation method is included in the use of the criterion layer, and it is assumed that there are m evaluation objects , q items of evaluation criteria, forming an evaluation matrix e=(eij )m×q , for one of the evaluation criteria, if the gap between the m values is larger, the index plays a greater role in the evaluation.定义第i个评价准则的熵为Define the entropy of the i-th evaluation criterion as
Figure FDA0003127528070000041
Figure FDA0003127528070000041
式中:
Figure FDA0003127528070000042
k=1/ln m;并且,假定fij=0时,fijln fij=0。
where:
Figure FDA0003127528070000042
k=1/ln m; and, assuming fij =0, fij ln fij =0.
则可定义第i个评价准则的熵权为Then the entropy weight of the i-th evaluation criterion can be defined as
Figure FDA0003127528070000043
Figure FDA0003127528070000043
式中,0≤ωi≤1且
Figure FDA0003127528070000044
where 0≤ωi ≤1 and
Figure FDA0003127528070000044
得出各准则的综合评价值,作标准化处理时如果已区分成本型指标和效益型指标,后续的标准化处理均认为是效益型指标,标准化处理后的指标层综合评价值。从而利用式(7)可得每个准则的熵值,利用式(8)可得其权重向量ω,从而再利用标准化处理后的指标层综合评价值数据进行简单加权后可得不同评价对象的最终评价值,得出评价对象的得分排序。在与其他方法得出的评估值进行排序比较时,可以进行评估值的灵敏度分析,灵敏度分析公式:The comprehensive evaluation value of each criterion is obtained. If the cost-type index and the benefit-type index have been distinguished during the standardization process, the subsequent standardization process will be regarded as the benefit-type index, and the comprehensive evaluation value of the index level after the standardized process. Therefore, the entropy value of each criterion can be obtained by using the formula (7), and its weight vector ω can be obtained by using the formula (8). The final evaluation value is obtained, and the score ranking of the evaluation object is obtained. When comparing with the evaluation values obtained by other methods, the sensitivity analysis of the evaluation values can be performed. The sensitivity analysis formula is:
Figure FDA0003127528070000045
Figure FDA0003127528070000045
式中,
Figure FDA0003127528070000046
表示评价值的最大值;
Figure FDA0003127528070000047
表示评价值的次大值。灵敏度含义:灵敏度越大,则使用的评价算法得出的评价值区分度越好,评选效果更好。
In the formula,
Figure FDA0003127528070000046
Represents the maximum value of the evaluation value;
Figure FDA0003127528070000047
Indicates the next largest value of the evaluation value. Meaning of sensitivity: The greater the sensitivity, the better the discrimination of the evaluation value obtained by the evaluation algorithm used, and the better the selection effect.
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