CN109543737B - Information system health degree evaluation method based on FAHP-FCA combined empowerment - Google Patents

Information system health degree evaluation method based on FAHP-FCA combined empowerment Download PDF

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CN109543737B
CN109543737B CN201811361185.3A CN201811361185A CN109543737B CN 109543737 B CN109543737 B CN 109543737B CN 201811361185 A CN201811361185 A CN 201811361185A CN 109543737 B CN109543737 B CN 109543737B
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黄林
王电钢
常健
王鑫
杨帆
唐震宇
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Abstract

The invention discloses an information system health degree evaluation method based on FAHP _ FCA combined empowerment, belonging to the field of information system operation and maintenance evaluation; which comprises the following steps of 1: constructing a calculation model; step 2: calculating the subjective and objective combination weight through a calculation model; and step 3: calculating the health degree by combining the index operation and maintenance data and the subjective and objective combination weight; the step 1 comprises the following steps: based on an index evaluation system, weighting optimization is carried out on the fuzzy hierarchy analysis process by comprehensively considering the transverse and longitudinal influence factors of the index hierarchy by using a DEMATEL method, and index weight of subjective weighting is obtained; performing reasonable dimensionality reduction analysis and optimization of a principal component division process by using a factor analysis method based on an index evaluation system to obtain objective weighted index weight; the method solves the problem that the evaluation rationality and accuracy are poor due to the fact that the traditional weighting algorithm adopted when the AHP and the PCA are adopted for combined weighting is only suitable for an information system with a simple structure and single data, and achieves the effect of improving the rationality of subjective evaluation and the accuracy of objective evaluation.

Description

Information system health degree evaluation method based on FAHP-FCA combined empowerment
Technical Field
The invention belongs to the field of information system operation and maintenance evaluation, and particularly relates to an information system health degree evaluation method based on FAHP _ FCA combined empowerment.
Background
In recent years, with the continuous development of informatization work, a plurality of power grid enterprises can rapidly expand the scale of each information system while continuously improving the work supporting force of company business and greatly integrating main business, and the system gradually presents the characteristics of complete infrastructure, numerous and complicated data, wide application and the like. Therefore, the supervision requirements on the overall stability and the operation state of the system are also improved, and the traditional operation, maintenance, overhaul and management means cannot meet the efficient management requirements of the complex system. In order to improve the guarantee capability of informatization operation, accurately and objectively evaluate the operation and maintenance level of an information system, and effectively guide the information system to operate safely, efficiently and economically, an information system health degree evaluation method capable of integrating various performance indexes of the system and realizing automatic evaluation is very important.
The genetic algorithm means that initial solutions of problems to be solved are randomly generated to form an initial population, each initial solution is a population individual, the purpose of population evolution is achieved through genetic operation, namely, excellent individual selection, population individual crossing, population individual variation and the like are performed through calculating population individual fitness to generate a new generation of individuals, genetic operation is performed on the population individuals generation by generation, and the algorithm is terminated at a convergence threshold value or a maximum evolution algebra.
The invention discloses a comprehensive evaluation method for sustainable development of a smart power grid, which is disclosed by the invention patent with the application number of CN201610268511.0 and the name of 'a comprehensive evaluation method for sustainable development of a smart power grid based on an AHP-PCA method', and belongs to the technical field of evaluation of the smart power grid, wherein in k months before the evaluation method is put into use, all evaluation factors are statically weighted based on an analytic hierarchy process AHP, and are scored according to the operation condition of the smart power grid to construct an AHP evaluation index; after the evaluation method is operated for k months, all evaluation factors are dynamically weighted from the k +1 month based on a Principal Component Analysis (PCA), effective principal components are screened out, a PCA evaluation index is constructed, and the PCA evaluation index and the AHP evaluation index are combined to serve as the sustainable development evaluation index of the smart grid; the evaluation method combines an Analytic Hierarchy Process (AHP) and a Principal Component Analysis (PCA), solves the problems of errors caused by subjective differences in smart grid evaluation and the problem that the principal component has no actual meaning due to empty information quantity, and provides an effective evaluation method for the sustainable development of the smart grid. Although the method considers the respective technical defects of the original AHP and PCA methods, the combination of the AHP and the PCA is adopted for the combined weighting method, so that the problems that the subjectivity is too strong or the objective weighting is too dependent on sample data and the like caused by the influence of human factors possibly encountered in the model evaluation process are solved; however, the method uses a traditional weighting algorithm, which is only suitable for evaluation scenes with simple index hierarchical structure and single data, the existing information systems such as enterprise systems have the characteristics of huge data, complex hierarchical structure, close association between structures and the like, and the traditional weighting algorithm cannot accurately perform objective evaluation on the aspect of overall system operation quality evaluation, so that the rationality and accuracy of the evaluation method are poor.
Disclosure of Invention
The invention aims to: the invention provides an information system health degree evaluation method based on FAHP _ FCA combined empowerment, which solves the problem that the evaluation reasonability and accuracy are poor because the traditional empowerment algorithm adopted when AHP and PCA are adopted for combined empowerment is only suitable for an information system with simple structure and single data.
The technical scheme adopted by the invention is as follows:
an information system health degree evaluation method based on FAHP _ FCA combined empowerment comprises the following steps:
step 1: constructing a calculation model of subjective and objective combination weight of a single index factor based on an index evaluation system;
step 2: calculating the subjective and objective combination weight of each index factor through a calculation model;
and step 3: calculating the health degree by combining the index operation and maintenance data and the subjective and objective combination weight of each index factor;
the step 1 comprises the following steps:
step 1.1: based on an index evaluation system, weighting optimization is carried out on the fuzzy hierarchy analysis process by comprehensively considering the transverse and longitudinal influence factors of the index hierarchy by using a DEMATEL method, and index weight of subjective weighting is obtained;
step 1.2: performing reasonable dimensionality reduction analysis and optimization of a principal component division process by using a factor analysis method based on an index evaluation system to obtain objective weighted index weight;
step 1.3: and calculating the subjective and objective combination weight of the single index factor according to the index weight of subjective weighting and the index weight of objective weighting to complete the construction of the calculation model.
Preferably, the step 1.1 comprises the following steps:
step 1.1.1: carrying out hierarchical analysis on the index factors to construct an index evaluation system;
step 1.1.2: based on an index evaluation system, a fuzzy judgment matrix A is constructed by adopting a 0-1 scale method:
Figure GDA0003100695490000021
wherein, the element auvRepresents the ratio of the importance of the u-th element to the importance of the v-th element, where u, v ═ 1, 2, …, N;
step 1.1.3: the initial characteristic vector w' of the fuzzy judgment matrix A is solved by using a square root method, and the calculation formula is as follows:
Figure GDA0003100695490000022
step 1.1.4: calculating the comprehensive influence weight theta of the index by utilizing a DEMATEL method and combining the influence degree and the influenced degree of the index factor;
step 1.1.5: calculating a single-layer weight vector w under the comprehensive influence factors based on the comprehensive influence weight theta of the index;
step 1.1.6: carrying out consistency check on the fuzzy judgment matrix A through a genetic algorithm based on the single-layer weight vector w to obtain the subjective weighting index weight w for carrying out subjective weighting under the influence of comprehensive factorsFAHP。
Preferably, the step 1.1.4 comprises the following steps:
step 1.1.4.1: calculating a relation matrix D of influence degree and influence degree among index factors:
d＝fT·e
wherein D represents each element in the relation matrix D, f represents the influence degree, e represents the influenced degree, and T represents the transposition of the matrix;
step 1.1.4.2: by taking a relation matrixD diagonal element calculation of comprehensive influence degree vector D about index factorsu：
du＝fu×eu
Wherein f isuIndicating the degree of influence of the index factor, euIndicating the degree of influence of the index factor;
step 1.1.4.3: for the vector d of comprehensive influence degreeuCarrying out normalization processing to obtain a comprehensive influence weight theta:
Figure GDA0003100695490000031
preferably, the step 1.1.5 comprises the following steps:
step 1.1.5.1: computing a composite feature vector wu：
wu＝θw′
Wherein theta represents the comprehensive influence weight of the index, and w' represents the initial characteristic vector of the fuzzy judgment matrix A;
step 1.1.5.2: for comprehensive characteristic vector wuAnd (3) carrying out normalization:
Figure GDA0003100695490000032
step 1.1.5.3: integrated feature vector based on normalization
Figure GDA0003100695490000033
Calculating single-layer weight vectors under the comprehensive influence factors of the indexes:
Figure GDA0003100695490000034
preferably, the step 1.2 comprises the following steps:
step 1.2.1: constructing an original matrix X based on an index evaluation system:
Figure GDA0003100695490000041
wherein n represents the number of structural layers, and p represents the number of index factors of each layer;
step 1.2.2: normalizing the original matrix X to obtain a matrix Y:
Figure GDA0003100695490000042
Figure GDA0003100695490000043
Figure GDA0003100695490000044
wherein, yijRepresenting values of variables, x, after normalizationijRepresenting the actual variable values in the original matrix X,
Figure GDA0003100695490000045
representing the mean value of the variables, sjRepresents the standard deviation;
step 1.2.3: analyzing the common factor of the original matrix X, and determining the number k of the principal components:
X＝ηE+ε
wherein eta represents a common factor, epsilon represents a special factor, and E represents a factor load matrix;
step 1.2.4: establishing a covariance matrix C based on the matrix Yx＝(cij) Calculating CxThe feature values are sorted to obtain k principal component elements F:
Figure GDA0003100695490000046
F1,F2,…Fk
wherein the content of the first and second substances,
Figure GDA0003100695490000047
representing the mean of the variables, yli、yljRepresenting the element variables in the matrix Y;
step 1.2.5: according to the covariance matrix Cx＝(cij) Constructing a normalized correlation coefficient matrix R ═ (R)ij) Calculating the characteristic value of R, sequencing the characteristic values to obtain a coefficient factor lambda:
Figure GDA0003100695490000051
λ1≥λ2≥…≥λp>0；
step 1.2.6: calculating index weight w under objective weighting based on k principal component elements F and coefficient factor lambdaFCA：
Figure GDA0003100695490000052
Preferably, the step 1.2.3 comprises the following steps:
step 1.2.3.1: the original matrix X formula is deformed:
XTX＝(ηE+ε)T(ηE+ε)；
step 1.2.3.2: removing special factors:
XTX≈(ηE)T(ηE)；
step 1.2.3.3: introducing an identity matrix gamma based on the formula of the step 1.2.3.2 to obtain a deformation formula, extracting beta in the deformation formula as a common factor, performing factor rotation on the common factor to complete grouping of index factors, and obtaining the number k of main components:
Figure GDA0003100695490000053
preferably, the step 1.3 comprises the following steps:
step 1.3.1: index weight based on subjective weightingWeight wFAHPAnd index weight w under objective weightingFCACalculating the importance coefficient alpha of the subjective weight of each index by combining the moment estimation theoryuAnd the importance coefficient beta of the objective weightu：
wFAHP＝[w1′,w2′,…,wN′]
wFCA＝[w1″,w2″,…,wN″]
Figure GDA0003100695490000061
Step 1.3.2: calculating the subjective and objective combination weight of a single index factor to complete the construction of a calculation model:
Figure GDA0003100695490000062
in summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. according to the method, subjective weighting is carried out after transverse and longitudinal influence factors of an index hierarchical structure are considered by a DEMATEL method to optimize fuzzy hierarchical analysis, a reasonable dimensionality reduction analysis optimization principal component division process is carried out by a factor analysis method, objective weighting is carried out, and the subjective and objective combination weight of the index factors is obtained, so that the problem that the evaluation rationality and accuracy are poor due to the fact that a traditional weighting algorithm adopted when AHP and PCA are adopted to carry out combined weighting is only suitable for an information system with a simple structure and single data is solved, and the effects of improving the rationality of subjective evaluation and the accuracy of objective evaluation are achieved;
2. the method optimizes the judgment process of the hierarchical influence degree among the indexes in the fuzzy hierarchical analysis process by combining a DEMATEL method, comprehensively considers the transverse weighting factors, namely the mutual influence degree among the indexes at the same level, on the basis of the original longitudinal weighting, namely the influence degree of the analysis sub-indexes relative to the father indexes, considers the influence degree and the influence degree, and improves the rationality of the whole subjective evaluation through weighting analysis;
3. the invention improves the traditional PCA weighting process based on a factor analysis method, analyzes the internal structure of an original matrix, reasonably groups object index factors by combining found common factors, obtains enough original information by less main components, reasonably groups the index factors by the common factors obtained by analysis, avoids the problem that the evaluation result excessively depends on a first main component and the like due to the excessive difference of matrix variance contribution rates among the main components, and improves the actual accuracy of objective evaluation;
4. the consistency check process of the fuzzy judgment matrix is optimized by using a genetic algorithm, the traditional complex consistency judgment method is converted into an intuitive nonlinear problem to solve an optimal solution, the optimal consistency of the judgment matrix is ensured, the accuracy and the rationality of the evaluation of the whole system are improved, the check is simplified, and the defect of high difficulty in the traditional consistency check is avoided; meanwhile, the importance between every two indexes is expressed by using a 0-1 scale method, the defect that the weighting result is too extreme due to too large interval difference is avoided, and the rationality of the overall system evaluation is improved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a graph of the comparison effect of single-layer index weight calculation according to the present invention;
FIG. 3 is a comparison of time used for consistency checking in accordance with the present invention;
fig. 4 is a comparison graph of the error of the objective evaluation of health degree according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The technical problem is as follows: the problem that the evaluation rationality and accuracy are poor due to the fact that the traditional empowerment algorithm adopted when AHP and PCA are adopted for combined empowerment is only suitable for an information system with a simple structure and single data is solved;
the technical means is as follows: an information system health degree evaluation method based on FAHP _ FCA combined empowerment comprises the following steps:
step 1: constructing a calculation model of subjective and objective combination weight of a single index factor based on an index evaluation system;
step 2: calculating the subjective and objective combination weight of each index factor through a calculation model;
and step 3: calculating the health degree by combining the index operation and maintenance data and the subjective and objective combination weight of each index factor;
the step 1 comprises the following steps:
step 1.1: based on an index evaluation system, weighting optimization is carried out on the fuzzy hierarchy analysis process by comprehensively considering the transverse and longitudinal influence factors of the index hierarchy by using a DEMATEL method, and index weight of subjective weighting is obtained;
step 1.2: performing reasonable dimensionality reduction analysis and optimization of a principal component division process by using a factor analysis method based on an index evaluation system to obtain objective weighted index weight;
step 1.3: and calculating the subjective and objective combination weight of the single index factor according to the index weight of subjective weighting and the index weight of objective weighting to complete the construction of the calculation model.
Step 1.1 comprises the following steps:
step 1.1.1: carrying out hierarchical analysis on the index factors to construct an index evaluation system;
step 1.1.2: based on an index evaluation system, a fuzzy judgment matrix A is constructed by adopting a 0-1 scale method:
Figure GDA0003100695490000081
wherein, the element auvRepresents the ratio of the importance of the u-th element to the importance of the v-th element, where u, v ═ 1, 2, …, N;
step 1.1.3: the initial characteristic vector w' of the fuzzy judgment matrix A is solved by using a square root method, and the calculation formula is as follows:
Figure GDA0003100695490000082
step 1.1.4: calculating the comprehensive influence weight theta of the index by utilizing a DEMATEL method and combining the influence degree and the influenced degree of the index factor;
step 1.1.5: calculating a single-layer weight vector w under the comprehensive influence factors based on the comprehensive influence weight theta of the index;
step 1.1.6: carrying out consistency check on the fuzzy judgment matrix A through a genetic algorithm based on the single-layer weight vector w to obtain the subjective weighting index weight w for carrying out subjective weighting under the influence of comprehensive factorsFAHP。
Step 1.1.4 comprises the following steps:
step 1.1.4.1: calculating a relation matrix D of influence degree and influence degree among index factors:
d＝fT·e
wherein D represents each element in the relation matrix D, f represents the influence degree, e represents the influenced degree, and T represents the transposition of the matrix;
step 1.1.4.2: calculating a comprehensive influence degree vector D related to index factors by taking diagonal elements of a relation matrix Du：
du＝fu×euWherein f isuIndicating the degree of influence of the index factor, euIndicating the degree of influence of the index factor;
step 1.1.4.3: for the vector d of comprehensive influence degreeuCarrying out normalization processing to obtain a comprehensive influence weight theta:
Figure GDA0003100695490000091
step 1.1.5 comprises the following steps:
step 1.1.5.1: computing a composite feature vector wu：
wu＝θw′
Wherein theta represents the comprehensive influence weight of the index, and w' represents the initial characteristic vector of the fuzzy judgment matrix A;
step 1.1.5.2: for comprehensive characteristic vector wuAnd (3) carrying out normalization:
Figure GDA0003100695490000092
step 1.1.5.3: integrated feature vector based on normalization
Figure GDA0003100695490000093
Calculating single-layer weight vectors under the comprehensive influence factors of the indexes:
Figure GDA0003100695490000094
step 1.2 comprises the following steps:
step 1.2.1: constructing an original matrix X based on an index evaluation system:
Figure GDA0003100695490000095
wherein n represents the number of structural layers, and p represents the number of index factors of each layer;
step 1.2.2: normalizing the original matrix X to obtain a matrix Y:
Figure GDA0003100695490000096
Figure GDA0003100695490000097
Figure GDA0003100695490000098
wherein, yijRepresenting values of variables, x, after normalizationijRepresenting the actual variable values in the original matrix X,
Figure GDA0003100695490000099
representing the mean value of the variables, sjRepresents the standard deviation;
step 1.2.3: analyzing the common factor of the original matrix X, and determining the number k of the principal components:
X＝ηE+ε
wherein eta represents a common factor, epsilon represents a special factor, and E represents a factor load matrix;
step 1.2.4: establishing a covariance matrix C based on the matrix Yx＝(cij) Calculating CxThe feature values are sorted to obtain k principal component elements F:
Figure GDA0003100695490000101
F1,F2,…Fk
wherein the content of the first and second substances,
Figure GDA0003100695490000102
representing the mean of the variables, yli、yljRepresenting the element variables in the matrix Y;
step 1.2.5: according to the covariance matrix Cx＝(cij) Constructing a normalized correlation coefficient matrix R ═ (R)ij) Calculating the characteristic value of R, sequencing the characteristic values to obtain a coefficient factor lambda:
Figure GDA0003100695490000103
λ1≥λ2≥…≥λp>0；
step 1.2.6: calculating index weight w under objective weighting based on k principal component elements F and coefficient factor lambdaFCA：
Figure GDA0003100695490000104
Step 1.2.3 comprises the following steps:
step 1.2.3.1: the original matrix X formula is deformed:
XTX＝(ηE+ε)T(ηE+ε)；
step 1.2.3.2: removing special factors:
XTX≈(ηE)T(ηE)；
step 1.2.3.3: introducing an identity matrix gamma based on the formula of the step 1.2.3.2 to obtain a deformation formula, extracting beta in the deformation formula as a common factor, performing factor rotation on the common factor to complete grouping of index factors, and obtaining the number k of main components:
Figure GDA0003100695490000111
step 1.3 comprises the following steps:
step 1.3.1: index weight w based on subjective weightingFAHPAnd index weight w under objective weightingFCACalculating the importance coefficient alpha of the subjective weight of each index by combining the moment estimation theoryuAnd the importance coefficient beta of the objective weightu：
wFAHP＝[w1′,w2′,…,wN′]
wFCA＝[w1″,w2″,…,wN″]
Figure GDA0003100695490000112
Step 1.3.2: calculating the subjective and objective combination weight of a single index factor to complete the construction of a calculation model:
Figure GDA0003100695490000113
the technical effects are as follows: according to the invention, the DEMATEL method is used for optimizing the fuzzy hierarchy analysis in consideration of the transverse and longitudinal influence factors of the index hierarchy structure, then subjective weighting is carried out, the factor analysis method is used for reasonably reducing the dimension, analyzing and optimizing the principal component division process, objective weighting is carried out, and the principal and objective combination weight of the index factors is obtained, so that the problem that the evaluation rationality and accuracy are poor due to the fact that the traditional weighting algorithm adopted when AHP and PCA are adopted for carrying out combined weighting is only suitable for an information system with simple structure and single data is solved, and the effects of improving the rationality of subjective evaluation and the accuracy of objective evaluation are achieved; optimizing a judgment process of the hierarchical influence degree among the indexes in the fuzzy hierarchical analysis process by combining a DEMATEL method, comprehensively considering transverse weighting factors, namely analyzing the mutual influence degree among the indexes at the same level on the basis of the original longitudinal weighting, namely analyzing the influence degree of the sub indexes relative to the parent indexes, and improving the rationality of the whole subjective evaluation through weighting analysis; the traditional PCA weighting process is improved based on a factor analysis method, the internal structure of an original matrix is analyzed, the found common factors are combined to reasonably group target index factors, enough original information is obtained through fewer principal components, the common factors obtained through analysis are reasonably grouped to the index factors, the problems that evaluation results depend on a first principal component excessively due to the excessive difference of matrix variance contribution rates among the principal components and the like are avoided, and the actual accuracy of objective evaluation is improved.
The features and properties of the present invention are described in further detail below with reference to examples.
Example 1
As shown in fig. 1 to 4, a method for evaluating health of an information system based on FAHP _ FCA combined authorization includes the following steps:
step 1: constructing a calculation model of subjective and objective combination weight of a single index factor;
step 2: calculating the subjective and objective combination weight of each index factor through a calculation model;
and step 3: calculating the health degree by combining the index operation and maintenance data and the subjective and objective combination weight of each index factor;
the step 1 comprises the following steps:
step 1.1: based on an index evaluation system, weighting optimization is carried out on the fuzzy hierarchy analysis process by comprehensively considering the transverse and longitudinal influence factors of the index hierarchy by using a DEMATEL method, and index weight of subjective weighting is obtained;
step 1.2: performing reasonable dimensionality reduction analysis and optimization of a principal component division process by using a factor analysis method based on an index evaluation system to obtain objective weighted index weight;
step 1.3: and calculating the subjective and objective combination weight of the single index factor according to the index weight of subjective weighting and the index weight of objective weighting to complete the construction of the calculation model.
Step 1.3.1: index weight w based on subjective weightingFAHPAnd index weight w under objective weightingFCACalculating the importance coefficient alpha of the subjective weight of each index by combining the moment estimation theoryuAnd the importance coefficient beta of the objective weightu：
wFAHP＝[w1′,w2′,…,wN′]
wFCA＝[w1″,w2″,…,wN″]
Figure GDA0003100695490000121
Step 1.3.2: calculating the subjective and objective combination weight of a single index factor to complete the construction of a calculation model:
Figure GDA0003100695490000122
the key point of the method is to calculate the weight, calculate the sum of products of the operation and maintenance data and the weight values of each index factor after calculating the subjective and objective combination weight of each index factor to obtain the health degree, and check the interval to which the value of the health degree belongs to judge the health condition of the whole information system, and the step 3 is the prior art in the field and is not described in detail herein; the method comprises the steps of carrying out subjective weighting after transverse and longitudinal influence factors of an index hierarchical structure are considered by a DEMATEL method to optimize fuzzy hierarchical analysis, carrying out reasonable dimensionality reduction analysis and optimization principal component division by a factor analysis method, carrying out objective weighting, obtaining principal and objective combination weights of the index factors, solving the problem that the evaluation rationality and accuracy are poor due to the fact that the traditional weighting algorithm adopted when AHP and PCA are adopted to carry out combination weighting is only suitable for an information system with simple structure and single data, and achieving the effect of improving the rationality of subjective evaluation and the accuracy of objective evaluation.
Example 2
Based on example 1, step 1.1 comprises the following steps:
step 1.1.1: carrying out hierarchical analysis on the index factors to construct an index evaluation system;
step 1.1.2: based on an index evaluation system, a fuzzy judgment matrix A is constructed by adopting a 0-1 scale method:
Figure GDA0003100695490000131
wherein, the element auvRepresents the ratio of the importance of the u-th element to the importance of the v-th element, where u, v ═ 1, 2, …, N;
0-1 fuzzy scale meaning: as shown in the following table:
Figure GDA0003100695490000132
step 1.1.3: the initial characteristic vector w' of the fuzzy judgment matrix A is solved by using a square root method, and the calculation formula is as follows:
Figure GDA0003100695490000133
step 1.1.4: calculating the comprehensive influence weight theta of the index by utilizing a DEMATEL method and combining the influence degree and the influenced degree of the index factor;
step 1.1.5: calculating a single-layer weight vector w under the comprehensive influence factors based on the comprehensive influence weight theta of the index;
step 1.1.6: carrying out consistency check on the fuzzy judgment matrix A through a genetic algorithm based on the single-layer weight vector w to obtain the subjective weighting index weight w for carrying out subjective weighting under the influence of comprehensive factorsFAHP。
Step 1.1.4 comprises the following steps:
step 1.1.4.1: calculating a relation matrix D of influence degree and influence degree among index factors:
d＝fT·e
wherein D represents each element in the relation matrix D, f represents the influence degree, e represents the influenced degree, and T represents the transposition of the matrix;
step 1.1.4.2: calculating a comprehensive influence degree vector D related to index factors by taking diagonal elements of a relation matrix Du：
du＝fu×eu
Wherein f isuIndicating the degree of influence of the index factor, euIndicating the degree of influence of the index factor;
step 1.1.4.3: for the vector d of comprehensive influence degreeuCarrying out normalization processing to obtain a comprehensive influence weight theta:
Figure GDA0003100695490000141
step 1.1.5 comprises the following steps:
step 1.1.5.1: computing a composite feature vector wu：
wu＝θw′
Wherein theta represents the comprehensive influence weight of the index, and w' represents the initial characteristic vector of the fuzzy judgment matrix A;
step 1.1.5.2: for comprehensive characteristic vector wuAnd (3) carrying out normalization:
Figure GDA0003100695490000142
step 1.1.5.3: integrated feature vector based on normalization
Figure GDA0003100695490000143
Calculating single-layer weight vectors under the comprehensive influence factors of the indexes:
Figure GDA0003100695490000144
DEMATEL method: the decision making trial and evaluation laboratory method mainly uses graph theory, takes matrix calculation of a constructed graph as a center, utilizes expert knowledge and experience to solve the problem of complexity in the real world, and is an effective method for factor identification and analysis. The DEMATEL method is applied to the traditional analytic hierarchy process for optimization, the thinking of factor identification and analysis in the DEMATEL method is mainly combined, the mutual influence factors of all object indexes in the analytic hierarchy process are analyzed, errors caused by subjective evaluation of experts are reduced to a certain extent, and therefore the accuracy and the objectivity of weight calculation of all indexes are improved.
The method optimizes the judgment process of the hierarchical influence degree among the indexes in the fuzzy hierarchical analysis process by combining the idea of the DEMATEL method, comprehensively considers the transverse weighting factors (analyzing the mutual influence degree among the indexes at the same level) on the basis of the original longitudinal weighting (analyzing the influence degree of the sub indexes relative to the parent indexes), performs weighting optimization by considering the influence degree and the influence degree, and ensures that the whole subjective evaluation process is more reasonable through weighting analysis.
In order to compare with the empowerment effect of the traditional method, the actual monitoring data of a certain operation and maintenance system is selected for testing. One layer of index evaluation system structure is extracted as an experimental object, and AHP (analytic hierarchy process), FAHP (fuzzy analytic hierarchy process) and DE-FAHP (fuzzy analytic hierarchy process based on DEMATEL method optimization) are respectively adopted to calculate the weight of each index of the layer as shown in the following table:
Figure GDA0003100695490000151
the specific effects are shown in fig. 2: the traditional AHP method adopts a 1-9 scale method when constructing a judgment matrix, has larger parameter interval, and enlarges the error of importance comparison between indexes generated based on artificial subjective evaluation to a certain extent, thereby generating the extreme difference phenomenon of index weight of 'network information' and 'service information' presented in a similar graph. When similar problems occur in the multi-layer index structure, the overall system evaluation is finally dependent on only index factors with high local weights, and the influence of the index factors with low weights on the system state is ignored.
Compared with the method, the FAHP method adopts a 0-1 scale method to construct the judgment matrix, and the concept of the fuzzy consistent matrix is introduced, so that the interval of the importance parameters among indexes is reduced, and the influence of an extreme weight distribution phenomenon on system evaluation is avoided to a certain extent. However, the method is only suitable for evaluation objects with a simpler index hierarchical structure, and for operation and maintenance systems with complex structures and various index factors such as enterprises, the final index factor weight distribution is over-equalized by the method, influence differences among different indexes are difficult to distinguish in actual system evaluation, and when a system operation fails, a key problem cannot be found in a targeted manner.
By combining the characteristics of the two methods, the invention optimizes the distinguishing and positioning of each index in the process of improving the weighting method, highlights the key influence index in the FAHP method and optimizes the condition that the index weighting distinguishing is not obvious; the existing AHP method optimized based on the DEMATEL method is based on the traditional analytic hierarchy process, and when the method is applied to system evaluation with a complex hierarchical structure, the extreme empowerment difference cannot be effectively relieved by weighting optimization based on index factor analysis; the improved FAHP method is optimized, the FAHP method effectively solves the extreme empowerment condition of the AHP method by introducing the concept of fuzzy consistent matrix, factor analysis is carried out by the DEMATEL method, and the importance of each index is highlighted and positioned. In conclusion, the DE-FAHP method provided by the invention introduces influenced factors between indexes and a hierarchy structure to carry out weighted analysis on the basis of the fuzzy analytic hierarchy process, and the combination mode not only can effectively solve the problem of extreme weighting possibly encountered in the analysis process of the AHP method, but also can highlight the importance of each index through the weighted analysis. When the method is applied to system evaluation with a complex actual hierarchical structure, conditions of missed evaluation, false evaluation and the like can be effectively reduced.
Example 3
Based on example 1 or 2, step 1.1.6: carrying out consistency check on the fuzzy judgment matrix A through a genetic algorithm based on the single-layer weight vector w to obtain the subjective weighting index weight w for carrying out subjective weighting under the influence of comprehensive factorsFAHPWhich comprises the following steps:
1) determining an objective function and a constraint condition, namely converting into a nonlinear optimization problem;
2) calculating the fitness of the new population individuals by taking the reciprocal of the target as a fitness function in a genetic algorithm, and selecting excellent individuals from the fitness function to perform crossing and variation operations;
3) continuously iterating, and stopping the algorithm when the difference between the fitness of the current generation and the fitness of the next generation is less than 0.001; otherwise, adjusting the fuzzy judgment matrix to continue iteration until the termination condition is met. After the consistency condition is met, the index weight w under subjective weighting under the influence of the comprehensive factors can be determinedFAHP。
Comparing the time used for solving the consistency problem by GA-FAHP (fuzzy analytic hierarchy process based on genetic algorithm optimization) with FAHP (simple fuzzy analytic hierarchy process) and AHP (traditional analytic hierarchy process), extracting 5 groups of data for comparison, wherein the number of single-layer index items is respectively 2, 3, 4, 5 and 6, and as shown in FIG. 3: the curve rising amplitude of the traditional analytic hierarchy process and the simple fuzzy analytic hierarchy process is continuously increased along with the increase of the number of single-layer index items, namely along with the increase of consistency test targets, the efficiency is obviously reduced; the fuzzy analytic hierarchy process based on genetic algorithm optimization has slow change trend of the whole curve, and shows that the algorithm is more effective and reliable in solving the consistency problem. The consistency check is carried out on the judgment matrix through the genetic algorithm, and compared with the traditional consistency judgment method, the consistency check is converted into the nonlinear optimization problem to obtain the optimal solution, so that the calculation steps are simplified, and the verification efficiency is greatly improved.
Example 4
Based on example 1, the step 1.2 comprises the following steps:
step 1.2 comprises the following steps:
step 1.2.1: constructing an original matrix X based on an index evaluation system:
Figure GDA0003100695490000161
wherein n represents the number of structural layers, and p represents the number of index factors of each layer;
step 1.2.2: normalizing the original matrix X to obtain a matrix Y:
Figure GDA0003100695490000171
Figure GDA0003100695490000172
Figure GDA0003100695490000173
wherein, yijRepresenting values of variables, x, after normalizationijRepresenting the actual variable values in the original matrix X,
Figure GDA0003100695490000174
representing the mean value of the variables, sjRepresents the standard deviation;
step 1.2.3: analyzing the common factor of the original matrix X, and determining the number k of the principal components:
X＝ηE+ε
wherein eta represents a common factor, epsilon represents a special factor, and E represents a factor load matrix;
step 1.2.4: establishing a covariance matrix C based on the matrix Yx＝(cij) Calculating CxThe feature values are sorted to obtain k principal component elements F:
Figure GDA0003100695490000175
F1,F2,…Fk
wherein the content of the first and second substances,
Figure GDA0003100695490000176
representing the mean of the variables, yli、yljRepresenting the element variables in the matrix Y;
step 1.2.5: according to the covariance matrix Cx＝(cij) Constructing a normalized correlation coefficient matrix R ═ (R)ij) Calculating the characteristic value of R, sequencing the characteristic values to obtain a coefficient factor lambda:
Figure GDA0003100695490000177
λ1≥λ2≥…≥λp>0；
step 1.2.6: calculating index weight w under objective weighting based on k principal component elements F and coefficient factor lambdaFCA：
Figure GDA0003100695490000181
Step 1.2.3 comprises the following steps:
step 1.2.3.1: the original matrix X formula is deformed:
XTX＝(ηE+ε)T(ηE+ε)；
step 1.2.3.2: removing special factors:
XTX≈(ηE)T(ηE)；
step 1.2.3.3: introducing an identity matrix gamma based on the formula of the step 1.2.3.2 to obtain a deformation formula, extracting beta in the deformation formula as a common factor, performing factor rotation on the common factor to complete grouping of index factors, and obtaining the number k of main components:
Figure GDA0003100695490000182
wherein, the factor rotation method adopts a variance maximization method or a quartic maximum rotation method or an equivalent maximum method;
in order to verify the advantages of FCA (principal component analysis based on factor analysis process optimization) compared with conventional PCA (principal component analysis), 2 different methods are respectively combined with actual system operation and maintenance data to perform a health assessment test in an experiment, and errors of assessment values under index structures with different complexity degrees are compared, here, 6 groups of data are extracted for comparison, the total number of index objects is respectively 10, 20, 30, 40, 50 and 60, and the test data is shown in the following table:
Figure GDA0003100695490000183
through the comparison of the test data, the following health errors of the two methods can be obtained:
Figure GDA0003100695490000191
the specific effects are shown in fig. 4: along with the increase of the total number of index factors of an evaluation system object, the structure of an overall index evaluation system is complex, and the error of the traditional PCA (principal component analysis) on the evaluation of the system health degree is increased; the evaluation error of the FCA method optimized based on index architecture analysis does not increase along with the complexity of the structure and is always kept in a controllable range. Therefore, compared with the traditional principal component analysis method, the principal component analysis method based on factor analysis process optimization has a more accurate evaluation effect and is more suitable for health diagnosis of a complex operation and maintenance system. The principal component analysis expresses the principal component as a linear combination of the variables, and the factor analysis expresses the variables as a linear combination of the factors. In the traditional principal component analysis process, the number of principal components is the same as the number p of index variables, but when the method is applied to practical problems, only the first k (k < p) principal components are generally selected, the traditional PCA method calculates the variance contribution rate of each principal component and sequences the variance contribution rate, then artificially specifies a contribution rate index, and takes the number of all the principal components larger than the contribution rate index as k, but the artificial influence factor of the method is larger; the number k is determined in a more reasonable and reliable manner. The invention improves the weighting process of principal component analysis based on a factor analysis method, reasonably groups object index factors by analyzing the internal structure of an original matrix and combining found common factors, acquires enough original information through less principal components as much as possible, simultaneously avoids the problems that the evaluation result excessively depends on the first principal component and the like due to the excessive difference of matrix variance contribution rates among the principal components, and greatly improves the actual accuracy of objective evaluation.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (6)

1. An information system health degree evaluation method based on FAHP _ FCA combined empowerment is characterized in that: the method comprises the following steps:
step 1: constructing a calculation model of subjective and objective combination weight of a single index factor based on an index evaluation system;
step 2: calculating the subjective and objective combination weight of each index factor through a calculation model;
and step 3: calculating the health degree by combining the index operation and maintenance data and the subjective and objective combination weight of each index factor;
the step 1 comprises the following steps:
step 1.1: based on an index evaluation system, weighting optimization is carried out on the fuzzy hierarchy analysis process by comprehensively considering the transverse and longitudinal influence factors of the index hierarchy by using a DEMATEL method, and index weight of subjective weighting is obtained;
step 1.2: performing reasonable dimensionality reduction analysis and optimization of a principal component division process by using a factor analysis method based on an index evaluation system to obtain objective weighted index weight;
the step 1.2 comprises the following steps:
step 1.2.1: constructing an original matrix X based on an index evaluation system:
Figure FDA0003100695480000011
wherein n represents the number of structural layers, and p represents the number of index factors of each layer;
step 1.2.2: normalizing the original matrix X to obtain a matrix Y:
Figure FDA0003100695480000012
Figure FDA0003100695480000013
Figure FDA0003100695480000014
wherein, yijRepresenting values of variables, x, after normalizationijRepresenting the actual variable values in the original matrix X,
Figure FDA0003100695480000015
representing the mean value of the variables, sjRepresents the standard deviation;
step 1.2.3: analyzing the common factor of the original matrix X, and determining the number k of the principal components:
X＝ηE+ε
wherein eta represents a common factor, epsilon represents a special factor, and E represents a factor load matrix;
step 1.2.4: establishing a covariance matrix C based on the matrix Yx＝(cij)，Calculating CxThe feature values are sorted to obtain k principal component elements F:
Figure FDA0003100695480000021
F1,F2,…Fk
wherein the content of the first and second substances,
Figure FDA0003100695480000022
representing the mean of the variables, yli、yljRepresenting the element variables in the matrix Y;
step 1.2.5: according to the covariance matrix Cx＝(cij) Constructing a normalized correlation coefficient matrix R ═ (R)ij) Calculating the characteristic value of R, sequencing the characteristic values to obtain a coefficient factor lambda:
Figure FDA0003100695480000023
λ1≥λ2≥…≥λp>0；
step 1.2.6: calculating index weight w under objective weighting based on k principal component elements F and coefficient factor lambdaFCA：
Figure FDA0003100695480000024
Step 1.3: and calculating the subjective and objective combination weight of the single index factor according to the index weight of subjective weighting and the index weight of objective weighting to complete the construction of the calculation model.
2. The FAHP _ FCA combination-empowerment-based information system health assessment method according to claim 1, wherein: the step 1.1 comprises the following steps:
step 1.1.1: carrying out hierarchical analysis on the index factors to construct an index evaluation system;
step 1.1.2: based on an index evaluation system, a fuzzy judgment matrix A is constructed by adopting a 0-1 scale method:
Figure FDA0003100695480000025
wherein, the element auvRepresents the ratio of the importance of the u-th element to the importance of the v-th element, where u, v ═ 1, 2, …, N;
step 1.1.3: the initial characteristic vector w' of the fuzzy judgment matrix A is solved by using a square root method, and the calculation formula is as follows:
Figure FDA0003100695480000031
step 1.1.4: calculating the comprehensive influence weight theta of the index by utilizing a DEMATEL method and combining the influence degree and the influenced degree of the index factor;
step 1.1.5: calculating a single-layer weight vector w under the comprehensive influence factors based on the comprehensive influence weight theta of the index;
step 1.1.6: carrying out consistency check on the fuzzy judgment matrix A through a genetic algorithm based on the single-layer weight vector w to obtain the subjective weighting index weight w for carrying out subjective weighting under the influence of comprehensive factorsFAHP。
3. The FAHP _ FCA combination-empowerment-based information system health assessment method according to claim 2, wherein: the step 1.1.4 comprises the following steps:
step 1.1.4.1: calculating a relation matrix D of influence degree and influence degree among index factors:
d＝fT·e
wherein D represents each element in the relation matrix D, f represents the influence degree, e represents the influenced degree, and T represents the transposition of the matrix;
step 1.1.4.2: calculating the index factors by taking the diagonal elements of the relation matrix DVector d of integrated influence degree of elementsu：
du＝fu×eu
Wherein f isuIndicating the degree of influence of the index factor, euIndicating the degree of influence of the index factor;
step 1.1.4.3: for the vector d of comprehensive influence degreeuCarrying out normalization processing to obtain a comprehensive influence weight theta:
Figure FDA0003100695480000032
4. the FAHP _ FCA combination-empowerment-based information system health assessment method according to claim 2 or 3, wherein: the step 1.1.5 comprises the following steps:
step 1.1.5.1: computing a composite feature vector wu：
wu＝θw′
Wherein theta represents the comprehensive influence weight of the index, and w' represents the initial characteristic vector of the fuzzy judgment matrix A;
step 1.1.5.2: for comprehensive characteristic vector wuAnd (3) carrying out normalization:
Figure FDA0003100695480000033
step 1.1.5.3: integrated feature vector based on normalization
Figure FDA0003100695480000041
Calculating single-layer weight vectors under the comprehensive influence factors of the indexes:
Figure FDA0003100695480000042
5. the FAHP _ FCA combination-empowerment-based information system health assessment method according to claim 1, wherein: the step 1.2.3 comprises the following steps:
step 1.2.3.1: the original matrix X formula is deformed:
XTX＝(ηE+ε)T(ηE+ε)；
step 1.2.3.2: removing special factors:
XTX≈(ηE)T(ηE)；
step 1.2.3.3: introducing an identity matrix gamma based on the formula of the step 1.2.3.2 to obtain a deformation formula, extracting beta in the deformation formula as a common factor, performing factor rotation on the common factor to complete grouping of index factors, and obtaining the number k of main components:
Figure FDA0003100695480000043
6. the FAHP _ FCA combination-empowerment-based information system health assessment method according to claim 1, 2 or 5, wherein: the step 1.3 comprises the following steps:
step 1.3.1: index weight w based on subjective weightingFAHPAnd index weight w under objective weightingFCACalculating the importance coefficient alpha of the subjective weight of each index by combining the moment estimation theoryuAnd the importance coefficient beta of the objective weightu：
wFAHP＝[w1′,w2′,…,wN′]
wFCA＝[w1″,w2″,…,wN″]
Figure FDA0003100695480000044
Step 1.3.2: calculating the subjective and objective combination weight of a single index factor to complete the construction of a calculation model:
Figure FDA0003100695480000051
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