CN102902882A - Method for evaluating operation quality of information systems - Google Patents

Abstract

The invention discloses a method for evaluating operation quality of information systems. The method comprises the steps of firstly, constructing an evaluation index system for the operation quality of information systems; secondly, using an analytic hierarchy process to evaluate the operation quality of the qualitative information system and calculate the subjective weight of evaluation indexes, using an entropy weight method to evaluate the operation quality of the quantitative information system and calculate the objective weight of evaluation indexes, and synthesizing the subjective weight of evaluation indexes and the objective weight of evaluation indexes to calculate the combined weight of all evaluation indexes; and finally, calculating evaluative values of all evaluation objects according to the combined weight, and conducting evaluation analyses on evaluative values of all evaluation objects. According to the method, the entropy weight method and the analytic hierarchy process are combined to evaluate the operation quality of information systems, the potential problems in operation of information systems are found out, the operation guaranteeing capability of information systems is improved, and the operation and maintenance level of information systems is evaluated accurately and objectively, so that the safe, high-efficiency and economical operation of information systems is effectively guided.

Description

A kind of evaluation method of infosystem running quality

Technical field

The present invention relates to the evaluation field of infosystem running quality, specifically a kind of method of the infosystem running quality being carried out comprehensive evaluation in conjunction with entropy power method and analytical hierarchy process.

Background technology

Analytical hierarchy process evaluation is generally adopted in the evaluation of present infosystem running quality, specifically contrast in twos judgment matrix, this situation is easy to occur successively problem of inconsistency of target, and the weight that analytical hierarchy process obtains is subjective weight, estimates inadequate overall scientific.

The concrete shortcoming of analytical hierarchy process shows as:

(1), can not provide new departure for decision-making

The effect of analytical hierarchy process is to select than the superior from alternatives.This effect has illustrated that just in time analytical hierarchy process can only choose from original scheme, and can not provide the new departure of dealing with problems for the decision maker.

(2), quantitative data is less, qualitative composition is many, is difficult for convincing

Analytical hierarchy process is a kind of method of the decision mode with simulating human brain, and is therefore inevitable with more qualitative color.

Summary of the invention

The technical problem to be solved in the present invention provides a kind of evaluation method of infosystem running quality, use entropy power method and analytical hierarchy process in conjunction with the infosystem running quality is estimated, excavate infosystem potential problem in service, purpose is to promote infosystem operational support ability, accurate and objectively evaluation information system O﹠M level, thereby effectively tutorial message security of system, efficient, economical operation.

Technical scheme of the present invention is:

A kind of evaluation method of infosystem running quality may further comprise the steps:

(1), makes up infosystem running quality assessment indicator system: obtain the respectively infosystem attribute data of the unit of evaluation, it is classified and set up corresponding attribute database;

(2), according to infosystem operating statistic data and the reported data of the unit of evaluation respectively, adopt analytical hierarchy process to carry out the assessment of qualitative information system running quality, and calculate the subjective weight of evaluation index;

(3), according to infosystem operating statistic data and the reported data of the unit of evaluation respectively, adopt entropy power method to carry out the assessment of quantitative information system running quality, and calculate the objective weight of evaluation index;

(4), the subjective weight of comprehensive evaluation index and the objective weight combining weights that calculates each evaluation index;

(5), calculate the evaluation of estimate of each evaluation object according to combining weights, then carry out evaluation analysis according to the size of the evaluation of estimate of each evaluation object.

Infosystem attribute data described in the step 1 is divided three classes, and is respectively infosystem run-level data, infosystem security of operation data, operation job specification data.

Adopt analytical hierarchy process to carry out the assessment of qualitative information system running quality in the step 2, specifically may further comprise the steps:

A, the scale of establishing thinking judgement quantification;

B, set up hierarchy Model, this model comprises destination layer, rule layer, solution layer;

C, Judgement Matricies use the method for comparing in twos, and each coherent element is relatively marked in twos, according to some indexs in middle layer, can obtain some in twos more in pairs than matrix;

D, the single order weight vector of calculating are also done consistency check;

E, vectorial to each paired comparator matrix calculating eigenvalue of maximum and characteristic of correspondence utilizes coincident indicator, random index and Consistency Ratio to do consistency check; If upcheck, the proper vector after the normalization is subjective weight vectors; If do not pass through, reappear Judgement Matricies;

F, calculating total ordering weight vector are also done consistency check: calculate orlop to the total weight vector that sorts of the superiors, utilize total ordering Consistency Ratio to test; If pass through, the result who then represents according to total ordering weight vector makes a strategic decision, otherwise rethink model or re-construct Consistency Ratio larger in pairs than matrix.

Adopt entropy power method to carry out the assessment of quantitative information system running quality in the step 3, specifically may further comprise the steps:

A, supposition are evaluated object m, and each evaluation index that is evaluated object has n, development of judgment matrix:

R＝(r _ij) _m×n i=1,2,...,m;j=1,2,...,n；

B, judgment matrix is carried out normalization R, obtain normalization matrix B, the element of B is

$b_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

In the following formula, min (r _Ij), max (r _Ij) be the most satisfied person or least satisfied person in the different things under the same index;

C, according to the entropy of traditional each evaluation index of entropy concept definable:

$H_j=-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{f}_{\mathrm{ij}}\ln f_{\mathrm{ij}}\right)/\ln m;$

In the following formula, $f_{\mathrm{ij}}=b_{\mathrm{ij}}/\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{b}_{\mathrm{ij}};$

Meaningful for making, be not contrary in the implication of entropy, will be modified to

D and then obtain the entropy power ω of j evaluation index _j, be defined as the objective weight vector:

Weight vector ω=(ω _j) _{1 * n},

In the following formula, ${\mathrm{\ω}}_j=\frac{1-H_j}{n-\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_j}.$

The concrete steps of the combining weights that the subjective weight of the comprehensive evaluation index described in the step 4 and objective weight are calculated each evaluation index include: the calculation combination weight: Comprehensive analytic hierarchy process weight vectors and entropy power method weight vectors obtain the combining weights vector, and computing method are as follows:

A, suppose to obtain subjective weight vectors W=(w by analytical hierarchy process _j) _{1 * n}

B, suppose to obtain objective weight vector ω=(ω by entropy power method _j) _{1 * n}

C, Comprehensive analytic hierarchy process and entropy power method obtain the combining weights vector and are:

In the following formula,

Index in the described quality evaluation system is carried out the standardization of evaluation index forward and nondimensionalization before analytical hierarchy process and entropy power method are assessed, concrete steps are:

As j item index x _jDuring for direct index, when namely being the bigger the better, it is done such as down conversion:

$t_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

In the following formula, i=1,2 ..., m; J=1,2 ..., n; M represents the unit's of evaluation number, and n represents the evaluation index number.

As j item index x _jDuring for negative index, when namely the smaller the better, its is done such as down conversion:

$t_{\mathrm{ij}}=\frac{\max \left(r_{\mathrm{ij}}\right)-r_{\mathrm{ij}}}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

Wherein: i=1,2 ..., m; J=1,2 ..., n; M represents the unit's of evaluation number, and n represents the evaluation index number.

As j item index x _jDuring interval index, be best and more near when better apart from this interval at interval [a, b] namely, to its work such as down conversion:

$t_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{a-\min \left(r_{\mathrm{ij}}\right)}& \min \left(r_{\mathrm{ij}}\right)\≤r_{\mathrm{ij}}\≤a\\ 1& a\≤r_{\mathrm{ij}}\≤b\\ \frac{\max \left(r_{\mathrm{ij}}\right)-r_{\mathrm{ij}}}{\max \left(r_{\mathrm{ij}}\right)-b}& b\≤r_{\mathrm{ij}}\≤\max \left(r_{\mathrm{ij}}\right)\end{array}\right.;$

Wherein: i=1,2 ..., m; J=1,2 ..., n; M represents unit to be evaluated number, and n represents the evaluation index number.

Described to each paired comparator matrix calculating eigenvalue of maximum and characteristic of correspondence vector, utilize coincident indicator, random index and Consistency Ratio to do consistency check; If upcheck, the proper vector after the normalization is subjective weight vectors; If do not pass through, reappear Judgement Matricies, it specifically may further comprise the steps:

1., at first each column element of judgment matrix is made normalized, its element general term is

$\stackrel{\‾}{p_{\mathrm{ij}}}=\frac{p_{\mathrm{ij}}}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\‾}{p_{\mathrm{ij}}}}(i,j=\mathrm{1,2},...,n);$

2., with the matrix after each row normalization by the row addition,

3., again will Institute's directed quantity

Normalization obtains:

$W_i=\frac{\stackrel{\‾}{W_i}}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\‾}{W_j}}(i,j=\mathrm{1,2},...,n);$

The W=[W that obtains ₁, W ₂..., W _n] ^TBe required proper vector;

4., the maximum characteristic root of calculating judgment matrix is:

In the formula, (pW) _iI component element for pW;

5., carry out consistency check:

Calculate coincident indicator CI:

Calculate coincident indicator CR:

CR is less, and the consistance of judgment matrix better; When CR＜0.1, judgment matrix satisfies consistency check; Otherwise the reply judgment matrix is suitably adjusted; In the following formula, RI is the mean random coincident indicator, is the enough conforming mean value that calculates of the judgment matrix that occurs at random of a plurality of bases.

Beneficial effect of the present invention is:

(1), integrated use analytical hierarchy process of the present invention, entropy power method, research information system running quality Appraising Methods and technology, form " based on the infosystem running quality evaluation model of entropy power analytical hierarchy process ", realize innovation at State Grid Corporation of China's infosystem running quality evaluation theory and method;

(2), the application of the invention can be weighed the infosystem running quality level of constituent parts, tutorial message system operation optimization structure and winding level;

(3), the present invention adopts the method that entropy power is combined with subjective weight to determine comprehensive weight, take into account subjective preferences and objective attribute, the calculating of each evaluation index weight realizes easily through computer programming, thereby can improve the efficient of infosystem running quality assessment, operability is stronger, realizes preferably the raising of the assessment of infosystem running quality and operation and maintenance level.

Embodiment

A kind of evaluation method of infosystem running quality may further comprise the steps:

(1), makes up infosystem running quality assessment indicator system: obtain the respectively infosystem attribute data of the unit of evaluation, the infosystem attribute data is divided three classes, be respectively infosystem run-level data, infosystem security of operation data, operation job specification data, it is classified and set up corresponding attribute database;

(2), carry out the standardization of evaluation index forward and nondimensionalization, concrete steps are:

As j item index x _jDuring for direct index, when namely being the bigger the better, it is done such as down conversion:

$t_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

In the following formula, i=1,2 ..., m; J=1,2 ..., n; M represents the unit's of evaluation number, and n represents the evaluation index number.As j item index x _jDuring for negative index, when namely the smaller the better, its is done such as down conversion:

$t_{\mathrm{ij}}=\frac{\max \left(r_{\mathrm{ij}}\right)-r_{\mathrm{ij}}}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

Wherein: i=1,2 ..., m; J=1,2 ..., n; M represents the unit's of evaluation number, and n represents the evaluation index number.

As j item index x _jDuring interval index, be best and more near when better apart from this interval at interval [a, b] namely, to its work such as down conversion:

$t_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{a-\min \left(r_{\mathrm{ij}}\right)}& \min \left(r_{\mathrm{ij}}\right)\≤r_{\mathrm{ij}}\≤a\\ 1& a\≤r_{\mathrm{ij}}\≤b\\ \frac{\max \left(r_{\mathrm{ij}}\right)-r_{\mathrm{ij}}}{\max \left(r_{\mathrm{ij}}\right)-b}& b\≤r_{\mathrm{ij}}\≤\max \left(r_{\mathrm{ij}}\right)\end{array}\right.;$

Wherein: i=1,2 ..., m; J=1,2 ..., n; M represents unit to be evaluated number, and n represents the evaluation index number;

(3), according to infosystem operating statistic data and the reported data of the unit of evaluation respectively, adopt analytical hierarchy process to carry out the assessment of qualitative information system running quality, and calculate the subjective weight of evaluation index; Specifically may further comprise the steps:

A, the scale of establishing thinking judgement quantification;

B, set up hierarchy Model, this model comprises destination layer, rule layer, solution layer;

C, Judgement Matricies use the method for comparing in twos, and each coherent element is relatively marked in twos, according to some indexs in middle layer, can obtain some in twos more in pairs than matrix;

D, the single order weight vector of calculating are also done consistency check;

E, vectorial to each paired comparator matrix calculating eigenvalue of maximum and characteristic of correspondence utilizes coincident indicator, random index and Consistency Ratio to do consistency check; If upcheck, the proper vector after the normalization is subjective weight vectors; If do not pass through, reappear Judgement Matricies; It specifically may further comprise the steps:

1., at first each column element of judgment matrix is made normalized, its element general term is

$\stackrel{\‾}{p_{\mathrm{ij}}}=\frac{p_{\mathrm{ij}}}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\‾}{p_{\mathrm{ij}}}}(i,j=\mathrm{1,2},...,n);$

2., with the matrix after each row normalization by the row addition,

3., again will

Institute's directed quantity

Normalization obtains:

$W_i=\frac{\stackrel{\‾}{W_i}}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\‾}{W_j}}(i,j=\mathrm{1,2},...,n);$

The W=[W that obtains ₁, W ₂..., W _n] ^TBe required proper vector;

4., the maximum characteristic root of calculating judgment matrix is:

In the formula, (pW) _iI component element for pW;

5., carry out consistency check:

Calculate coincident indicator CI:

Calculate coincident indicator CR:

CR is less, and the consistance of judgment matrix better; When CR＜0.1, judgment matrix satisfies consistency check; Otherwise the reply judgment matrix is suitably adjusted; In the following formula, RI is the mean random coincident indicator, is the enough conforming mean value that calculates of the judgment matrix that occurs at random of a plurality of bases;

F, calculating total ordering weight vector are also done consistency check: calculate orlop to the total weight vector that sorts of the superiors, utilize total ordering Consistency Ratio to test; If pass through, the result who then represents according to total ordering weight vector makes a strategic decision, otherwise rethink model or re-construct Consistency Ratio larger in pairs than matrix.

(4), according to infosystem operating statistic data and the reported data of the unit of evaluation respectively, adopt entropy power method to carry out the assessment of quantitative information system running quality, and calculate the objective weight of evaluation index; Specifically may further comprise the steps:

A, supposition are evaluated object m, and each evaluation index that is evaluated object has n, development of judgment matrix:

R＝(r _ij) _m×n i=1,2,...,m;j=1,2,...,n；

B, judgment matrix is carried out normalization R, obtain normalization matrix B, the element of B is

$b_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

In the following formula, min (r _Ij), max (r _Ij) be the most satisfied person or least satisfied person in the different things under the same index;

C, according to the entropy of traditional each evaluation index of entropy concept definable:

$H_j=-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{f}_{\mathrm{ij}}\ln f_{\mathrm{ij}}\right)/\ln m;$

In the following formula, $f_{\mathrm{ij}}=b_{\mathrm{ij}}/\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{b}_{\mathrm{ij}};$

Meaningful for making, be not contrary in the implication of entropy, will be modified to

D and then obtain the entropy power ω of j evaluation index _j, be defined as the objective weight vector:

Weight vector ω=(ω _j) _{1 * n},

In the following formula, ${\mathrm{\ω}}_j=\frac{1-H_j}{n-\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_j};$

(5), the subjective weight of comprehensive evaluation index and the objective weight combining weights that calculates each evaluation index; Computing method are as follows:

A, suppose to obtain subjective weight vectors W=(w by analytical hierarchy process _j) _{1 * n}

B, suppose to obtain objective weight vector ω=(ω by entropy power method _j) _{1 * n}

C, Comprehensive analytic hierarchy process and entropy power method obtain the combining weights vector and are:

In the following formula,

(6), calculate the evaluation of each evaluation object according to combining weights:

According to x _iSize, estimate each evaluation object.x _iLarger, show that i object is more excellent.

Claims (7)

1. the evaluation method of an infosystem running quality is characterized in that: may further comprise the steps:

(1), makes up infosystem running quality assessment indicator system: obtain the respectively infosystem attribute data of the unit of evaluation, it is classified and set up corresponding attribute database;

(2), according to infosystem operating statistic data and the reported data of the unit of evaluation respectively, adopt analytical hierarchy process to carry out the assessment of qualitative information system running quality, and calculate the subjective weight of evaluation index;

(3), according to infosystem operating statistic data and the reported data of the unit of evaluation respectively, adopt entropy power method to carry out the assessment of quantitative information system running quality, and calculate the objective weight of evaluation index;

(4), the subjective weight of comprehensive evaluation index and the objective weight combining weights that calculates each evaluation index;

(5), calculate the evaluation of estimate of each evaluation object according to combining weights, then carry out evaluation analysis according to the size of the evaluation of estimate of each evaluation object.

2. the evaluation method of a kind of infosystem running quality according to claim 1, it is characterized in that: the infosystem attribute data described in the step 1 is divided three classes, and is respectively infosystem run-level data, infosystem security of operation data, operation job specification data.

3. the evaluation method of a kind of infosystem running quality according to claim 1 is characterized in that: adopt analytical hierarchy process to carry out the assessment of qualitative information system running quality in the step 2, specifically may further comprise the steps:

A, the scale of establishing thinking judgement quantification;

B, set up hierarchy Model, this model comprises destination layer, rule layer, solution layer;

C, Judgement Matricies use the method for comparing in twos, and each coherent element is relatively marked in twos, according to some indexs in middle layer, can obtain some in twos more in pairs than matrix;

D, the single order weight vector of calculating are also done consistency check;

E, vectorial to each paired comparator matrix calculating eigenvalue of maximum and characteristic of correspondence utilizes coincident indicator, random index and Consistency Ratio to do consistency check; If upcheck, the proper vector after the normalization is subjective weight vectors; If do not pass through, reappear Judgement Matricies;

F, calculating total ordering weight vector are also done consistency check: calculate orlop to the total weight vector that sorts of the superiors, utilize total ordering Consistency Ratio to test; If pass through, the result who then represents according to total ordering weight vector makes a strategic decision, otherwise rethink model or re-construct Consistency Ratio larger in pairs than matrix.

4. the evaluation method of a kind of infosystem running quality according to claim 1 is characterized in that: adopt entropy power method to carry out the assessment of quantitative information system running quality in the step 3, specifically may further comprise the steps:

A, supposition are evaluated object m, and each evaluation index that is evaluated object has n, development of judgment matrix:

R＝(r _ij) _m×n i=1,2,...,m;j=1,2,...,n；

B, judgment matrix is carried out normalization R, obtain normalization matrix B, the element of B is

$b_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

In the following formula, min (r _Ij), max (r _Ij) be the most satisfied person or least satisfied person in the different things under the same index;

C, according to the entropy of traditional each evaluation index of entropy concept definable:

$H_j=-\left(\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{f}_{\mathrm{ij}}\ln f_{\mathrm{ij}}\right)/\ln m;$

In the following formula, $f_{\mathrm{ij}}=b_{\mathrm{ij}}/\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{b}_{\mathrm{ij}};$

Meaningful for making, be not contrary in the implication of entropy, will be modified to

D and then obtain the entropy power ω of j evaluation index _jBe defined as the objective weight vector:

Weight vector ω=(ω _j) _{1 * n},

In the following formula, ${\mathrm{\ω}}_j=\frac{1-H_j}{n-\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_j}.$

5. the evaluation method of a kind of infosystem running quality according to claim 1, it is characterized in that: the concrete steps of the combining weights that the subjective weight of the comprehensive evaluation index described in the step 4 and objective weight are calculated each evaluation index include: the calculation combination weight: Comprehensive analytic hierarchy process weight vectors and entropy power method weight vectors obtain the combining weights vector, and computing method are as follows:

A, suppose to obtain subjective weight vectors W=(w by analytical hierarchy process _j) _{1 * n}

B, suppose to obtain objective weight vector ω=(ω by entropy power method _j) _{1 * n}

C, Comprehensive analytic hierarchy process and entropy power method obtain the combining weights vector and are:

In the following formula,

6. the evaluation method of a kind of infosystem running quality according to claim 1, it is characterized in that: the index in the described quality evaluation system is before analytical hierarchy process and entropy power method are assessed, carry out the standardization of evaluation index forward and nondimensionalization, concrete steps are:

As j item index x _jDuring for direct index, when namely being the bigger the better, it is done such as down conversion:

$t_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

In the following formula, i=1,2 ..., m; J=1,2 ..., n; M represents the unit's of evaluation number, and n represents the evaluation index number.

As j item index x _jDuring for negative index, when namely the smaller the better, its is done such as down conversion:

$t_{\mathrm{ij}}=\frac{\max \left(r_{\mathrm{ij}}\right)-r_{\mathrm{ij}}}{\max \left(r_{\mathrm{ij}}\right)-\min \left(r_{\mathrm{ij}}\right)};$

Wherein: i=1,2 ..., m; J=1,2 ..., n; M represents the unit's of evaluation number, and n represents the evaluation index number.

As j item index x _jDuring interval index, be best and more near when better apart from this interval at interval [a, b] namely, to its work such as down conversion:

$t_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{r_{\mathrm{ij}}-\min \left(r_{\mathrm{ij}}\right)}{a-\min \left(r_{\mathrm{ij}}\right)}& \min \left(r_{\mathrm{ij}}\right)\≤r_{\mathrm{ij}}\≤a\\ 1& a\≤r_{\mathrm{ij}}\≤b\\ \frac{\max \left(r_{\mathrm{ij}}\right)-r_{\mathrm{ij}}}{\max \left(r_{\mathrm{ij}}\right)-b}& b\≤r_{\mathrm{ij}}\≤\max \left(r_{\mathrm{ij}}\right)\end{array}\right.;$

Wherein: i=1,2 ..., m; J=1,2 ..., n; M represents unit to be evaluated number, and n represents the evaluation index number.

7. the evaluation method of a kind of infosystem running quality according to claim 3, it is characterized in that: described to each paired comparator matrix calculating eigenvalue of maximum and characteristic of correspondence vector, utilize coincident indicator, random index and Consistency Ratio to do consistency check; If upcheck, the proper vector after the normalization is subjective weight vectors; If do not pass through, reappear Judgement Matricies, it specifically may further comprise the steps:

1., at first each column element of judgment matrix is made normalized, its element general term is

$\stackrel{\‾}{p_{\mathrm{ij}}}=\frac{p_{\mathrm{ij}}}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\‾}{p_{\mathrm{ij}}}}(i,j=\mathrm{1,2},...,n);$

2., with the matrix after each row normalization by the row addition,

3., again will

Institute's directed quantity

Normalization obtains:

$W_i=\frac{\stackrel{\‾}{W_i}}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\‾}{W_j}}(i,j=\mathrm{1,2},...,n);$

The W=[W that obtains ₁, W ₂..., W _n] ^TBe required proper vector;

4., the maximum characteristic root of calculating judgment matrix is:

In the formula, (pW) _iI component element for pW;

5., carry out consistency check:

Calculate coincident indicator CI:

Calculate coincident indicator CR:

CR is less, and the consistance of judgment matrix better; When CR＜0.1, judgment matrix satisfies consistency check; Otherwise the reply judgment matrix is suitably adjusted; In the following formula, RI is the mean random coincident indicator, is the enough conforming mean value that calculates of the judgment matrix that occurs at random of a plurality of bases.