CN103366090B - Index weight assessment method based on section rating of experts - Google Patents

Abstract

The invention aims to a multi-objective decision problem, provides an index weight assessment method based on section rating of experts, and mainly solves the problem of consistency in index weight assessment of the experts. The method comprises the following steps: when comprising rating on two indexes is performed, the experts are not required to give a determined judgment result, while the judgment result can be represented by a discrete section containing one or more than one judgment result; an iterative search algorithm is designed to search a pairwise index comparison matrix which has the optimal consistency in section rating results of the experts; according to the optimal-consistency matrix, a logarithm least square method is utilized to calculate weights of each indexes. According to the invention, the section rating is used to replace the determined rating, on one hand, the rating difficulty of the experts is reduced, and on the other hand, the inconsistency of rating results can be effectively improved.

Description

Based on the index weights appraisal procedure of expert interval marking

Technical field

The present invention relates to multiobjectives decision or information fusion field, particularly a kind of method assessed of index weights.

Background technology

In the field such as multiobjectives decision, information fusion, the importance assessment between different index and attribute and weight calculation are FAQs.Traditional index weights assessment, compares marking by expert between two to different index, generates index pairwise comparison matrix, utilize logarithmic least square priority method to calculate each index weights.

Expert carries out important ratio comparatively according to the experience of oneself and professional knowledge, but due to experience and the limitation of professional knowledge and the complicacy of decision problem, expert is often difficult to provide determinacy to index importance and judges.And in traditional index weight estimation method, require that expert provides unique marking, cause expert can only provide judgement according to uncertain understanding, add difficulty and the workload of expert estimation on the one hand, may cause on the other hand between marking result and there is inconsequent, be difficult to the transitivity and the reciprocity that ensure index significance level, cause index pairwise comparison matrix consistance to reduce and index weights miscount.

At present, for the expert estimation result not meeting coherence request, disposal route mainly comprises two kinds: 1) require that expert evaluates again; 2) by the part marking result of automatic search and Change impact index significance level transitivity and reciprocity, generate new index pairwise comparison matrix, make its consistent sexual satisfaction requirement.But said method all exists restriction in application process, its subject matter is: 1) require that expert evaluates expense again too large, and the assessment result of expert often represents the subjective judgement of expert, is difficult to by again evaluating the consistance improving net result; 2) revise the judged result that expert estimation the possibility of result changes expert, cause the appraisal result that obtains and expert judgments not to meet, be difficult to the target realizing expert analysis mode.

Summary of the invention

For index weights assessment in, expert face part index number be difficult to provide determine judge, provide inconsistent marking, cause the problem of index weights miscount; The invention provides a kind of index weights appraisal procedure based on the marking of expert interval, assist expert to provide the higher index pairwise comparison matrix of consistance, improve the correctness of index weights.

Object of the present invention is achieved through the following technical solutions:

Based on the index weights appraisal procedure of expert interval marking, comprise the steps:

S101, needing the requirement of corresponding ratings between the index assessed and index according to user, generating for specifying the interval grade form of the expert of index;

S102, expert, according to the interval grade form of expert, carry out interval scoring to each index;

S103, expert is converted into numerical value set to the scoring of the interval of different index, the set of values symphysis of marking between two in conjunction with all indexs becomes interval rating matrix collection;

S104, each matrix is concentrated to generate initial pairwise comparison matrix according to Different Strategies from interval rating matrix, strategy comprises maximum selection rule, minimum value is selected, median is selected and Stochastic choice, and initial pairwise comparison matrix is set to current pairwise comparison matrix;

S105, utilize the consistance guided based on adjoint matrix to optimize matrix searching algorithm, concentrate the optimization matrix searching for current pairwise comparison matrix from interval rating matrix;

S106, calculate current pairwise comparison matrix and optimize the parameter of consistency of matrix, judging whether to meet optimal conditions, if do not meet, optimization matrix is set to pairwise comparison matrix, proceeds to step S105; If meet optimal conditions, proceed to step S107;

S107, according to optimization matrix, calculate the weighted value of each index.

The present invention further improves and is: the interval grade form generation step of the expert described in described step S101 is:

A), index corresponding ratings k requires as odd number, significance level between two indices X and Y is divided into 1 from small to large, 2, k level, wherein 1 grade represents index X to compare index Y completely inessential, and (1+k)/2 grade represent that two indices is of equal importance, and k level represents that index X is completely important in index Y;

B), the number n of evaluation index as required, generate the form of a n × n, wherein the comparing result of i-th index and a jth index is shown in the i-th row jth list;

C), by the comparing result that the i-th row on form diagonal line and jth arrange be set to (1+k)/2 grade, represent that the significance level of identical index is equal;

D), by the comparing result below form diagonal line be set to sky, expert is without the need to marking, and its marking value is calculated by the comparing result above form diagonal line.

The present invention further improves and is: the interval scoring described in affiliated step S102, refers to that the discrete segment comprising multiple judged result with represents when to a pair index contrast scoring.

The present invention further improves and is: the generation step of the interval rating matrix collection described in described step 103 is:

1), according to the marking result of expert's first gust in grade form, the value of second gust is calculated, if the comparing result a in form above any diagonal line _ij; a _ijrepresent that i-th index compares the important level of a jth index, i>j; Comparing result a below the diagonal line that then form is corresponding _jiequal k+1-a _ij; a _jirepresent that a jth index compares the important level of i-th index, i>j;

2), according to formula f (a)=c^ ((1/2) * (a-5)), Scoring System a is converted into numerical value, and wherein c is weight coefficient, c be greater than 1 integer; By the interval appraisal result (a of index i and index j _p, a _p+1..., a _q), be converted into score value set { f (a _p), f (a _p+1) ..., f (a _q);

3) the score value set, using index contrasted between two is as element, and generate n rank matrix, this matrix is interval rating matrix collection.

The present invention further improves and is: the initial pairwise comparison matrix generation method described in described step S104 comprises four kinds:

1), maximum selection rule, on interval rating matrix collection triangle each score value set in, choose wherein maximal value as the element of initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix;

2), minimum value selects, on interval rating matrix collection triangle each score value set in, choose wherein minimum value as the element of initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix;

3), intermediate value selects, on interval rating matrix collection triangle each score value set in, according to size sequence, choose the element of rank value placed in the middle as initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix;

4), Stochastic choice, on interval rating matrix collection triangle each score value set in, one of them value of random selecting as the element of initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix.

The present invention further improves and is: the consistance based on adjoint matrix guiding described in step S105 is optimized matrix searching algorithm step and is: the weight contrast matrix calculating current pairwise comparison matrix; From each position of rating matrix collection between contrast district, find and contrast the immediate value of matrix with weight, generate and optimize matrix.

The present invention further improves and is: the computing method of weight contrast matrix are: for matrix A=(a _ij) _{n × n}, calculate the geometrical mean of the i-th row calculate the weight of the i-th row geometrical mean in all row geometrical means calculate the value of weight adjoint matrix i-th row jth column element ${\hat{a}}_{\mathrm{ij}}=w_i/w_j,$ Weight generation contrast matrix $\hat{A}={\left({\hat{a}}_{\mathrm{ij}}\right)}_{n\×n}.$

The present invention further improves and is: the optimal conditions described in step S106 can be one of three kinds:

A), the consistency coefficient of current pairwise comparison matrix is equal with optimization matrix consistency coefficient;

B), to optimize matrix consistency coefficient be zero, namely optimizes matrix and reached optimum;

C), optimize matrix consistency coefficient and reached user and set requirement, namely optimize matrix and meet user's request.

Compared with prior art, tool has the following advantages in the present invention:

1) the present invention proposes a kind of interval marking mode, in scoring process, do not require that expert must provide a judged result determined, but the discrete segment that can comprise multiple judged result with represents, on the one hand, can reduce to the difficulty judged between uncertain index in expert estimation process, reduce expert's workload; On the other hand, expert can be avoided to occur that mistake judges to during uncertain index marking, reduce the possibility that inconsistent marking result occurs.

2) the present invention proposes a kind of consistance optimization matrix searching algorithm guided based on adjoint matrix, and this algorithm automatically from the interval marking that expert provides, can search out the good index pairwise comparison matrix of consistance, improve the correctness of index weights.

Accompanying drawing illustrates:

Fig. 1 is the index weights appraisal procedure process flow diagram based on the marking of expert interval;

Fig. 2 is interval grade form product process figure;

Fig. 3 is that consistance optimizes matrix searching method process flow diagram;

Fig. 4 is the process flow diagram judging whether to complete consistance optimization.

Embodiment:

Below in conjunction with accompanying drawing and example in detail embodiments of the present invention.

Example: the evaluation index (functional (functionality) of 8 mass propertys as software quality supposing to choose ISO/IEC25010, reliability (reliability), validity (efficiency), operability (operability), security (security), compatible (compatibility), maintainable (maintainability) and portable (portability)), expert please carry out importance contrast to 8 indexs in the importance of software quality, corresponding ratings be divided into from low to high 9 grades (absolutely not important, very inessential, substantially inessential, inessential a little, of equal importance, important a little substantially important, extremely important, definitely important), and calculate each index weights according to expert estimation result.

The index weights appraisal procedure idiographic flow based on the marking of expert interval that the present invention proposes, as shown in Figure 1, the method can comprise the following steps (step S101-step S107).

Step S101, according to implementation requirements, generates for specifying the interval grade form of the expert of index.As shown in Figure 2, according to index set to be assessed, generate index significance level scoring form, wherein the main body that compares of behavior, is classified as the object compared, as shown in table 1; According to Indexes Comparison grade, definition index significance level grade expression formula, " absolutely not important "-1, " very inessential "-2, " substantially inessential "-3, " inessential a little "-4, " of equal importance "-5, " important a little "-6, " substantially important "-7, " extremely important "-8, " definitely important "-9; In conjunction with significance level scoring form and significance level grade expression formula, generate the interval grade form of expert, as shown in table 1.

Table 1

Functional

Reliability

Validity

Operability

Security

Compatible

Maintainable

Portable

Functional

Reliability

Validity

Operability

Security

Compatible

Maintainable

Portable

Step S102, according to implementation requirements, expert, according to the interval grade form of expert, carries out interval scoring to each index.During scoring, do not require that expert provides unique judged result, the discrete segment that can comprise multiple judged result with represents, as shown in table 2.

Table 2

Functional

Reliability

Validity

Operability

Security

Compatible

Maintainable

Portable

Functional

5

[2,4]

[1,3]

[6,7]

[1,4]

[2,4]

[2,4]

[2,4]

Reliability

Null

5

[5,6]

[6,8]

[4,6]

[5,6]

[6,8]

[6,8]

Validity

Null

Null

5

[7,8]

[4,5]

[6,8]

[6,8]

[7,9]

Operability

Null

Null

Null

5

[2,4]

[1,3]

[4,5]

[4,5]

Security

Null

Null

Null

Null

5

[5,7]

[6,8]

[6,8]

Compatible

Null

Null

Null

Null

Null

5

[5,6]

[5,6]

Maintainable

Null

Null

Null

Null

Null

Null

5

[2,4]

Portable

Null

Null

Null

Null

Null

Null

Null

5

Step S103, according to the marking result a of expert in grade form _ij(i-th index compares the important level of a jth index, i>j), calculates the value a not filling out comparative run corresponding in grade form _ji, computing formula is a _ji=k+1-a _ij, k is the number of degrees of Indexes Comparison grade; Result is as shown in table 3;

Table 3

Functional

Reliability

Validity

Operability

Security

Compatible

Maintainable

Portable

Functional

5

[2,4]

[1,3]

[6,7]

[1,4]

[2,4]

[2,4]

[2,4]

Reliability

[6,8]

5

[5,6]

[6,8]

[4,6]

[5,6]

[6,8]

[6,8]

Validity

[7,9]

[4,5]

5

[7,8]

[4,5]

[6,8]

[6,8]

[7,9]

Operability

[3,4]

[2,4]

[2,3]

5

[2,4]

[1,3]

[4,5]

[4,5]

Security

[6,9]

[4,6]

[5,6]

[6,8]

5

[5,7]

[6,8]

[6,8]

Compatible

[6,8]

[4,5]

[2,4]

[7,9]

[3,5]

5

[5,6]

[5,6]

Maintainable

[6,8]

[2,4]

[2,4]

[5,6]

[2,4]

[4,5]

5

[2,4]

Portable

[6,8]

[2,4]

[1,3]

[5,6]

[2,4]

[4,5]

[6,8]

5

By the comparing result a of expert to different index, according to formula f (a)=c^ ((1/2) * (a-5)) (wherein coefficient c is set to 2 in this example), calculate its numerical result, it is as follows that the assessment result of table 3 generates interval rating matrix collection U:

Step S104, according to implementation requirements, concentrates from interval rating matrix, according to stochastic generation strategy, on interval rating matrix collection triangle each score value set in, one of them value of random selecting as the element of initial pairwise comparison matrix same position, and according to positive reciprocal property a _ji=1/a _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix.As matrix A:

$\left[\begin{array}{cccccccc}1.000000& 0.353553& 0.250000& 1.414214& 0.250000& 0.353553& 0.353553& 0.353553\\ 2.828427& 1.000000& 1.000000& 1.414214& 0.707107& 1.000000& 1.414214& 1.414214\\ 4.000000& 1.000000& 1.000000& 2.000000& 0.707107& 1.414214& 1.414214& 2.000000\\ 0.707107& 0.707107& 0.500000& 1.000000& 0.353553& 0.250000& 0.707107& 0.707107\\ 4.000000& 1.414214& 1.414214& 2.828427& 1.000000& 1.000000& 1.414214& 1.414214\\ 2.828427& 1.000000& 0.707107& 4.000000& 1.000000& 1.000000& 1.000000& 1.000000\\ 2.828427& 0.707107& 0.707107& 1.414214& 0.707107& 1.000000& 1.000000& 0.500000\\ 2.828427& 0.707107& 0.500000& 1.414214& 0.707107& 1.000000& 2.000000& 1.000000\end{array}\right]$

Step S105, utilizes the consistance guided based on adjoint matrix to optimize matrix searching algorithm (algorithm flow as shown in Figure 3), concentrates the optimization matrix searching for current pairwise comparison matrix from interval rating matrix.

The geometrical mean p of each row of compute matrix A _i(i=1,2 ..., 8), computing formula is:

$p_i=\sqrt[n]{\underset{j=1}{\overset{n}{\mathrm{\Π}}}{a}_{\mathrm{ij}}}$

Obtain p _i(i=1,2 ..., 8) and be respectively 0.439063,1.241858,1.476826,0.569394,1.610491,1.296840,0.957603,1.090508;

Calculate the weight of the i-th row geometrical mean in all row geometrical means, computing formula is:

$w_i=p_i/\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{p}_k$

Obtain w _i(i=1,2 ..., 8) and be respectively 0.050568,0.143029,0.170091,0.065579,0.185485,0.149361,0.110290,0.125597;

The ratio of compute matrix A i-th row and jth row geometrical mean weight as the weight contrast matrix of matrix A element, obtain matrix

$\left[\begin{array}{cccccccc}1.000000& 0.353553& 0.297302& 0.771105& 0.272627& 0.338564& 0.458502& 0.402623\\ 2.828427& 1.000000& 0.840896& 2.181015& 0.771105& 0.957603& 1.296840& 1.138789\\ 3.363586& 1.189207& 1.000000& 2.593679& 0.917004& 1.138789& 1.542211& 1.354256\\ 1.296840& 0.458502& 0.385553& 1.000000& 0.353553& 0.439063& 0.594604& 0.522137\\ 3.668016& 1.296840& 1.090508& 2.828427& 1.000000& 1.241858& 1.681793& 1.476826\\ 2.953652& 1.044274& 0.878126& 2.277577& 0.805245& 1.000000& 1.354256& 1.189207\\ 2.181015& 0.771105& 0.648420& 1.681793& 0.594604& 0.738413& 1.000000& 0.878126\\ 2.483716& 0.878126& 0.738413& 1.915207& 0.677128& 0.840896& 1.138789& 1.000000\end{array}\right]$

Search and matrix in matrix stack U with immediate matrix B, on interval rating matrix collection triangle each score value set in, for arbitrary i, j (i<j), the numerical value set of its correspondence position has m element, is designated as u ^p _ij(p=1,2 ..., m).Calculate if the element in this numerical value set make $|\ln {\hat{a}}_{\mathrm{ij}}-\ln u_{\mathrm{ij}}^{p_0}|=\underset{p}{\min }|\ln {\hat{a}}_{\mathrm{ij}}-\ln u_{\mathrm{ij}}^p|,$ Then make $b_{\mathrm{ij}}=u_{\mathrm{ij}}^{p_0},$ And b _ii=1, b _ji=1/b _ij.The like identical process is carried out to all score value set of triangle on interval rating matrix collection, just can be optimized matrix B:

$\left[\begin{array}{cccccccc}1.000000& 0.353553& 0.353553& 1.414214& 0.250000& 0.353553& 0.500000& 0.353553\\ 2.828427& 1.000000& 1.000000& 2.000000& 0.707107& 1.000000& 1.414214& 1.414214\\ 2.828427& 1.000000& 1.000000& 2.828427& 1.000000& 1.414214& 1.414214& 2.000000\\ 0.707107& 0.500000& 0.353553& 1.000000& 0.353553& 0.500000& 0.707107& 0.707107\\ 4.000000& 1.414214& 1.000000& 2.828427& 1.000000& 1.414214& 1.414214& 1.414214\\ 2.828427& 1.000000& 0.707107& 2.000000& 0.707107& 1.000000& 1.414214& 1.000000\\ 2.000000& 0.707107& 0.707107& 1.414214& 0.707107& 0.707107& 1.000000& 1.000000\\ 2.828427& 0.707107& 0.50000& 1.414214& 0.707107& 1.000000& 1.000000& 1.000000\end{array}\right]$

Step S106, judge whether to complete consistance optimization (idiographic flow is as shown in Figure 4), calculate its coincident indicator CR (B) to matrix B, computing formula is as follows:

wherein λ _max(B) be the eigenvalue of maximum of matrix B, n is the exponent number of matrix B, and RI is random index, can table look-up and obtain.

Calculate CR (B)=0.009989

If the coincident indicator CR (B) optimizing matrix is less than given threshold value e, then illustrates and complete consistance optimization, export and optimize matrix B, transfer to step S107, in this example, threshold value e is set to 0.005;

If do not complete optimization: if it is equal with objective matrix A to optimize matrix B, this illustrates to optimize and cannot improve consistance, exports and optimizes matrix B, transfer to step S107; If unequal, export and optimize matrix B, transfer to step S105, in this example, A and B is unequal, again carries out consistance to B and optimizes matrix search.

In this example, by 7 circulations, generate and optimize matrix:

$\left[\begin{array}{cccccccc}1.000000& 0.500000& 0.353553& 1.414214& 0.353553& 0.500000& 0.707107& 0.500000\\ 2.000000& 1.000000& 1.000000& 2.000000& 0.707107& 1.000000& 1.414214& 1.414214\\ 2.828427& 1.000000& 1.000000& 2.828427& 1.000000& 1.414214& 2.000000& 2.000000\\ 0.707107& 0.500000& 0.353553& 1.000000& 0.353553& 0.500000& 0.707107& 0.707107\\ 2.828427& 1.414214& 1.000000& 2.828427& 1.000000& 1.414214& 2.000000& 2.000000\\ 2.000000& 1.000000& 0.707107& 2.000000& 0.707107& 1.000000& 1.414214& 1.414214\\ 1.414214& 0.707107& 0.500000& 1.414214& 0.500000& 0.707104& 1.000000& 1.000000\\ 2.000000& 0.707107& 0.500000& 1.414214& 0.500000& 0.707107& 1.000000& 1.000000\end{array}\right]$

Its coincident indicator is 0.003826.

Step S107, according to optimization matrix, calculates the weighted value of each index.

In this example, in the computing method of index weights and step S105, calculate w _i(i=1,2 ..., 8) method consistent.

In this example, the weight calculating index is respectively: 0.069089, and 0.144295,0.187128,0.066160,0.195413,0.138178,0.097706,0.102032.

Claims (7)

1., based on the index weights appraisal procedure of expert interval marking, it is characterized in that, comprise the steps:

S101, needing the requirement of corresponding ratings between the index assessed and index according to user, generating for specifying the interval grade form of the expert of index;

S102, expert, according to the interval grade form of expert, carry out interval scoring to each index;

S103, expert is converted into numerical value set to the scoring of the interval of different index, the set of values symphysis of marking between two in conjunction with all indexs becomes interval rating matrix collection;

S104, each matrix is concentrated to generate initial pairwise comparison matrix according to Different Strategies from interval rating matrix, strategy comprises maximum selection rule, minimum value is selected, median is selected and Stochastic choice, and initial pairwise comparison matrix is set to current pairwise comparison matrix;

S105, utilize the consistance guided based on adjoint matrix to optimize matrix searching algorithm, concentrate the optimization matrix searching for current pairwise comparison matrix from interval rating matrix;

S106, calculate current pairwise comparison matrix and optimize the parameter of consistency of matrix, judging whether to meet optimal conditions, if do not meet, optimization matrix is set to pairwise comparison matrix, proceeds to step S105; If meet optimal conditions, proceed to step S107;

S107, according to optimization matrix, calculate the weighted value of each index;

The interval grade form generation step of expert described in described step S101 is:

A), index corresponding ratings k requires as odd number, significance level between two indices X and Y is divided into 1 from small to large, 2, k level, wherein 1 grade represents index X to compare index Y completely inessential, and (1+k)/2 grade represent that two indices is of equal importance, and k level represents that index X is completely important in index Y;

B), the number n of evaluation index as required, generate the form of a n × n, wherein the comparing result of i-th index and a jth index is shown in the i-th row jth list;

C), by the comparing result that the i-th row on form diagonal line and jth arrange be set to (1+k)/2 grade, represent that the significance level of identical index is equal;

D), by the comparing result below form diagonal line be set to sky, expert is without the need to marking, and its marking value is calculated by the comparing result above form diagonal line.

2. the index weights appraisal procedure based on the marking of expert interval according to claim 1, it is characterized in that, affiliated interval scoring described in step S102, refers to that the discrete segment comprising multiple judged result with represents when to a pair index contrast scoring.

3. the index weights appraisal procedure based on the marking of expert interval according to claim 1, it is characterized in that, the generation step of the interval rating matrix collection described in affiliated step 103 is:

1), according to the marking result of expert's first gust in grade form, the value of second gust is calculated, if the comparing result a in form above any diagonal line _ij; a _ijrepresent that i-th index compares the important level of a jth index, i>j; Comparing result a below the diagonal line that then form is corresponding _jiequal k+1-a _ij; a _jirepresent that a jth index compares the important level of i-th index, i>j;

2), according to formula f (a)=c^ ((1/2) * (a-5)), Scoring System a is converted into numerical value, and wherein c is weight coefficient, c be greater than 1 integer; By the interval appraisal result (a of index i and index j _p, a _p+1..., a _q), be converted into score value set { f (a _p), f (a _p+1) ..., f (a _q);

3) the score value set, using index contrasted between two is as element, and generate n rank matrix, this matrix is interval rating matrix collection.

4. the index weights appraisal procedure based on the marking of expert interval according to claim 1, it is characterized in that, the initial pairwise comparison matrix generation method described in described step S104 comprises four kinds:

1), maximum selection rule, on interval rating matrix collection triangle each score value set in, choose wherein maximal value as the element of initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix;

2), minimum value selects, on interval rating matrix collection triangle each score value set in, choose wherein minimum value as the element of initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix;

3), intermediate value selects, on interval rating matrix collection triangle each score value set in, according to size sequence, choose the element of rank value placed in the middle as initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix;

4), Stochastic choice, on interval rating matrix collection triangle each score value set in, one of them value of random selecting as the element of initial pairwise comparison matrix same position, and according to positive reciprocal property f _ji=1/f _ijextrapolate the value of triangle element under initial pairwise comparison matrix, on diagonal line, element is set to 1, generates initial pairwise comparison matrix.

5. the index weights appraisal procedure based on the marking of expert interval according to claim 1, it is characterized in that, the consistance based on adjoint matrix guiding described in step S105 is optimized matrix searching algorithm step and is: the weight contrast matrix calculating current pairwise comparison matrix; From each position of rating matrix collection between contrast district, find and contrast the immediate value of matrix with weight, generate and optimize matrix.

6. the index weights appraisal procedure based on the marking of expert interval according to claim 1, is characterized in that, the computing method of weight contrast matrix are: for matrix A=(a _ij) _{n × n}, calculate the geometrical mean of the i-th row calculate the weight of the i-th row geometrical mean in all row geometrical means calculate the value of weight adjoint matrix i-th row jth column element weight generation contrast matrix $\hat{A}={\left({\hat{a}}_{\mathrm{ij}}\right)}_{n\&times;n}.$

7. the index weights appraisal procedure based on the marking of expert interval according to claim 1, it is characterized in that, the optimal conditions described in step S106 can be one of three kinds:

A), the consistency coefficient of current pairwise comparison matrix is equal with optimization matrix consistency coefficient;

B), to optimize matrix consistency coefficient be zero, namely optimizes matrix and reached optimum;

C), optimize matrix consistency coefficient and reached user and set requirement, namely optimize matrix and meet user's request.