CN103366090A - 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

Index weights appraisal procedure based on the interval marking of expert

Technical field

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

Background technology

In fields such as multiobjectives decision, information fusion, importance assessment and weight calculation between different indexs and attribute are FAQs.Traditional index weights assessment is relatively given a mark to different indexs in twos by the expert, generates the paired comparator matrix of index, utilizes the logarithm least square method to calculate each index weights.

The expert carries out important ratio according to oneself experience and professional knowledge, but because experience and the limitation of professional knowledge and the complicacy of decision problem, the expert often is difficult to provide determinacy to index importance and judges.And require the expert to provide unique marking in the traditional index weight estimation method, cause the expert to provide judgement according to uncertain understanding, difficulty and the workload of expert's marking have been increased on the one hand, may cause on the other hand between the marking result and have inconsequent, be difficult to guarantee transitivity and the reciprocity of index significance level, cause the paired comparator matrix consistance of index to reduce and the index weights miscount.

At present, for the expert who does not the satisfy coherence request result that gives a mark, disposal route mainly comprises two kinds: 1) require the expert again to evaluate; 2) by the part marking result of automatic search and Change impact index significance level transitivity and reciprocity, generate the new paired comparator matrix of index, so that its consistent sexual satisfaction requirement.Yet all there is restriction in said method in application process, and its subject matter is: 1) require the expert again to evaluate expense too large, and expert's assessment result often representing expert's subjective judgement, be difficult to improve by evaluation again the consistance of net result; 2) revise expert's the possibility of result of giving a mark and change expert's judged result, the appraisal result and the expert judgments that cause obtaining do not meet, and are difficult to the target that realizes that the expert marks.

Summary of the invention

In the index weights assessment, the expert faces part index number and is difficult to provide definite judgement, provides inconsistent marking, causes the problem of index weights miscount; The invention provides a kind of index weights appraisal procedure based on the interval marking of expert, assist the expert to provide the paired comparator matrix of the higher index of consistance, improve the correctness of index weights.

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

Index weights appraisal procedure based on the interval marking of expert comprises the steps:

S101, according to the requirement of corresponding ratings between the index of user's needs assessments and index, generate the interval grade form for the expert who specifies index;

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

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

S104, concentrate each matrix to generate initial in pairs comparator matrix according to Different Strategies from interval rating matrix, strategy comprises that maximum selection rule, minimum value are selected, median is selected and random the selection, and initial in pairs comparator matrix is made as current paired comparator matrix;

S105, utilization are optimized the matrix searching algorithm based on the consistance of adjoint matrix guiding, concentrate the optimization matrix of the current paired comparator matrix of search from interval rating matrix;

S106, calculate current paired comparator matrix and optimize the parameter of consistency of matrix, judge whether to satisfy optimal conditions, will optimize matrix and be made as paired comparator matrix if do not satisfy, change step S105 over to; If satisfy optimal conditions, change step S107 over to;

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

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

A), index corresponding ratings k requires for odd number the significance level between two index X and Y to be divided into 1,2 from small to large,, the k level, wherein to compare index Y fully inessential for 1 grade of expression index X, (1+k)/2 grade two indexs of expression are of equal importance, and the k level represents that index X is fully 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 index and j index is shown in the capable j tabulation of i;

C), the capable comparing result with j row of i on the form diagonal line is made as (1+k)/2 grade, represent that the significance level of identical index equates;

D), the comparing result of form diagonal line below is made as sky, the expert need not marking, and its marking value is calculated by the comparing result of form diagonal line top.

The present invention further improves and is: the interval scoring described in the affiliated step S102 refers to represent with a discrete segment that comprises a plurality of judged results to a pair of index contrast scoring the time.

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

1), according to the marking result of expert's first gust in grade form, calculate the value of second gust, establish in the form the arbitrarily comparing result a of diagonal line top _Ija _IjRepresent that i index compare the important level of j index, i〉j; The comparing result a of the diagonal line below that then form is corresponding _JiEqual k+1-a _Ija _JiRepresent that j index compare the important level of i index, i〉j;

2), according to formula f (a)=c^ ((1/2) * (a-5)), the classification a that will mark is converted into numerical value, wherein c is weight coefficient, c is the integer greater than 1; Interval appraisal result (a with 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 that contrasts in twos with index is as element, generates n rank matrix, this matrix is interval rating matrix collection.

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

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

2), minimum value selects, and on interval rating matrix collection in each score value set of triangle, chooses wherein minimum value as the initial in pairs element of comparator matrix same position, and according to positive reciprocal property f _Ji=1/f _IjExtrapolate the value of triangle element under the initial in pairs comparator matrix, element is made as 1 on the diagonal line, generates initial in pairs comparator matrix;

3), intermediate value selects, and in each score value set of triangle, according to the size ordering, chooses rank value placed in the middle as the initial in pairs element of comparator matrix same position on interval rating matrix collection, and according to positive reciprocal property f _Ji=1/f _IjExtrapolate the value of triangle element under the initial in pairs comparator matrix, element is made as 1 on the diagonal line, generates initial in pairs comparator matrix;

4), the random selection, on interval rating matrix collection, in each score value set of triangle, choose at random one of them value as the element of initial paired comparator matrix same position, and according to positive reciprocal property f _Ji=1/f _IjExtrapolate the value of triangle element under the initial in pairs comparator matrix, element is made as 1 on the diagonal line, generates initial in pairs comparator matrix.

The present invention further improves and is: the consistance based on the adjoint matrix guiding described in the step S105 is optimized matrix searching algorithm step and is: the weight contrast matrix that calculates current paired comparator matrix; From each position of rating matrix collection between the contrast district, find and the immediate value of weight contrast matrix, 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 capable geometrical mean of i

Calculate the capable geometrical mean of i in the weight of all row geometrical means

The value of the capable j column element of Determining Weights adjoint matrix i ${\hat{a}}_{\mathrm{ij}}=w_i/w_j,$ 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 the step S106 can be one of three kinds:

A), the consistency coefficient of current paired comparator matrix equates with optimization matrix consistency coefficient;

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

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

The present invention has following advantage compared with prior art:

1) the present invention proposes a kind of interval marking mode, in the marking process, do not require that the expert must provide a definite judged result, but can represent with a discrete segment that comprises a plurality of judged results, on the one hand, can reduce the difficulty to judging between uncertain index in expert's marking process, reduce expert's workload; On the other hand, wrong judgement occurs in the time of can avoiding the expert to uncertain index marking, reduce the possibility that inconsistent marking result occurs.

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

Description of drawings:

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

Fig. 2 is interval grade form product process figure;

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

Fig. 4 judges whether to finish the process flow diagram that consistance is optimized.

Embodiment:

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

Example: suppose to choose 8 mass propertys of ISO/IEC25010 as the evaluation index (functional (functionality) of software quality, reliability (reliability), validity (efficiency), operability (operability), security (security), compatible (compatibility), maintainable (maintainability) and portable (portability)), please the expert carry out the importance contrast to 8 indexs in the importance of software quality, corresponding ratings be divided into from low to high 9 grades (important anything but, 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 the expert result that gives a mark.

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

Step S101 according to the example requirement, generates the interval grade form for the expert who specifies index.As shown in Figure 2, according to index set to be assessed, generate index significance level scoring form, behavior main body is relatively wherein classified the object of comparison as, and is as shown in table 1; According to the index comparison scale, definition index significance level grade expression formula, " important anything but "-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 the example requirement, the expert carries out the interval scoring according to the interval grade form of expert to each index.During scoring, do not require that the expert provides unique judged result, can represent with a discrete segment that comprises a plurality of judged results, 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 is according to the marking of expert in grade form a as a result _Ij(i index compared the important level of j index, i〉j), calculate the value a that does not fill out comparative run corresponding in the grade form _Ji, computing formula is a _Ji=k+1-a _Ij, k is the number of degrees of index comparison scale; The 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

With the comparing result a of expert to different indexs, according to formula f (a)=c^ ((1/2) * (a-5)) (wherein coefficient c is made as 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 the example requirement, concentrates from interval rating matrix, according to random generation strategy, on interval rating matrix collection, in each score value set of triangle, choose at random one of them value as the initial in pairs element of comparator matrix same position, and according to positive reciprocal property a _Ji=1/a _IjExtrapolate the value of triangle element under the initial in pairs comparator matrix, element is made as 1 on the diagonal line, generates initial in pairs comparator matrix.Such 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 based on the consistance of adjoint matrix guiding and optimizes matrix searching algorithm (algorithm flow as shown in Figure 3), concentrates the optimization matrix of the current paired comparator matrix of search 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 capable geometrical mean of i in the weight of 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 capable ratio with the capable geometrical mean weight of j of compute matrix A i

Weight contrast matrix as 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 in each score value of triangle set, for i arbitrarily, (i＜j), the set of the numerical value of its correspondence position has m element to j, is designated as u ^p _Ij(p=1,2 ..., m).Calculate If the element in this numerical value set So that $|\ln {\hat{a}}_{\mathrm{ij}}-\ln u_{\mathrm{ij}}^{p_0}|=\underset{p}{\min }|\ln {\hat{a}}_{\mathrm{ij}}-\ln u_{\mathrm{ij}}^p|,$ Then order $b_{\mathrm{ij}}=u_{\mathrm{ij}}^{p_0},$ And b _Ii=1, b _Ji=1/b _IjThe like identical processing is carried out in all score value set of triangle on the interval rating matrix collection, matrix B just can be optimized:

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

Step S106 judges whether to finish consistance optimization (idiographic flow is as shown in Figure 4), and matrix B is calculated its coincident indicator CR (B), and computing formula is as follows:

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

Calculate CR (B)=0.009989

If optimize the coincident indicator CR (B) of matrix less than given threshold value e, then consistance optimization has been finished in explanation, and matrix B is optimized in output, transfers to step S107, and threshold value e is made as 0.005 in this example;

If do not finish optimization: equate with objective matrix A if optimize matrix B, this explanation optimization can't be improved consistance, and matrix B is optimized in output, transfers to step S107; If unequal, matrix B is optimized in output, transfers to step S105, and A and B are unequal in this example, again B is carried out consistance and optimizes the 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 optimizing matrix, calculates the weighted value of each index.

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

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

Claims (8)

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

S101, according to the requirement of corresponding ratings between the index of user's needs assessments and index, generate the interval grade form for the expert who specifies index;

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

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

S104, concentrate each matrix to generate initial in pairs comparator matrix according to Different Strategies from interval rating matrix, strategy comprises that maximum selection rule, minimum value are selected, median is selected and random the selection, and initial in pairs comparator matrix is made as current paired comparator matrix;

S105, utilization are optimized the matrix searching algorithm based on the consistance of adjoint matrix guiding, concentrate the optimization matrix of the current paired comparator matrix of search from interval rating matrix;

S106, calculate current paired comparator matrix and optimize the parameter of consistency of matrix, judge whether to satisfy optimal conditions, will optimize matrix and be made as paired comparator matrix if do not satisfy, change step S105 over to; If satisfy optimal conditions, change step S107 over to;

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

2. the index weights appraisal procedure based on the interval marking of expert according to claim 1 is characterized in that, the interval grade form of the expert described in the described step S101 generates step and is:

A), index corresponding ratings k requires for odd number the significance level between two index X and Y to be divided into 1,2 from small to large,, the k level, wherein to compare index Y fully inessential for 1 grade of expression index X, (1+k)/2 grade two indexs of expression are of equal importance, and the k level represents that index X is fully 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 index and j index is shown in the capable j tabulation of i;

C), the capable comparing result with j row of i on the form diagonal line is made as (1+k)/2 grade, represent that the significance level of identical index equates;

D), the comparing result of form diagonal line below is made as sky, the expert need not marking, and its marking value is calculated by the comparing result of form diagonal line top.

3. according to claim 1 based on the interval index weights appraisal procedure of giving a mark of expert, it is characterized in that, interval scoring described in the affiliated step S102 refers to represent with a discrete segment that comprises a plurality of judged results to a pair of index contrast scoring the time.

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

1), according to the marking result of expert's first gust in grade form, calculate the value of second gust, establish in the form the arbitrarily comparing result a of diagonal line top _Ija _IjRepresent that i index compare the important level of j index, i〉j; The comparing result a of the diagonal line below that then form is corresponding _JiEqual k+1-a _Ija _JiRepresent that j index compare the important level of i index, i〉j;

2), according to formula f (a)=c^ ((1/2) * (a-5)), the classification a that will mark is converted into numerical value, wherein c is weight coefficient, c is the integer greater than 1; Interval appraisal result (a with 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 that contrasts in twos with index is as element, generates n rank matrix, this matrix is interval rating matrix collection.

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

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

2), minimum value selects, and on interval rating matrix collection in each score value set of triangle, chooses wherein minimum value as the initial in pairs element of comparator matrix same position, and according to positive reciprocal property f _Ji=1/f _IjExtrapolate the value of triangle element under the initial in pairs comparator matrix, element is made as 1 on the diagonal line, generates initial in pairs comparator matrix;

3), intermediate value is selected, during each score value of triangle is gathered on interval rating matrix collection, sort according to size, choose rank value placed in the middle as the initial in pairs element of comparator matrix same position, and extrapolate the value of triangle element under the initial in pairs comparator matrix according to positive reciprocal property fji=1/fij, element is made as 1 on the diagonal line, generates initial in pairs comparator matrix;

4), the random selection, on interval rating matrix collection, in each score value set of triangle, choose at random one of them value as the element of initial paired comparator matrix same position, and according to positive reciprocal property f _Ji=1/f _IjExtrapolate the value of triangle element under the initial in pairs comparator matrix, element is made as 1 on the diagonal line, generates initial in pairs comparator matrix.

6. according to claim 1 based on the interval index weights appraisal procedure of giving a mark of expert, it is characterized in that, the consistance based on the adjoint matrix guiding described in the step S105 is optimized matrix searching algorithm step and is: the weight contrast matrix that calculates current paired comparator matrix; From each position of rating matrix collection between the contrast district, find and the immediate value of weight contrast matrix, generate and optimize matrix.

7. the index weights appraisal procedure based on the interval marking of expert 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 capable geometrical mean of i

Calculate the capable geometrical mean of i in the weight of all row geometrical means

The value of the capable j column element of Determining Weights adjoint matrix i The contrast matrix $\hat{A}={\left({\hat{a}}_{\mathrm{ij}}\right)}_{n\×n}.$

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

A), the consistency coefficient of current paired comparator matrix equates with optimization matrix consistency coefficient;

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

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

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