Analytic Hierarchy Process Model (AHP) and its MATLAB implementation

Today with nearly a day to learn the analytic Hierarchy process (AHP), the main reference to a PDF, this site, and Jinan University chapter Teacher's courseware, now write some of their own summary of the points.　

First, the basic steps of analytic Hierarchy process:

Angle One:

The actual problem----------------

-Determine the relative importance of the factors----compute--weights--

-Judgment---comprehensive decision-making

Angle two:

Build a hierarchy model----Construct judgment matrix---level order----consistency check--level total order.

　　Ii. the focus of several understandings

1. Positive and negative matrices

If the Matrix a= (AIJ) MXN satisfies the following characteristics: (1) aij>0 (2) Aij=1/aji is called The matrix A is a positive reciprocal inverse matrix. 2. The Uniform arrayDefinition: Satisfies a (IJ) A (JK) =a (IK), i,j,k=1,2,,n Positive reciprocal array A-called uniform array. Property: The rank of A is the only non-0 characteristic root of 1,a is n; Any of the columns of a vector is a characteristic vector corresponding to n, and a normalized eigenvector can be used as a weight vector.

Attention:

In this case, it is possible to replace A with the eigenvector of the maximum feature root, possibly in order to maximize the amount of information (a) of the original data (not sure ...). ）

3. Conformance Testing

Consistency test, the specific also involves the combination of consistency test.

Third, the realization of MATLAB

Here first search the data, see this code, the code is very clear, here directly posted here.

Clc;clear; A=[1 1.2 1.5 1.5;0.833  1 1.2 1.2;0.667  0.833  1 1.2;0.667  0.833  0.833  1];                                                   % factor contrast matrix A, only need to change the matrix A[m,n]=size (a);                     % gets the number of indicators ri=[0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51]; R=rank (A);                         The rank of the Judgment matrix [V,d]=eig (A);                      % the eigenvalues and eigenvectors of the Judgment Matrix, v eigenvalues, d eigenvectors; Tz=max (d); B=max (TZ);                         % maximum eigenvalue [row, Col]=find (d==b);             % Maximum Eigenvalue location c=v (:, col);                        % corresponds to eigenvector ci= (b-n)/(n-1);                    % Calculation Consistency Test indicator CICR=CI/RI (1,n);   If cr<0.10    disp (' ci= ');d ISP (CI);    Disp (' cr= ');d ISP (CR);    Disp (' contrast matrix A through consistency test, each vector weight vector q is: ');    Q=zeros (n,1);    For I=1:n        Q (i,1) =c (i,1)/sum (C (:, 1));% eigenvector normalization    end    Q                              % output weight vector else    disp (' Contrast matrix A failed conformance check, Need to reconstruct the contrast matrix A '); end

Here is a preliminary understanding of the AHP, after further study, then continue to summarize.

Analytic Hierarchy Process Model (AHP) and its implementation of MATLAB