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Analytic hierarchy process of mathematical modeling (including Matlab code)
2022-07-05 15:29:00 【Yi EBA】
Mathematical modeling analytic hierarchy process
1. The basic principle and steps of analytic hierarchy process
The basic principle and steps of analytic hierarchy process
People are engaged in social 、 In the systematic analysis of problems in the field of economy and scientific management , Often faced with
One is interrelated 、 A complex system composed of many factors that restrict each other and often lack quantitative data . level
Analytical method provides a new method for the decision-making and sequencing of this kind of problems 、 Simple and practical modeling method .
The basic principle
Use analytic hierarchy process to model , Generally, it can be carried out according to the following four steps :
(i) Establish a hierarchical structure model ;
(ii) Construct all judgment matrices in each level ;
(iii) Hierarchical single sorting and consistency test ;
(iv) Hierarchical total ranking and consistency test .
1.1 Hierarchical single sorting and consistency test
give an example
1.2 Hierarchical total ranking and consistency test
give an example
example 2 Choose the right job . After earnest discussion between both parties , Three units have expressed their willingness to employ a certain graduate . The
Students have established a hierarchical structure model based on the existing information , Pictured 2 Shown .
2. matlab Code
% Analytic hierarchy process and consistency check code use :
%(1) Construct judgment matrix A
%(2) Copy and paste the following code into Matlab Then you can
% for example :A=[1 3 5;0.33 1 3;0.2 0.33,1]
disp(' Please enter the criterion layer judgment matrix A(n rank )');
A=input('A=');
[n,n]=size(A); % Get the order of the matrix
[V,D]=eig(A); % Get the eigenvector and eigenvalue
% Find the maximum eigenvalue and its corresponding eigenvector
tempNum=D(1,1); % Initial value of eigenvalue
pos=1; % The first number of marks
for h=1:n
if D(h,h)>tempNum
tempNum=D(h,h);
pos=h; % The position of the maximum eigenvalue
end
end
w=abs(V(:,pos)); % Find the eigenvector corresponding to the maximum eigenvalue
w=w/sum(w); % normalization
t=D(pos,pos); % t It refers to the maximum eigenvalue
disp(' Criterion layer eigenvector w=');disp(w);disp(' Maximum characteristic root of criterion layer t=');disp(t);
% Consistency check
CI=(t-n)/(n-1);RI=[0 0 0.52 0.89 1.12 1.26 1.36 1.41 1.46 1.49 1.52 1.54 1.56 1.58 1.59 1.60 1.61 1.615 1.62 1.63];
CR=CI/RI(n);
if CR<0.10
disp(' The consistency of this matrix is acceptable !');
disp('CI=');disp(CI);
disp('CR=');disp(CR);
else disp(' Consistency verification of this matrix failed , Please re rate !');
end
3. Examples of application process
4. Reference material
《 Mathematical modeling algorithm and Application 》( Si keeping )
《 Mathematical modeling algorithm and application problem solving 》( Si keeping )
- >> bilibili Mathematical modeling learning tutorial
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