Analytic hierarchy process of mathematical modeling (including Matlab code)

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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 .

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1.1 Hierarchical single sorting and consistency test

give an example

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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 .

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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

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3. Examples of application process

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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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