topsis法

topsis法是另一种评价法,可以解决多属性决策问题。

step1:对数据进行归一化处理。归一化方式取下图的方式:

step2:将归一化的矩阵乘上各指标的权重。

step3:设置最优方案和最差方案,最优方案是指各指标中值最大的所组成的向量。

最差方案是指各指标里最小值组成的向量。

step4:分别计算每个方案到最优最差方案的距离,距离计算公式如下图:

step5:D加/(D加+D减)即为综合评价指数,然后排序。

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附样例代码如下:

clear all
clc
a=[18.0 6.0 230.0 15.0 32.0 3.0
52.0 13.0 4000.0 15.0 60.0 1.0
37.0 4.0 306.0 11.0 60.0 1.0
12.0 1.0 1533.0 5.0 30.0 5.0
8.0 3.0 552.0 8.0 19.9 8.0
17.5 9.0 580.0 16.0 50.0 1.0
15.0 8.0 1159.0 16.0 50.0 1.0
18.0 0.0 257.0 12.0 19.0 9.0
58.0 0.0 523.0 8.0 50.0 9.0
22.0 0.0 454.0 30.0 50.0 1.0 ];
[m,n]=size(a);
m;
n;
for j=1:n
b(:,j)=a(:,j)/norm(a(:,j)); %向量归还化
end
b;
w=[0.1898 0.1724 0.1899 0.1897 0.1654 0.0928];%设置权重
w;
c=b.*repmat(w,m,1); %求加权矩阵
Cstar=max(c); %求正理想解,,,,即每个指标的理想解
Cstar(4)=min(c(:,6)); %属性 4 位成本型的
C0=min(c); %求负理想解,,,,,即每个指标的理想解
C0(4)=max(c(:,6));
for i=1:m
Sstar(i)=norm(c(i,:)-Cstar); %求到正理想解的距离
S0(i)=norm(c(i,:)-C0); %求到负理想解的距离
end
Sstar;
S0;%显示到正理想解的距离以及到负理想解的距离
f=S0./(Sstar+S0);
[sf,inf]=sort(f,’descend’) %求排序结果

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