topsis mtalab

TOPSIS算法是一种多属性决策方法，用于评估多个方案的优劣。其基本思想是通过归一化后的原始数据矩阵，找出最优方案和最劣方案，然后计算各评价对象与最优方案的距离，以此作为评价优劣的依据。\[2\]

在MATLAB中，可以使用以下代码实现TOPSIS算法：

clc,clear;
x=\[21584 76.7 7.3 1.01 78.3 97.5 2.0;
   24372 86.3 7.4 0.80 91.1 98.0 2.0;
   22041 81.8 7.3 0.62 91.1 97.3 3.2;
   21115 84.5 6.9 0.60 90.2 97.7 2.9;
   24633 90.3 6.9 0.25 95.5 97.9 3.6\];

\[n,m\]=size(x);

% 将3，4，7的低优指标去倒数转化为高优指标并且把所有指标换成接近的大小
x(:,1)=x(:,1)/100;
x(:,3)=(1./x(:,3))*100;
x(:,4)=(1./x(:,4))*100;
x(:,7)=(1./x(:,7))*100;

% 主要是要将其转化为极大型指标
zh=zeros(1,m);
d1=zeros(1,n); %最小值矩阵
d2=zeros(1,n); %最大值矩阵
c=zeros(1,n); %接近程度

% 标准化
for i=1:m
    for j=1:n
        zh(i)=zh(i)+x(j,i)^2;
    end
end

for i=1:m
    for j=1:n
        x(j,i)=x(j,i)/sqrt(zh(i));
    end
end

% 计算距离
xx=min(x);
dd=max(x);

for i=1:n
    for j=1:m
        d1(i)=d1(i)+(x(i,j)-xx(j))^2;
    end
    d1(i)=sqrt(d1(i));
end

for i=1:n
    for j=1:m
        d2(i)=d2(i)+(x(i,j)-dd(j))^2;
    end
    d2(i)=sqrt(d2(i));
end

% 计算接近程度
for i=1:n
    c(i)=d1(i)/(d2(i)+d1(i));
end

\[sf,ind\]=sort(c,'descend'); %按降序排序

以上是一个简单的TOPSIS算法的MATLAB实现示例。你可以根据自己的数据进行相应的修改和调整。\[2\]
#### 引用[.reference_title]
- *1* [【数学模型】TOPSIS](https://blog.csdn.net/suic009/article/details/126138524)[target="_blank" data-report-click={"spm":"1018.2226.3001.9630","extra":{"utm_source":"vip_chatgpt_common_search_pc_result","utm_medium":"distribute.pc_search_result.none-task-cask-2~all~insert_cask~default-1-null.142^v91^koosearch_v1,239^v3^insert_chatgpt"}} ] [.reference_item]
- *2* [Topsis 模型](https://blog.csdn.net/weixin_62558615/article/details/128815537)[target="_blank" data-report-click={"spm":"1018.2226.3001.9630","extra":{"utm_source":"vip_chatgpt_common_search_pc_result","utm_medium":"distribute.pc_search_result.none-task-cask-2~all~insert_cask~default-1-null.142^v91^koosearch_v1,239^v3^insert_chatgpt"}} ] [.reference_item]
- *3* [TOPSIS法 —— matlab](https://blog.csdn.net/qq_25990967/article/details/122754308)[target="_blank" data-report-click={"spm":"1018.2226.3001.9630","extra":{"utm_source":"vip_chatgpt_common_search_pc_result","utm_medium":"distribute.pc_search_result.none-task-cask-2~all~insert_cask~default-1-null.142^v91^koosearch_v1,239^v3^insert_chatgpt"}} ] [.reference_item]
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