Entropy weight method of evaluation model

1. Algorithm principle

The entropy weight method is an objective value assignment method. In the process of specific use, the entropy weight method uses information entropy to calculate the entropy weight of each index according to the degree of variation of each index, and then corrects the weight of each index through the entropy weight to obtain a more objective index weight. Generally speaking, if the entropy weight method of the information entropy index weight determination method of a certain index is smaller, it indicates that the index value is more variable, the amount of information provided is more, and the role it can play in the comprehensive evaluation is also greater. , the greater its weight. On the contrary, if the entropy weight method of the information entropy index weight determination method of a certain index is larger, it indicates that the index value has a smaller degree of variation, the amount of information provided is less, and the role played in the comprehensive evaluation is also smaller. The weight is also smaller.

    

2. Algorithm steps

(1) Data standardization processing

The standardization method adopted here is the data normalization method. 

 (2) Calculate information entropy

The formula for calculating the information entropy of each indicator is

in

(3) Calculate index weight 

(4) Compute the composite score

3. Example analysis

The table shows the data of 11 indicators in 16 prefecture-level cities in Anhui Province in 2020. The entropy weight method is used to comprehensively evaluate the economic development level of these 16 regions.

 Matlab code:

clc;clear;
data=xlsread('2020.xlsx');%读取数据
%数据标准化 mapminmax对行进行标准化，所以转置一下
data1=mapminmax(data‘,0.002,0.996); %标准化到0.002-0096之间
data1=data1';
[m,n]=size(data1);
p=zeros(m,n);
for j=1:n
    p(:,j)=data1(:,j)/sum(data1(:,j));
end
for j=1:n
    E(j)=-1/log(m)*sum(p(:,j).*log(p(:,j)));%计算信息熵
end
w=(1-E)/sum(1-E);%计算权重
s=data1*w'%计算得分

 Comprehensive score sorting results:

1	2	3	4	5	6	7	8
0.9960	0.3857	0.2494	0.2399	0.2189	0.1845	0.1835	0.1808
Hefei	Wuhu	Chuzhou	Fuyang	Ma On Shan	Xuancheng	Bengbu	Anqing
9	10	11	12	13	14	15	16
0.1203	0.1195	0.1194	0.1157	0.0946	0.0935	0.0842	0.0574
Suzhou	Bozhou	Tongling	Lu'an	Huangshan	Huainan	Huaibei	Chizhou

From the sorted score results, it can be seen that Hefei City ranks first, and its score is far ahead of other cities. It can be seen that the consumption level of residents in the provincial capital city is high, and it also reflects that the economic development level of Hefei City is better! 

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