Evaluation Model – Gray Relational Analysis
Gray relational analysis
basic idea
The basic idea of gray relational analysis is to judge whether the connection is close according to the similarity of the geometric shapes of the sequence curves. The closer the curves are, the greater the correlation between the corresponding sequences is, and vice versa.
This method can be used for system analysis and can also be used for comprehensive evaluation of problems .
Analyze primary and secondary factors
General abstract systems, such as social system, economic system, agricultural system, ecological system, education system, etc., contain many factors, and the result of the joint action of various factors determines the development trend of the system. People often want to know which of the many factors are the main factors and which are the secondary factors; which factors have a greater impact on system development and which factors have little impact on system development; Factors that hinder the development of the system need to be suppressed ; these are common concerns in system analysis. For example, in the grain production system, people want to increase the total grain output, and there are many factors that affect the total grain output, such as planting area, water conservancy, fertilizer, soil, seeds, labor, climate, farming technology and policy environment. In order to achieve more output with less investment, and to obtain good economic, social and ecological benefits, it is necessary to carry out systematic analysis.
case analysis
Multi-factor index, the impact on a single factor index (gray correlation analysis)
Principle analysis to solve the degree of correlation
Multi-factor indicators, the impact on multi-factor indicators (gray correlation analysis)
In this case, 5 investments are the sub- factors to be compared , and 6 incomes are the reference series, the parent factors . Here the resolution p=0.5 is taken.
clc;
close;
clear all;
% 控制输出结果精度
format short;
% 原始数据
x=[308.58 310 295 346 367
195.4 189.9 187.2 205 222.7
24.6 21 12.2 15.1 14.57
20 25.6 23.3 29.2 30
18.98 19 22.3 23.5 27.655
170 174 197 216.4 235.8
57.55 70.74 76.8 80.7 89.85
88.56 70 85.38 99.83 103.4
11.19 13.28 16.82 18.9 22.8
4.03 4.26 4.34 5.06 5.78
13.7 15.6 13.77 11.98 13.95];
n1=size(x,1);
% 数据标准化处理
for i = 1:n1
x(i,:) = x(i,:)/x(i,1);
end
% 保存中间变量，亦可省略此步，将原始数据赋予变量data
data=x;
% 分离参考数列（母因素）
consult=data(6:n1,:);
m1=size(consult,1);
% 分离比较数列（子因素）
compare=data(1:5,:);
m2=size(compare,1);
for i=1:m1
for j=1:m2
t(j,:)=compare(j,:)-consult(i,:);
end
min_min=min(min(abs(t')));
max_max=max(max(abs(t')));
% 通常分辨率都是取0.5
resolution=0.5;
% 计算关联系数
coefficient=(min_min+resolution*max_max)./(abs(t)+resolution*max_max);
% 计算关联度
corr_degree=sum(coefficient')/size(coefficient,2);
r(i,:)=corr_degree;
end
% 输出关联度值
r