“This is the 11th day of my participation in the First Challenge 2022. For details: First Challenge 2022”
preface
This piece blog is just a note blog, slightly improper place must be corrected! Hope every big guy not stingy give advice!
Grey prediction
There is no more history of what grey forecasting is. We’re more interested in what this thing can do, what kinds of predictions it fits into, and what are the principles involved? What problems can the corresponding grey prediction solve? · Grey prediction is to predict the system containing both known information and uncertain information, which is to predict the time-related grey process that changes within a certain range.
Comparison of grey correlation degree
This was actually a bit similar to our analytic hierarchy process (ahp), they all can carry on the appraisal of a certain event, the comparison, but the difference is that the weight of use of the analytic hierarchy process (ahp) that we need to develop related, the need for consistency check, in other words, in this respect, if we use the analytic hierarchy process (ahp), then will have certain subjectivity, objectivity and the lack of the corresponding, Although we may be able to pass the consistency test, there seems to be a lack of conviction overall. So in the gray comparison, it’s more like we’ve provided a perfect sample, how similar is the sample that we have here? The closer it is, the closer the current sample is to perfection, so we can use this to realize the comparison between samples. For example, we evaluate the best employees and teachers through this method. If we use hierarchical analysis, we need to consider the weight of each skill, which will inevitably lead to different opinions and even find that the consistency test fails in the modeling process. So let’s take a look at a concrete example of how to use it. Now we need to evaluate the performance of a group of teachers.
Grey correlation degree case
Grey forecasting model
First of all, gray prediction is more suitable for small sample prediction, that is, when the data given is not very much. In addition, gray prediction is actually a positive prediction along the time line, such as the prediction of rainfall in previous years, the most typical example is next year’s rainfall. And the old one about SARS. Then the main core of gray prediction is to process the data. The seemingly irregular data is processed through the process of accumulation and subtraction, weighted accumulation, and then the predicted data is obtained through integration. Usually, several data are predicted, and fitting may be used no matter how complicated it is.
cumulative
You just add up the first N numbers to get a new sequence. For example, after processing 1, 2, 3, 4, 5:1, 3, 6, 10, 15 Let’s write the initial sequence as:
After treatment:
b-b
So that’s even easier, that’s the latter term minus the former term. For example, 1 2 3 4 5 after processing: 0 1 1 1 1 1
Weighted neighborhood generation
That’s adding two adjacent pieces of data to scale. Original sequence:
Grey model GM(1,1)
This is what we use to wear the front thing for prediction.
Model is derived
Again, this is based on the previous example. Let’s assume the original sequence is:
And we can see that this is similar to least squares, but we can also do it with matrices.
Grey prediction example
The title
Noise prediction, data are as follows:
| year | Noise rating |
|---|---|
| 1986 | 71.4 |
| 1987 | 72.4 |
| 1988 | 72.4 |
| 1989 | 72.1 |
| 1990 | 71.4 |
| 1991 | 72.0 |
| 1992 | 71.6 |
The problem solving
Level than detection
Let’s construct the original sequence
Incremental processing
Plug it in to solve for a, b
Error operation
So let’s do that
code
The front BB so much the most important or code, hand is impossible this life is impossible.
Associated with the code
x1=[
8 9 8 7 5 2 9;
7 8 7 5 7 3 8;
9 7 9 6 6 4 7;
6 8 8 8 4 3 6;
8 6 6 9 8 3 8;
8 9 5 7 6 4 8;
] % The sequence to compare
x=x1;
[r,c]=size(x1);
biaozhun = [9 9 9 9 9 9 9] % Standard sequence
for i=1:r
for j=1:c
x(i.j) =abs(biaozhun(j)-x(i.j))
end
end
max=x(1.1)
min=x(1.1)
for i=1:r
for j=1:c
if x(i.j) > =max
max=x(i.j)
end
end
end
for i=1:r
for j=1:c
if x(i.j) < =min
min=x(i.j)
end
end
end
k=0.5 % Resolution coefficient value
l=(min+k*max)./(x+k*max)Find the correlation coefficient matrix
guanliandu=sum(l')/c
[rs,rind]=sort(guanliandu,'descend') % to sort the correlation degree
Copy the code
Prediction code
y=input('Please enter data');
n=length(y);
jibi1=exp(1) ^ (2 -/(n+1));
jibi2=exp(1) ^ (2/(n+1));
for i=2:n
jibi = y(n)/y(n- 1);
if jibi>jibi1 && jibi<jibi2
disp("Grade ratio passed")
else
disp("Grade ratio failed.")
end
end
yy=ones(n,1);
yy(1)=y(1);
for i=2:n
yy(i)=yy(i- 1)+y(i)
end
B=ones(n- 1.2);
for i=1:(n- 1)
B(i.1)=-(yy(i)+yy(i+1)) /2;
B(i.2) =1;
end
BT=B';
for j=1:(n- 1)
YN(j)=y(j+1);
end
YN=YN';
A=inv(BT*B)*BT*YN;
a=A(1);
u=A(2);
t=u/a;
t_test=input('Enter the number of predictions');
i=1:t_test+n;
yys(i+1)=(y(1)-t).*exp(-a.*i)+t;
yys(1)=y(1);
for j=n+t_test:- 1:2
ys(j)=yys(j)-yys(j- 1);
end
x=1:n;
xs=2:n+t_test;
yn=ys(2:n+t_test);
plot(x,y,'-r',xs,yn,'*b');
det=0;
yuce = [];
yunce(1)=y(1);
yunce(2:n+t_test)=yn;
yunce
for i=2:n
det=det+abs(yn(i)-y(i));
end
det=det/(n- 1);
disp([The absolute error is:,num2str(det),The '%']);
disp(['Predicted value is:',num2str(ys(n+1:n+t_test))]);
Copy the codeHere the main input is []
conclusion
By understanding this, we can know that grey prediction can be compared in relevance, that is to say, it can solve the work of analytic hierarchy process to some extent. In terms of data prediction, it is suitable for small-scale prediction, such as air water quality prediction, national population prediction, novel Coronavirus infection prediction. Of course, if the data is accurate and other factors are ignored.