How to calculate the positive and negative ideal solution and the positive and negative ideal distance in TOPSIS method?

One 、 application

TOPSIS Method is used to study the sequential optimization technique which is similar to the ideal scheme , Popular understanding means that data size has a good or bad relationship , The larger the data, the better , The smaller the data, the worse , Therefore, find out the positive and negative ideal solutions and the distance between the positive and negative ideal solutions by combining the size of the data , And finally get close to the program C value , And combine it with C Value sorting results in good and bad scheme sorting .

Two 、 operation

SPSSAU operation

（1） Click on SPSSAU Comprehensive evaluation ‘TOPSIS’ Button . Here's the picture

SPSSAU The dashboard

（2） Drag and drop the data and click start analysis

3、 ... and 、SPSSAU Analysis steps

Four 、 Case study

Yes 5 A coal mine about “ Dust concentration ”,“ Amount of sulfur dioxide ” and “ Prevalence of lung disease ” common 3 Index data ; Hope to pass TOPSIS Method comparison 5 Advantages and disadvantages of coal mines .（TOPSIS There are two points to note , First, the data should be all in the same trend , That is, the larger the data must be, the better it will be （ If not , You need to SPSSAU Data processing -> Reverse the function of generating variables / Countdown function for processing ） The data are as follows ：

5、 ... and 、 Data processing

1. Prepare the data , And carry out the same trend processing （PS： It needs to be handled by the researcher ）

2. Data normalization to solve dimensional problems （ Data processing -> Generating variables ）

3. the SPSSAU After processing , give the result as follows

Dust concentration	Amount of sulfur dioxide	Prevalence of lung disease
0.194	0.328	0.034
0.049	0.288	0.041
0.138	0.564	0.059
0.100	0.381	0.110
0.965	0.588	0.991

The normalized matrix is A, Write it down as ：

6、 ... and 、 result

SPSSAU The resulting analysis results are as follows ：

1. Positive and negative ideal solutions

The analysis results come from SPSSAU

（1） Positive ideal solution A+

The maximum value in the indicator data ; example ： The maximum dust concentration is 0.965;

（2） Negative ideal solution A-

The maximum value in the indicator data ; example ： The maximum dust concentration is 0.049;

2. TOPSIS Evaluate the calculation results

The analysis results come from SPSSAU

（1） Distance of positive ideal solution D+

In style , Optimal scheme    For matrix A Medium element .

 （2） Negative ideal solution distance D-

In style , Worst case scenario   ;

 

（3） Relative proximity C

example ：0.15/（0.15+1.256）=0.107;

7、 ... and 、 summary

Sum up , in the light of 3 Indicators ( Dust concentration , Amount of sulfur dioxide , Prevalence of lung disease ), Conduct TOPSIS evaluation , At the same time, the evaluation object is 5 individual （ The number of samples is the number of evaluation objects ）;
TOPSIS The method first finds out the positive and negative ideal solution of the evaluation index (A+ and A-), Then calculate the distance between each evaluation object and the positive and negative ideal solution D+ and D-.
according to D+ and D- value , Finally, the proximity between each evaluation object and the optimal scheme is calculated (C value ), And for C Value to sort .