TOPSIS method
It can be translated as the approaching ideal solution sorting method, which is often referred to as the distance method of good and bad solutions in China. The TOPSIS method is a commonly used comprehensive evaluation method, which can make full use of the information of the original data, and its results can accurately reflect the relationship between the evaluation schemes. gap.
If we want to rate a person, but if there are multiple indicators for scoring him, we can convert all the indicators.
If the index is as high as possible, then such an index is a very large index (benefit index); if the index is as small as possible, then such an index is a very small index (cost index).
Unified indicator type
We generally convert all indicators into extremely large indicators, which is called index positive (the most commonly used)
formula for converting extremely small indicators into extremely large indicators =max-x
Standardization
In order to eliminate the influence of different index dimensions, it is necessary to standardize the matrix that has been forwarded.
Seeing this formula, we can now think about what is the evaluation distance of good and bad solutions.
Let us use examples to let everyone know better how to calculate
Summarize
Step 1: Normalize the original matrix
①I have just introduced how very small indicators can be transformed into extremely large indicators.
The formula for converting an extremely small indicator to an extremely large indicator: max-x;
if all elements are positive, then you can also use: 1/x;
② Convert an intermediate indicator to an extremely large indicator
If it is water, the pH value is 7
③ Interval indicators are transformed into extremely large indicators
Step 2: Normalize the normalization matrix
Step 3: Calculate the score and normalize
practice questions
We can first import the data in EXCEL into Matlab
model extension
When we just calculated D+/D-, the weights of our indicators are the same by default.
So when we calculate, we use w to replace the weight, and then calculate the weight, think about how the previous AHP determines the weight, and here is how to determine it.
We also call this TOPSIS with weights
Several problems with code operation
1. The first is to run load xxx.mat. This mat file should be in the current running folder.
2. When we draw a graph, we should try our best to make the data clearer and easier to see.
3. When the TOPSIS evaluation index needs to be weighted, we can use the entropy weight method.
Modification of TOPSIS Model Based on Entropy Weight Method
The degree of variation is also called variance.
The steps of the entropy weight method
Finally, let me say that this entropy weight method, if you are writing a thesis, try not to use this method, but if you are participating in a competition, you can use it. Because the theoretical basis of this method is not particularly solid.