1. Basic principles
In information theory, entropy is a measure of uncertainty. The greater the uncertainty, the greater the entropy, and the greater the amount of information contained; the smaller the uncertainty, the smaller the entropy, and the smaller the amount of information contained.
According to the characteristics of entropy, the randomness and disorder of an event can be judged by calculating the entropy value, and the degree of dispersion of an index can also be judged by entropy value. The greater the degree of dispersion of the index, the impact of the index on the comprehensive evaluation (weight) is larger.
If the sample data have the same value under a certain indicator, then the impact (contribution) of the indicator on the overall evaluation is 0 , so its weight should also be 0.
The entropy weight method is an objective weighting method because it only relies on the discreteness of the data itself.
2. Steps of entropy weight method
1. For n samples and m indicators, xij is the value of the jth indicator of the i-th sample (i=1,2...,n;j=1,2,...,m)
2. Normalization of indicators: homogenization of heterogeneous indicators
Since the measurement units of various indicators are not uniform, before using them to calculate the comprehensive indicators, it is necessary to carry out standardized processing, that is, to convert the absolute value of the indicators into relative values, so as to solve the homogeneity problem of the different indicators. .
In addition, the values of positive and negative indicators have different meanings (the higher the value of the positive indicator, the better, and the lower the value of the negative indicator, the better), therefore, different algorithms are required for data standardization for positive and negative indicators deal with:
Here is the range transformation method mentioned earlier
Example: In order to improve its own service level, a logistics company has assessed its 11 departments, including 9 assessment criteria , and rewarded departments with better service levels. The following table shows the scoring results after the assessment of the indicators of each department.
1. Entropy weight method for weighting
1 ) Data standardization
According to the original scoring table, the following data standardization table can be obtained after standardizing the data
2 ) Calculate P ij
3 ) Calculate the entropy value of each index
4 ) Calculate the weight of each indicator
| entropy value |
0.95 |
0.87 |
0.84 |
0.96 |
0.94 |
0.96 |
0.96 |
0.96 |
0.96 |
|
| Redundancy |
0.05 |
0.13 |
0.16 |
0.04 |
0.06 |
0.04 |
0.04 |
0.04 |
0.04 |
0.6 |
| Weights |
0.08 |
0.22 |
0.27 |
0.07 |
0.10 |
0.07 |
0.07 |
0.07 |
0.07 |
1.00 |
Finally, calculate the scores of each department
| X1 |
x2 |
X3 |
X4 |
X5 |
X6 |
X7 |
X8 |
X9 |
Score |
|
| A |
1 |
0 |
1 |
0 |
0.5 |
1 |
1 |
1 |
1 |
0.69 |
| B |
1 |
1 |
0 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.71 |
| C |
0 |
1 |
0.33 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.71 |
| D |
1 |
1 |
0 |
1 |
0.5 |
1 |
0.87 |
1 |
1 |
0.70 |
| E |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
0.67 |
| F |
1 |
1 |
1 |
1 |
0.5 |
1 |
1 |
0 |
1 |
0.91 |
| G |
1 |
1 |
0 |
1 |
0.5 |
1 |
0 |
1 |
1 |
0.64 |
| H |
0.5 |
1 |
0.33 |
1 |
1 |
1 |
1 |
1 |
1 |
0.81 |
| I |
1 |
1 |
0.67 |
1 |
0 |
1 |
1 |
1 |
1 |
0.83 |
| J |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0.81 |
| K |
1 |
1 |
0.67 |
1 |
0.5 |
1 |
1 |
1 |
1 |
0.89 |
| Weights |
0.08 |
0.22 |
0.27 |
0.07 |
0.11 |
0.07 |
0.07 |
0.07 |
0.07 |
8.35 |