Foreword: The method of using AHP to determine weights is introduced in detail above, but the disadvantage of AHP is also obvious, that is, the subjectivity is too strong, and the judgment matrix is basically filled out by individuals, which is often most suitable for no data. Case.
When we have data, can we start directly from the data and determine the weights?
For example, in the above topic, common sense can hardly help us determine which factor is the most important for judging the overall situation of the class, and it is also difficult to tell us how to measure the importance of the other indicators. If there is no relevant information, then we really can only be completely subjective empowerment. There are already nine indicators here. If you encounter dozens of them again, it will be more troublesome just for subjective empowerment...
Having said so much, we can lead to a method of determining the weight completely based on the data - the entropy weight method
1.1 The principle of entropy weight method
The basic idea of the entropy weight method is to determine the objective weight according to the variability of the index.
Entropy weight method, a term in physics, according to the explanation of the basic principles of information theory, information is a measure of the degree of order of the system, and entropy is a measure of the degree of disorder of the system; according to the definition of information entropy, for a certain index, the entropy value can be used In general, if the information entropy of an index is smaller, it indicates that the index is worth the greater variation, the more information it provides, and the more effective it can play in comprehensive evaluation. The larger it is, the greater its weight will be . If the values of an indicator are all equal, the indicator does not work in the comprehensive evaluation. Therefore, the information entropy tool can be used to calculate the weight of each index, which provides a basis for comprehensive evaluation of multiple indicators.
1.2 Application steps of entropy weight method
When using the entropy weight method to make decisions, you need to go through the following three steps:
1.21 Data Normalization
(1) Normalize each factor according to the number of each option
In order to avoid the influence of dimension, the index should be standardized first. According to the meaning of the indicators, indicators can be divided into positive indicators (the larger the value, the better) and reverse indicators (the smaller the value is, the better), which are standardized by the following methods:
For positive indicators:
For negative indicators:
All in all, it is necessary to ensure that the normalized data are all positive numbers.
1.22 Find the ratio of each indicator under each scheme
Calculate the proportion of the i-th sample under the j-th indicator, and regard it as the probability used in the information entropy calculation.
1.23 Find the information entropy of each indicator
According to the definition of information entropy in information theory, the information entropy of a set of data is:
where ej≥0. If yij=0, define ej=0, and m is the number of influencing factors to be considered.
1.24 Determine the weight of each indicator
1.25 Calculating the composite score
2 Application example of entropy weight method
2.1 Background introduction
At the end of each academic year, a college will conduct assessments on 11 classes in the grade. The assessment criteria include nine aspects: grades, discipline, work style, ideology and morality, daily management, class teacher work, quality, disciplinary violations, late arrivals and early departures. The class with better results will be rewarded. The following table shows the scoring results after the assessment of each class indicator.
Due to the different degrees of difficulty of each indicator, it is necessary to give weights to 9 indicators so that the overall level of each class can be evaluated more reasonably. The higher the value of the first seven indicators, the better the performance, and the lower the value of the last two indicators, the better the performance.
2.2 Data preprocessing
Standardized table of scores for 9 indicators in 11 classes:
For example, the performance of a class is an indicator, we use the positive indicator formula to get
And the disciplinary behavior of the first class is this indicator, we use the negative indicator formula to get
By analogy, the above result table can be obtained.
In this school, the first seven indicators are positive indicators, and the last two indicators are negative indicators (positive and negative indicators are defined by individuals)
2.3 Find the ratio of each indicator under each scheme
For example, the grades of a class for this indicator, we use the formula
By analogy, the above result table can be obtained.
2.4 Find the information entropy of each indicator
For example, the performance indicator, we use the formula
By analogy, the above result table can be obtained.
2.5 Calculate the weight of each indicator
For example, the performance indicator, we use the formula
By analogy, the above result table can be obtained.
2.6 Grade each class
For example to grade a class, we use the formula
S1 = 100 * 0.052 + 90 * 0.151 + 100 * 0.186 + 84 * 0.045 + 90 * 0.072 + 100 * 0.045 + 100 * 0.045 + 50 * 0.209 + 30 * 0.195
=72.95
By analogy, the above result table can be obtained.
Therefore, among the eleven classes, the best overall situation is Class 6, followed by Class 3 and Class 2.
3. Implementation of case tools
3.1 Using tools
3.11 SPSSPRO (free online, all functions are free) —> [Weight Analysis (Entropy Weight Method)]
3.12 Case Operation
Step1: Create a new analysis;
Step2: upload data;
Step3: Select the corresponding data to open and preview it, and click to start the analysis after confirming that it is correct;
step4: Select [Weight Analysis (Entropy Weight Method)];
Step5: Check the corresponding data data format, [Weight analysis (entropy weight method)] requires the feature sequence to be a class variable, and there are at least two;
step6: Click [Start Analysis] to complete all operations
3.13 Interpretation of Analysis Results
The results generated below are derived from the analysis results exported by SPSSPRO software
Output result 1: Weight analysis calculation result
The weight calculation results of the entropy weight method show that the weight of grades is 5.205%, the weight of discipline is 15.05%, the weight of style is 18.637%, the weight of ideology and morality is 4.505%, the weight of daily management is 7.225%, and the weight of class teacher work is 4.504%, the weight of quality is 4.541%, the weight of disciplinary behavior is 20.877%, and the weight of late arrival and early departure is 19.456%, of which the maximum weight of the indicator is disciplinary behavior (20.877%), and the minimum value is the work of the class teacher (4.504%).
Output 2: Indicator importance histogram
The above figure shows the importance order of the indicators in the form of a histogram (descending order)
On this basis, it is easier and more convenient for us to use the formula of 1.25 to grade each class.
Note:
- SPSSPRO will process the positive and negative indicators by default. After processing, the data does not need to be standardized again;
- After the entropy weight method obtains the weight value, the data is multiplied by the corresponding weight and accumulated, and finally a column of data is obtained as the 'comprehensive score';
- The calculation formula of the entropy value method will take the logarithm, so if the logarithm of the number less than or equal to 0 is taken as the logarithm, a null value will appear. SPSSPRO uses non-negative translation for processing, that is, if the data of a column (an indicator) is less than or equal to 0, then add a 'translation value' to the data in this column at the same time [this value is the absolute value of the minimum value of the data in a certain column + 0.01], so that all the data is greater than 0, thus meeting the algorithm requirements.
4 Conclusion
The entropy weight method has a simple algorithm and is an objective weighting method. Compared with the subjective weighting, it has higher reliability and accuracy, and can deeply reflect the distinguishing ability of the indicators, and then determine the weighting weight with high reliability and accuracy. Accuracy. But at the same time, it also has limitations. It only obtains the weight based on the fluctuation degree of the data, or the so-called amount of information, without considering the actual meaning of the data, and it is likely to arrive at a result that goes against common sense. Therefore, when business experience does not distort the weights, it is more suitable for the entropy weight method; on the contrary, if the weight distortion often occurs, it is necessary to combine expert scoring or evaluation to better utilize the advantages of the entropy weight method. At the same time, before determining the weight, it is necessary to determine the influence direction of the index on the target score, and the nonlinear index should be preprocessed or eliminated.