Evaluating the overall situation of each class in a university based on entropy weight method (formula explanation + simple tool introduction)

Preface ： The above describes in detail the method of using analytic hierarchy process to determine the weight , But the disadvantages of analytic hierarchy process are also obvious , That is, subjectivity is too strong , The judgment matrix is basically filled in by individuals , It is often best used when there is no data .

When we have data , Can we start with the data directly , Determine the weight ？

For example, the title above , Common sense can hardly help us determine which factor is the most important in judging the overall situation of the class , It is also difficult to tell us how to measure the importance of other indicators . If no relevant information is available , Then we really have to be completely subjective . Here are nine indicators , In case there are dozens of them , Subjective empowerment alone is troublesome ……

Said so much , Then we can introduce a method to determine the weight completely from the data —— Entropy weight method

1.1 Principle of entropy weight method

The basic idea of entropy weight method is based on The magnitude of index variability To determine the objective weight

Entropy weight method , Physical terms , According to the basic principles of information theory , Information is a measure of the order of a system , Entropy is a measure of the disorder of a system ; According to the definition of information entropy , For an indicator , Entropy can be used to judge the dispersion degree of an index , Generally speaking , If the information entropy of an index is smaller , It indicates that the greater the variation degree of the index value , The more information you provide , The greater the role it can play in the comprehensive evaluation , The greater the weight . If the values of an indicator are all equal , Then the index does not play a role in the comprehensive evaluation . therefore , Information entropy can be used as a tool , Calculate the weight of each index , Provide basis for multi index comprehensive evaluation .

1.2 Application steps of entropy weight method

When using entropy weight method to make decision , You need to experience the following 3 A step ：

1.21 Data standardization

（1） Each factor is normalized according to the number of each option

In order to avoid the influence of dimension , First, we should standardize the indicators . According to the meaning of the index , Indicators can be divided into positive indicators （ The larger the value, the better ） And reverse indicators （ The smaller the value, the better ）, Standardization is carried out by the following methods ：

For positive indicators ：

For negative indicators ：

To make a long story short , It is necessary to ensure that the standardized data are all positive numbers .

1.22 Calculate the ratio of each index under each scheme

Computation first j Item... Under this indicator i Proportion of samples , It is regarded as the probability used in the calculation of information entropy .

1.23 Find the information entropy of each index

According to the definition of information entropy in information theory , The information entropy of a set of data is ：

among ej≥0. if yij=0, Definition ej=0,m Is the number of influencing factors considered .

1.24 Determine the weight of each indicator

1.25 Calculate the comprehensive score

2 An application example of entropy weight method

2.1 Background introduction

At the end of each academic year, a certain university will give 11 Classes will be assessed , The assessment criteria include performance 、 Discipline 、 Style 、 Ideology and morality 、 Daily management 、 The work of the head teacher 、 Quality 、 Disciplinary violations 、 There are nine aspects of being late and leaving early , And reward the classes with good assessment results . The following table shows the scoring results after the assessment of each class index .

Due to the different degrees of difficulty of various indicators , So you need to 9 The indicators are weighted , In order to evaluate the overall level of each class more reasonably . The higher the value of the first seven indicators, the better the performance , The lower the value of the last two indicators, the better .

2.2 Data preprocessing

11 A class 9 Standardized table of item index scores ：

For example, the grade of class 1 is the indicator , We use the positive indicator formula , have to

This indicator is applicable to the disciplinary violations of class 1 , We use the negative indicator formula , have to

And so on , The above result table can be obtained .

In this school , The first seven indicators are positive indicators , The latter two indicators belong to negative indicators （ Positive and negative indicators are defined by individuals ）

2.3  Calculate the ratio of each index under each scheme

For example, the grade of class 1 is the indicator , We use the formula

And so on , The above result table can be obtained .

2.4  Find the information entropy of each index

For example, the indicator of achievement , We use the formula

And so on , The above result table can be obtained .

2.5 Calculate the weight of each indicator

For example, the indicator of achievement , We use the formula

And so on , The above result table can be obtained .

2.6 Grade each class

For example, grade class one , 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

And so on , The above result table can be obtained .

therefore , In eleven classes , The best thing about the overall situation is 6 class , The second is 3 Class and 2 class .

3、 Case tool implementation

3.1 Using tools

3.11SPSSPRO（ Free online , All functions are free ）—>【 Weight analysis （ Entropy weight method ）】

3.12 Case operation

Step1： New analysis ;

Step2： Upload data ;

Step3： Select the corresponding data to open and preview , Click start analysis after confirmation ;

step4： choice 【 Weight analysis ( Entropy weight method ）】;

step5： View the corresponding data format ,【 Weight analysis ( Entropy weight method ）】 The feature sequence is required to be a class variable , And there are at least two ;

step6： Click on 【 To analyze 】, Complete the operation

3.13 Analysis results interpretation

The following generated results are from SPSSPRO The analysis results of the software are exported

Output results 1： Weight analysis calculation results

The weight calculation result of entropy weight method shows 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%、 The weight of the head teacher's work is 4.504%、 The weight of quality is 4.541%、 The weight of disciplinary violations is 20.877%、 The weight of late and early leave is 19.456%, Among them, the maximum weight of the index is the violation of discipline (20.877%), The minimum value is the work of the class teacher (4.504%)

Output results 2： Index importance histogram

The above figure shows the importance ranking of indicators in the form of histogram （ Descending ）

On this basis , We'll use it again 1.25 It is easier and more convenient to grade each class with the formula of .

notes ：

• SPSSPRO By default, the indicator will be positive 、 Negative indicator processing , By dealing with , There is no need to standardize the data ;
• After the weight value is obtained by entropy weight method , At this point, the data is multiplied by the corresponding weight , And accumulate , Finally, a column of data is obtained ‘ Comprehensive score ’;
• There will be logarithm in the calculation formula of entropy method , So if less than or equal to 0 Take the logarithm of the number , It will appear null value ,SPSSPRO Non negative translation is used for processing , That is, if a column （ Some index ） The data is less than or equal to 0, Then let this column of data add a ‘ Translation value ’【 This value is the absolute value of the minimum value of a column of data +0.01】, So that all the data is greater than 0, Therefore, it meets the requirements of the algorithm .

4. Conclusion

The entropy weight method is simple , It is an objective weighting method , Compared with subjective weighting, it has higher reliability and accuracy , It can deeply reflect the distinguishing ability of indicators , Then the weight weight is determined to have high reliability and accuracy . But it also has limitations , It depends only on the volatility of the data , Or the so-called amount of information to get the weight , Regardless of the actual meaning of the data , It is likely to result in a violation of common sense . therefore , When business experience does not distort the weight , It is more suitable for entropy weight method ; conversely , If weight distortion often occurs , It needs to be combined with expert scoring or evaluation in order to give better play to the advantages of entropy weight method . meanwhile , Before determining the weight, it is necessary to determine the influence direction of the index on the target score , The nonlinear indexes should be preprocessed or eliminated .