Application of analytic hierarchy process in college teaching evaluation system (principle + example + tool)

1 The principle and steps of analytic hierarchy process

1.1 The principle of analytic hierarchy process

20 century 70 End of the decade , American operations research scientist 、 Professor at the University of Pittsburgh T.L. Sadi （T.L.Saaty） Put forward analytic hierarchy process （Analysis Hierarchy Process, abbreviation AHP）. It divides people's thinking process into target level 、 Criterion layer and scheme layer , With the help of mathematical model , It is a practical decision analysis method that effectively combines qualitative judgment and quantitative calculation of decision makers . This method is systematic , Flexible use 、 Simple and convenient , It is suitable for large-scale and complex systems . Especially when the scale of the system is huge 、 Complicated structure 、 Diverse attributes and objectives , And many elements and indicators in the system have only qualitative relationships , Using analytic hierarchy process to evaluate and make decisions is very efficient . The basic principle of analytic hierarchy process (AHP) is to divide complex problems into hierarchical structures according to their dominant relations , Each level is composed of interrelated and interacting elements . The relative importance of each element in the hierarchy is quantified through pair by pair comparison , Finally, the overall ranking of relative importance .

1.2 Application steps of analytic hierarchy process

Application AHP When making a decision , You need to experience the following 4 A step ：

1.2.1 Build a multi-level hierarchical structure model

The evaluation index system is established from top to bottom according to the dominant relationship ：

（1） At the top ： Also called the target layer or the target layer , It is the goal or result that the system wants to achieve , It is the primary criterion of system evaluation （ Such as evaluating the teaching quality of college teachers ）.

（2） Criterion layer ： It is the criterion set for the realization of the target layer 、 Subcriteria, etc .

（3） At the bottom ： Also called scheme layer . It is a variety of schemes adopted to achieve the goal 、 Measures, etc .

1.2.2 Construct pairwise comparison judgment matrix

For elements belonging to the same level , The elements of the above level are used as the criteria for pair by pair comparison , Establish a judgment matrix .

Compare n Elements B=(B1,B2,Bn) For target layer elements A Influence : Compare in pairs , use aij Representation element Bi And elements Bj To the goal A The ratio of the degree of influence .

In order to quantify judgment , according to 1-9 The scale determines the relative importance of each element .

1.2.3 Weight calculation

（1） The approximate value of the eigenvector of the judgment matrix is calculated by the root seeking method .

（2） The weight vector is obtained by standardizing the feature vector W=(W1,W2,…,Wn)T.

1.2.4 Consistency check

To ensure the correctness and rationality of the weight obtained , Consistency checks are also required .

Calculate the consistency index C.I.

among ,

obviously ,n The bigger it is ,C.I. The greater the error . therefore , The random consistency ratio is introduced in the test C.R.

When n=1,2,…,15 when ,R.I. See the following table for the values of .

When the random consistency ratio

It is considered that the calculated hierarchical sorting weight is correct 、 reasonable , otherwise , The judgment matrix needs to be readjusted , Until the conformity inspection is passed .

1.2.5 Calculation of comprehensive importance

The scheme with the largest weight is the best choice to achieve the goal .

2 The evaluation index system of College Teachers' teaching quality

The purpose of teaching quality evaluation of university teachers is to make valuable judgments on the evaluated objects , In order to promote teaching . The primary problem of teaching quality evaluation is to establish a scientific evaluation index system . The evaluation index system shall be accurate 、 Reflect the current teaching level of teachers sensitively .

According to the characteristics and operability of the evaluation index system of College Teachers' teaching quality , Four criteria layers and three scheme objects are set .

For the criteria layer : Teaching preparation , Teaching thought , Teaching execution , Teaching effect and characteristics , We can build such a 4*4 Judgment matrix of ：

The diagonal line is the judgment of each indicator , For example, for 【 Teaching preparation 】 And 【 Teaching preparation 】, Its importance is 1, Because it must be the comparison between the indicators themselves 1：1. For the second row, the first column , That is to say 【 Teaching thought 】 And 【 Teaching preparation 】 contrast , Maybe I think 【 Teaching preparation 】 Than 【 Teaching thought 】 Obviously important , Then it can be marked as 0.7, And so on , Until a complete judgment matrix is built .

Weight after standardization W by ：

among A*W by ：

AW：

λmax=AW1/W1+AW2/W2+AW3/W3+···+AWn/Wn=x

Maximum eigenvalue λmax=x/ Matrix order =4.0489

Maximum eigenvalue λmax After solving it ,C.I Value is much better ,
according to C.I Value formula ,λmax=4.0489,n=4, Substituting to obtain C.I value =0.0163

according to CI、RI Value solving CR value , Determine whether the consistency is passed .

RI The value can be known by looking up the table , This is Satty simulation 1000 Random consistency index obtained for times R.I. Value table （ As shown in the following table ）：

And our matrix is 4 rank （ Number of criteria layer factors ）, The order of the matrix is 4 Time corresponds to RI The value is 0.90, Generation into the formula ：

therefore C.R.=0.018<0.1 when , Indicates the judgment matrix A The degree of consistency is considered to be within the allowable range , Available at this time A To calculate the weight vector ; if C.R.≥0.1, It shows that we made a logical error when building the judgment matrix .

For the scheme layer ： Zhang San , Li Si , Wang Wu , We can build such a 3*3 Judgment matrix of ：

The comparison of teaching preparation of each scheme is compared in pairs by sorting the hierarchy , We can get Zhang San , Li Si , The weight of Wang Wu , Then this weight can be used as Zhang San , Li Si , Wang Wu's score in teaching preparation .
By analogy , We construct Zhang San , Li Si , Wang Wu is preparing for teaching 、 Teaching thought 、 Teaching execution 、 Score matrix of teaching effect and characteristics ：

The calculated score is ：

Zhang San , Li Si , Wang Wu's weight on teaching preparation is 【0.5954,0.2764,0.1283】

Zhang San , Li Si , Wang Wu's weight on teaching thought is 【0.0819,0.2363,0.6817】

Zhang San , Li Si , The weight of Wang Wu's teaching execution is 【0.6337,0.1919,0.1744】

Zhang San , Li Si , Wang Wu's weight on teaching effect and characteristics is 【0.1667,0.1667,0.6667】

PS： Consistency test is required for all the above judgment matrices .

So for the scheme object B1（ Zhang San ）, Its total score is ：
Zhang San's score in teaching preparation * The weight of teaching preparation + Zhang San's score in teaching thought * The weight of teaching ideas + Zhang San's score in teaching execution * The weight of teaching execution + Zhang San's scores in teaching effect and characteristics * The weight of teaching effect and characteristics =0.5954*0.2082+0.819*0.199+0.6337*0.4247+0.1667*0.1681=0.5841
And so on , The scheme object can be calculated B2（ Li Si ） by ：
0.2764*0.2082+0.2363*0.199+0.1919*0.4247+0.1667*0.1681=0.2141
Scheme object B3（ Wang Wu ）：
0.1283*0.2082+0.6817*0.199+0.1744*0.4247+0.6667*0.1681=0.3485
So Zhang San got the highest score , The second is Wang Wu , Finally, Li Si .

3、 Case and tool implementation

3.1 The most important factor in evaluating teaching quality

The function here is actually to find the factor weight , Therefore, only the hierarchical single sort is calculated , There is no solution layer , That is, there is no need for total hierarchical sorting .

3.1.1 Using tools
SPSSPRO（ Free online , All functions are free ）—>【 Analytic hierarchy process （AHP Simplified edition )】

3.1.2 Case operation

step1： choice 【 Analytic hierarchy process （AHP Simplified edition )】;
step2： Select the judgment matrix hierarchy
step3： Set the judgment matrix （ The judgement matrix is a symmetric matrix ）
step4： Click on 【 To analyze 】, Complete the operation .

3.1.3 Analysis results interpretation
The following generated results are from SPSSPRO The analysis results of the software are exported
Output results 1： Build judgment matrix results

This is the judgment matrix filled in the previous operation page

Output results 2：AHP Analytic hierarchy process results

Analytic hierarchy process ( Square root method ) The weight calculation results show that , The weight score of teaching preparation is 0.2082, The weight score of teaching thought is 0.199, The weight score of teaching execution is 0.4247, The weight score of teaching effect and characteristics is 0.1681.

Output results 3： Consistency test results

The result of analytic hierarchy process shows that , The maximum characteristic root is 4.0814, according to RI The corresponding table is found RI The value is 0.882, therefore CR=CI/RI=0.0308<0.1, Pass the one-time inspection , Explain the rationality of the weight determination method , There is no need to modify the judgment matrix .

3.1.4 Summary

from 3.1.3 You know , The most important factor in evaluating teaching quality is teaching execution , Its weight score is 0.4247, The second is teaching preparation , Teaching thought , Finally, the teaching effect and characteristics .

3.2 Choose the best teacher

The function here is to calculate the quantitative score of the scheme , Therefore, it is necessary to sort the calculation hierarchy of the criteria layer , Sort the scheme layer .
3.2.1 Using tools
SPSSPRO（ Free online , All functions are free ）—>【 Analytic hierarchy process （AHP pro )】
3.2.2 Case operation

Step1： Choose analytic hierarchy process （AHP pro ）;
Step2： Choose to build a decision model ;

Step3： Input the constructed evaluation index ;
Step4： Enter the final solution ;
Step5： Confirm to proceed to the next step of index scoring （ Accept only integers ）;

Step6： Enter the importance value of pairwise comparison between indicators ;

Step7： Input the importance evaluation of the corresponding evaluation values of different schemes ;

3.1.3 Analysis results interpretation
The following generated results are from SPSSPRO The analysis results of the software are exported
Output results 1： Program score

After single sorting based on indicator level and total sorting based on scheme level , The best plan to evaluate teachers' teaching quality is Wang Wu , Its quantitative score is 0.9561.

Output results 2： Hierarchical decision model

The figure is visible , The two most important determinants are teaching execution and teaching preparation , And the teaching idea 、 The teaching effect and characteristics belong to low weight .

Output results 3： The judgment matrix summarizes the results

The maximum eigenvalue of the judgment matrix is 4.117,CI The value is 0.039,RI The value is 0.882,CR The value is 0.0442, Consistency verification passed .

Output results 4： Summary results of scheme level judgment matrix

The above table shows the weight calculation results of the scheme layer of the analytic hierarchy process （ That is, total hierarchy sorting ）, A judgment matrix with the number of leaf node indexes is constructed to analyze the weight of each index , By showing the consistency test results , It is used to judge whether there is a logical problem of constructing the judgment matrix in the scheme layer weight matrix .

Because the score of the upper level node can be based on the score of its child nodes * Weight calculation results in , Therefore, when constructing the scheme level judgment matrix , Only leaf nodes are built , namely N A leaf node is built N A judgment matrix , It is used to compare the two situations , Get the score of the scheme layer for a leaf node ;

Requirements for consistency inspection results CR value （CR=CI/RI） Less than 0.1, You can see , The scores of the schemes meet the consistency test .

3.2.4 Summary

from 3.2.3 You can know , The teacher with the highest evaluation score for teachers' teaching quality is Wang Wu , Its quantitative score is 0.956

4 Conclusion

The use of analytic hierarchy process in teaching evaluation can greatly reduce subjective factors . One side , When constructing judgment matrix in analytic hierarchy process , Compared to certain values , What it needs is the relative ratio of the two influencing factors , This greatly reduces the subjective randomness of evaluation experts ; On the other hand , When judging whether the subjective judgment of experts deviates from the objective reality , The consistency of the test judgment matrix is used to analyze and evaluate , So as to make correct adjustment . However , Analytic hierarchy process also has some problems , For example, the weight calculation of influencing factors is not accurate . This is because the judgment matrix can not meet the consistency requirements in the traditional analytic hierarchy process . This paper aims at this problem , Based on the traditional analytic hierarchy process, a new method of man-machine integration is proposed , The accuracy and efficiency are improved when judging the consistency of the matrix , The accuracy of weight calculation is guaranteed , Effectively improve the traditional analytic hierarchy process .