What are the indicators of VIKOR compromise?

One 、 application

VIKOR（ A compromise ） It is a multi-attribute decision-making method , It is used to sort the advantages and disadvantages of various schemes , And SPSSAU In the comprehensive evaluation TOPSIS（ Or entropy weight TOPSIS） The function is similar to . For example, sort alternative supplier schemes , Comprehensive evaluation of the candidate's abilities , Find out the candidate's priorities, etc .

Such as the A,B,C,D,E,F,G common 7 Candidates , A total of four abilities of candidates are scored , The lowest is 1 branch , Up to 10 branch , The higher the score, the stronger the ability . Now I hope to combine the four abilities （ Namely, four indicators ） Evaluate and rank the candidates' comprehensive abilities , Finally find the right candidate .

Two 、 operation

SPSSAU operation

（1） Click on SPSSAU Comprehensive evaluation ‘VIKOR’ Button . Here's the picture

（2） Drag and drop the data and click start analysis

normalization ：

3、 ... and 、 Case background

A company is recruiting , And conducted several rounds of interviews , In the end 7 A suitable candidate , Hope from now on 7 Selected from candidates 3 position . The data is shown in the figure below ： There are A,B,C,D,E,F,G common 7 Candidates , The four abilities of candidates are scored on the data , The lowest is 1 branch , Up to 10 branch , The higher the score, the stronger the ability . Now I hope to combine the four abilities （ Namely, four indicators ） Evaluate and rank the candidates' comprehensive abilities , Finally find the right candidate , Use compromise VIKOR To study .

PS: Parameter description

Four 、 analysis

Put data into analysis box ,SPSSAU The system automatically generates analysis results

1. Vikor Summary of analysis results

Calculation formula

（1） The sum of the distance ratios of the optimal scheme S

（2） The maximum distance ratio of the optimal scheme R

（3) Benefit ratio Q value

  Lambda Value represents risk appetite , The default value is 0.5, This value >0.5 It means risk preference , This value <0.5 The explanation is conservative .

  The table above shows 6 Two evaluation objects （ Applicant ） Corresponding Q Values and rankings , namely Q Value is the index value of the final quality , It can be seen that ,E and D The two candidates ranked... Respectively 1 And the 2 name , besides ,B and G The two candidates tied for the No 3 name , So if you want to choose 3 A word of , It may also need to be combined with subjective judgment B still G.

  In the table ‘ Sum of distance ratios of the final scheme S’, This value represents the comprehensive evaluation of each evaluation object , Its comprehensive score is the same as ‘ Best ’ Ratio of schemes , In short, the analysis will simulate a ‘ Best ’ Of applicants , Then find out the current evaluation objects （ Applicant ） And ‘ Best ’ The candidate's comprehensive score ratio ; The smaller the value, the better. The smaller the value, the better ‘ Best ’ lately ;

  In the table ‘ The maximum value of the separation ratio in the optimal scheme R’, This value represents the comprehensive evaluation of each evaluation object , The scores of each index are the same as ‘ Best ’ The maximum value of the ratio of the scheme , In short, the analysis will simulate a ‘ Best ’ Of applicants , Then find out the current evaluation objects （ Applicant ） The scores of each index are the same as ‘ Best ’ The maximum value of the candidate's score ratio ; The smaller the value, the better. The smaller the value, the better ‘ Best ’ lately ;

  Whether it's ‘ Sum of distance ratios of the final scheme S’ still ‘ The maximum distance ratio of the optimal scheme R’, The purpose is to calculate the final benefit ratio Q value ,Q The smaller the value, the better ,Q Value represents the evaluation object （ Evaluation program , Applicant ） And ‘ Best ’ The distance between , Smaller means closer .

2. Best and worst value

（1） Positive ideal solution

（2） Negative ideal solution

  The above table shows the evaluation indicators （ The cases are four abilities ） The best solution R+ Or the worst solution R-;

  The positive ideal solution of the optimal scheme R+ Indicates the optimal value of the evaluation index ; The negative ideal solution of the worst case R- Indicates the worst value of the evaluation index . These two index values are intermediate calculation process values , The purpose is to calculate S Value or R value .

3. Other process indicators

    The table above shows the intermediate process values ,S+,S-,R+ and R- value , They represent respectively ‘VIKOR Summary of analysis results ’ In the table S The maximum or minimum value of , Or R The maximum or minimum value of . It is also used to calculate the final benefit ratio Q value . In addition to this, list lambda value （ Decision making mechanism coefficient ）,SPSSAU The default is 0.5.

4. Lambda Value to benefit ratio Q value

  The table above shows different lambda The benefit ratio corresponding to the value Q value ,lambda value （ Decision making mechanism coefficient ）, The value is a ‘ Adjustment value ’, The value is between [0,1] Between ,SPSSAU The default is 0.5; The value is greater than 0.5 The more you prefer utility, the more you maximize your benefits , It belongs to the risk preference type ; The value is less than 0.5 It means that the more preference for reducing regret, the more risk conservative ; This value is generally taken as 0.5 Intermediate value .

  As can be seen from the figure below , Apart from E Outside , in addition 5 Candidates , With lambda The bigger the value is. （ That is, when the risk preference is increased ）,Q The value will become smaller and smaller, i.e. relative ‘ The better ’. but E This candidate , When risk appetite is increased randomly ,Q The value will get bigger and bigger , It shows that the more risk preference, the more likely it is that you should not choose E This candidate （ Probably E The candidate's abilities are relatively stable , however E Our comprehensive strength is relatively strong , So I will choose anyway E）.