Study on Internship Employee Performance Evaluation Based on the Gray
Correlation Analysis and Analytic Hierarchy Process
Ze-hong Li, Meng-zhu Chen
Department of Economics and Management，North China Electric Power University, Baoding, China
(chenmengzhu1989@163.com)
Abstract- Currently, more and more company
find out and reserve talents through intern’s
enrollment. In order to help the company evaluate
the potential and performance of the intern
effectively and scientifically, this paper introduce an
evaluation method based on the gray correlation
analysis and Analytic Hierarchy Process (AHP) and
take a case to further explain this method.
Keywords- AHP, evaluation ， gray correlation
analysis, interns
Ⅰ Introduction
At present, most companies have realized the
advantage of interns, they can found and cultivate the
backup talents through the intern trial and it is good for
the enterprise personnel echelon construction. Generally,
large enterprises, especially foreign-funded enterprises,
have a complete set of intern recruitment, assessment and
application systems[1]. However, companies often have
problems in the performance evaluation of the intern. At
present, it is difficult to find a method that is effective and
feasible and can truly reflect the performance of the
intern. This makes difficult for enterprises to judge
whether the intern into the enterprise truly bring benefits
for the enterprises. The paper use the AHP method, which
combines the qualitative and quantitative characteristics,
to determine the weights of various performance
indicators, again according to the uncertainty of the
performance evaluation and gray characteristics, use the
gray connection analytic method to extract the gain target
and the business goal target interrelatedness, to determine
the level of the internship employees, and ultimately help
the enterprise to make decisions.
Ⅱ Particularity of intern performance evaluation and the
limitations of traditional methods
Firstly, the working time of the intern is very short.
General practice time ranging from 2 to 6 months, in such
a short period of time an employee's work performance is
not adequate. The enterprise is difficult to find clear and
____________________
This article is the outcome of the Social Science Fund of
Hebei Province (project number: HB11YDG010)
quantifiable indicators to judge the employees. Therefore,
usually applied scale assessment method, comparing the
assessment method and 360-degree performance appraisal
method does not apply2. Secondly, the internship period
is actually a learning period. During this period they
usually do some simple task, contact people are ordinary
people in the inner circle around, application of critical
incident technique and the opinion poll method are
inappropriate. Therefore, from the traditional evaluation
method is difficult to find a method suitable for
companies to judge the performance of the intern3.
However, it is suitable for the AHP to determine the
weight of each index to find out the correlation between
the target index and the getting index.
Ⅲ The principle of performance evaluation based on the
AHP and gray correlation analysis
The AHP method is proposed by the United States
Operations Research expert T.L. Saaty in the 1970s, it is
refers to break down the elements about decisions into
goals, standards, programs and other levels4. On this
basis, carries on qualitative and the quantitative analysis.
An important part is to determine the judgment matrix. In
making this judgment, Satie use 1 ~ 9 and its reciprocal as
signs. 1 indicates that the two elements have the same
importance, 9 expressed that the former is extremely more
important than the latter, reciprocal indicates the
importance comparison when exchange the order of the
corresponding two factors5.
A． Establish stratification structure
Establish stratification structure, break the problem
into several levels. The first layer is the overall goal; the
middle layer according to the nature of the problem can
be divided into the target layer, departmental layer and
constrained layer; the lowest level is program layer or
measures layer. After full discussion and analysis, and
finally draw the hierarchy chart
B． Using AHP to determine the weight of each indicator
Seek the right value from the top layer to the bottom
layer. Set the current level factors as C1, C2,…,Ci,
Related upper layer is B （Can be more than one）. Then
aim at factor B, carries on pairwise comparisons to all
factors. According to the scale of judgment matrix, get the
value as aij (i,j=1,2,…,n):
 a11


a
 m1
CB=(aij)m×n=
a1n 


amn 
(1)
CB is the judgment matrix of the factors C1,
C2,…,Ci’s relative upper level B. CB's maximum
characteristic root is λmax. Standardized eigenvectors of
λmax is
  1 2
n 
T
, then

gives a sort
based on the relative importance of the factors C1,
C2,…,Ci to B. Standardized
i 
i
(i  1, 2,
n

k 1
i
, n)
ni
n
n
i

a
ki
k 1
k
ni
k 1
Calculate the combination scaling coefficient on the
same level.
Set the current level factors for the C1, C2,…,Cn,
related upper layer factors for the B1 , B2 , , Bn , every
Bi has a weight vector
i  1i 2i
ni   i  1,2, , n 
T
The weight of the factors in the upper layer is
b   b1 b2
bn 
T
currently,
each
factor's
combination scaling coefficient is[6][7]
m
m
b ,b , ,b
i 1
i
1
i 1
i
i
2
i 1
i
i
n
(5)
Go on, until all the combination scaling coefficient
of the bottom layer is worked out. Finally, find out the
weight of every index according to the coefficient of the
bottom layer. So, the combination of the weight
coefficient vector of the K-th layer is
WK  YK YK 1
Test the
, m)
Consistency.
yij 
xij
x0 j
(i  1, 2,
, m; j  1, 2,
, n)
(7)

min min xoj  xij   max max xoj  xij
Generally speaking,
max  n
n 1
r
j
r
j
xoj  xij   max max xoj  xij
r
(8)
j
ρ is the distinguishing coefficient, generally select
between 0 and 1, usually take 0.5[10][11].
Calculate the gray relational grade,
1 n
ij
n j 1
(9)
In the gray relational analysis, the index set is the
time series, each time interval should be the average
weight, but it is not suitable for the assessment of the
internship positions, therefore, in accordance with the
second step in the AHP method to calculate the weight of
the index in this layer relative to the upper layer[12][13].
  1 2
n 
n
Ri  r ( x0 , xi )   k ij (k is the k-th layer)
(10)
j 1
if
Use equation (10) to calculate the correlation of
every layer from the bottom layer. Finally draw the
correlation of the target layer. In order to judge the
performance level of each tested internship positions.
,
Ⅳ The example analysis
Y1 (Y1  1)
CI  0.1 , we think CB is good. CI 
set CR 
, xin  (i  1, 2,
(6)
Ri 
(4)
i
xi   xi1 , xi 2 ,
(xij is the original sequence; xoj is the reference sequence)
Calculate the correlation coefficient. Use the
following formula to calculate the correlation coefficient
between xi and xo based on the element j. (j=1,2,…,n)
(3)
m
, xm
Standardize the sequence. Usually use the following
formula to standardize9
 A 
k 1
x1 , x2 ,
unit.
k
This is the i-th component of the eigenvectors ω, the
maximum characteristic root is:
max  
Determine the reference sequence and comparative
sequence. Set a reference sequence
x0  ( x01 , x02 , , x0 n ) and some comparative sequence
The elements in x0 is selected from the best intern or
the goal index in the company. In the comparative
sequence, xi1 , xi 2 , , xin is the value for the evaluation
:
(2)
n
C． Gray correlation analysis
CI
, is a random consistency ratio, if CR<0.1,
RI
the judgment matrix has satisfied consistency. Otherwise
need to adjust the judgment matrix, to reach a satisfied
consistency8.
Set one company has four internship positions and
four interns P1,P2,P3,P4. Use AHP and gray relational
analysis to assess their performance.
A． Determine the index system
According to the characteristics of the interns and
corporate focus to develop the four-layer index system
(enterprise can adjust this standard according to its own
characteristics and requirements) 14, as shown in Figure 1.
Goal
Performance A1
Attitude B1
Work
seriousl
y
C1
Behavior A2
Skill B2
Effort B3
Temperament B4
Respons
ibility
Degree
Knowle
dge
Workin
g time
C2
C3
C4
C5
Efficien
cy
Speakin
g
manner
Character B5
Clothes
C6
C8
Fig. C7
1
Intern performance evaluation index
Intelligence B6
Social
skill
Recover
ability
Innovati
on
ability
Study
ability
C9
C 10
C 11
C 12
B． Construct judgment matrix
C． The relative weight calculations and the consistency
test
According to Figure 1, we can elect 1 contrast
matrix in the second layer, 2 in the third layer and 6 in the
Calculate the relative weight of the comparative
element to the reference element and test the consistency.
fourth layer. AZ’s judgment matrix is AZ
 1 3

 , AZ
1/ 31 
is the judgment matrix is
 1 1/ 4 1/ 3 
 1 1/ 5 2 

,


BA1   4 1 3 / 2  BA2   5
1 4
3 2/3 1 
1/ 2 1/ 4 1 




BA1 is the comparison of B   B1 B2 B3  and
A1, BA2 is the comparison of
B   B4
B5
B6  and
A2. CiBj’s judgment matrix is
 1
C12 B1  
1/ 2
 1
C56 B 3  
1/ 8
2

1
,
8

1
,
 1
C34 B 2  
1/ 4
 1
C78 B 4  
1/ 5
4

1
,
5

1
,
 1 4
C910 B 5  
,
1/ 4 1 
C12B1
 1 1/ 6 
C1112 B 6  

6 1 
is the comparison of C   C1 C2  and B1,
C34B2 is the comparison of
is the comparison of
C   C3 C4  and B2, C56B3
C   C5 C6  and B3, C78B4 is the
comparison of
C   C7 C8  and B4, C910B5 is the
comparison of
C   C9 C10  and B5, C1112B6 is the
comparison of
C   C11 C12  and B6.
 1 1/ 5 2 
Standardization


BA1   5
1 4
1/ 2 1/ 4 1 


 0.153 0.151 0.182 

 Sun the line
0.770
0.755
0.727


 0.077 0.094 0.091


 0.486 
Decide the number of the columns


 2.252 
 0.262 


 0.162 

 3
 0.751  = 2
 0.087 


 3
BA2 2
The
 1 1/ 5 2  0.162   0.486 


 

 5
1 4  0.751    2.252 
1/ 2 1/ 4 1  0.087   0.262 


 

largest
1
 0.486
eigenvalue
2.257
0.262 
max   


  3.006
3  0.162 0.751 0.087 
max  3
Consistency index CI 
3 1
,
is
.
 0.003 . Look-up
the table, the random consistency index RI=0.58, so
CR 
CI 0.003

 0.005  0.1 , BA2's inconsistency
IR 0.58
can accept. So the weight of
A2 is
B   B4
2   0.125 0.517 0.087 
 3
B6  to
B5
T
, go on,
  2   0.5 0.5
T
,
13   0.125 0.517 0.358
T
According to the equation (7), dimensionless
0 , 1 , 2 , 3 , 4 , we can get x0 , x1 , x2 , x3 , x4
x0  1,1,1,1,1,1,1,1,1,1,1,1
x1   0.7,0.5,0.4,0.5,0.33,0.7,0.714,0.25,0.83,0.7,0.2,0.714
x2   0.8,0.625,0.5,0.7,0.67,0.5,0.57,0.625,0.83,0.4,0.7,0.57
T
1   0.67 0.33
2   0.2 0.8
T
3   0.89 0.11
4   0.89 0.11
x4   0.7,0.625,0.6,0.4,0.83,0.8,0.714,0.5,0.67,0.3,0.8,0.85
5 4   0.2 0.8
6 4   0.89 0.11
G． Calculate the correlation coefficient
 4
 4
 4
T
 4
T
T
x3   0.5,0.875,0.6,0.9,0.83,0.6,0.714,1,0.83,0.9,0.5,0.286
T
D． Experts to evaluate the interns
According
The expert group organized by the Human
Resources Department, as well as department heads and
colleagues around, who is very familiar with their
corresponding work15. The result is shown in Table 1.
Table Ⅰ
Index score
to
the
equation
(10),
calculate
 0 j  x0 j  xij
01   0.3,0.5,0.6,0.67,0.3,0.286,0.75,0.17,0.3,0.8,0.286
02  (0.2,0.375,0.5,0.3,0.33,0.5,0.43,0.375,0.17,0.6,0.3,0.43)
03  (0.5,0.125,0.4,0.1,0.17,0.4,0.286,0,0.17,0.1,0.5,0.714)
Reference
04  (0.3,0.375,0.4,0.6,0.17,0.2,0.286,0.5,0.33,0.7,0.2,0.143)
score
So, min min xoj  xij  0, min min xoj  xij  0.8, s
index
P1
P2
P3
P4
C1
7
8
5
7
10
C2
4
5
7
5
8
C3
4
5
6
6
10
C4
5
7
9
4
10
C5
2
4
5
5
6
correlation
C6
7
5
6
8
10
coefficient
C7
5
4
5
5
7
C8
2
5
8
4
8
r
j
r
j
et   0.5 , take the equations above into equation (8),
we can get a correlation coefficient table, as follows:
Table Ⅱ
Correlation coefficient table
P1
P2
P3
P4
C1
0.570
0.670
0.440
0.570
C2
0.440
0.516
0.762
0.516
C9
5
5
5
4
6
C3
0.400
0.440
0.500
0.500
C10
7
4
9
3
10
C4
0.440
0.570
0.800
0.400
C11
2
7
5
8
10
C5
0.374
0.548
0.702
0.702
C12
5
4
2
6
7
C6
0.570
0.440
0.500
0.670
C7
0.583
0.482
0.583
0.583
C8
0.348
0.516
0.000
0.440
E． Determine the comparative sequence and reference
sequence
Reference sequence:
0  10,8,10,10,6,10,7,8,6,10,10,7 
comparative sequence:
1   7, 4, 4,5, 2,7,5, 2,5,7, 2,5
2  8,5,5,7, 4,5, 4,5,5, 4,7, 4 
C9
0.702
0.702
0.702
0.548
C10
0.570
0.400
0.800
0.364
C11
0.330
0.570
0.440
0.670
C12
0.583
0.482
0.351
0.730
Calculate the correlation of the third layer (B),
according to the equation (10)
3   5,7,6,9,5,6,5,8,5,9,5, 2 
RB1   B1C12  1 4   0.5271 0.6192 0.5463 0.5222 
4   7,5,6, 4,5,8,5, 4, 4,3,8,6 
RB 2   B 2C 34  2 4   0.432 0.6588 0.74 0.42 
T
T
RB3   B3C 56  3 4   0.3956 0.5361 0.6798 0.6985
T
F． Dimensionless
RB 4   B 4C 78  4 4   0.5572 0.4857 0.5189 0.5494 
T
RB5   B5C 910  5 4   0.5964 0.4604 0.7804 0.4008
T
RB 6   B 6C1112  6 4   0.5471 0.4945 0.3636 0.7275
T
Calculate the correlation of the second layer (A)
RA1   r1 , r2 , r3    RB1 , RB 2 , RB 3  1  
3
 0.4307
0.6094 0.6011 0.5364 
T
RA 2   r4 , r5 , r6    RB 4 , RB 5 , RB 6  2  
3
 0.5824
0.4697 0.6756 0.4721
T
Calculate the correlation of the goal layer
R0   RA1 , RA2    4
 0.4307 0.5824 


0.6094 0.4697   0.5 


 0.60110.6756   0.5 


 0.5364 0.4721 
  0.5066 0.5396 0.6384 0.5043 
T
ⅤResults
According to
R0 ，we can draw the conclusion that
P3  P2  P1  P4 , that is to say， P3 is the best while
P4 is the worst. Companies can make hiring decisions
according to this
Ⅵ Conclusion
At present, companies recruit more and more interns.
It becomes a hot topic that how to evaluate these people.
This paper integrates the advantages of the AHP method
and gray relational analysis. Use these two methods gives
an effective method to evaluate the performance of the
interns. Play a supporting role in the enterprise
management.
ACKNOWLEDGMENT
First of all, I would like to extend my sincere
gratitude to my supervisor, for her instructive advice and
useful suggestions on my thesis. I am deeply grateful of
her help in the completion of this thesis. I also deeply
indebted to all the other tutors in translation studies for
their help to me. Finally, special thanks should give to my
friends who have put considerable time into their
comments on the draft.
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