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 CHEMICAL ENGINEERING TRANSACTIONS  
 

 VOL. 46, 2015 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Peiyu Ren, Yanchang Li, Huiping Song 
Copyright © 2015, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-37-2; ISSN 2283-9216  

An Evaluation System and Grey Clustering Evaluation Model 
of Sunshine Sports Overall Capacity of Colleges and 
Universities Based on Whitening Weight Functions 

Zhi’er Liu 
Department of Sports & Human Science, Jilin Institute of Physical Education 
p8956k@163.com 

Sunshine sport is one of the important contents of sports education in colleges and universities. Weaknesses 
and problems of sunshine sports of colleges and universities are studi ed and discussed in this paper. Firstly, 
evaluation indexes of sunshine sports are confirmed. And a comprehensive evaluation system is established. 
Secondly, under the evaluation system, different evaluation indexes are analyzed and the whitening weight 
functions corresponding to those indexes are constructed. Next, with the weight of index taken into account, a 
grey clustering evaluation model of sunshine sports for colleges and universities is taken shape and the 
overall sunshine sports capacity of colleges and universities are obtained based on weighted grey clustering 
coefficients. Results show that the model is reliable and can be applied to various cases. Last but not the 
least, the efficacy and the practicality of the model are verified through case s tudy. 

1. Introduction 

In order to respond to national policies and plans on sports education, colleges and universities started to 
implement sunshine sports step by step and have yielded fruitful results [Wang (2007) and Shi (2014) 
reported]. However, some problems of sunshine sports of colleges and universities were identified, one of 
which was that quality and health of students didn’t improve, even degraded in some institutions of higher 

education. Meanwhile, during the implementation of sunshine sports, the goal is far from clear and relevant 
measures have no precise target, which result in a lack of mechanism and planning for long -term 
development. Currently, some experts and scholars have studied the issue from different views and tried to 
interpret the policy on sunshine sports. They also analyzed the content of sunshine sports as well as planning 
and strategies on sunshine sports of colleges and universities [Xu (2009), Liang (2011), Zhang et al (2011), 
Chen (2011) and Cai et al (2014) reported]. However, current evaluation of the sunshine sports evaluation of 
colleges and universities fails to reach the underlying part of the issue. And it is significant to evaluate the 
implementation of sunshine sports in a direct and quantified way. Therefore, on th e basis of previous 
research, this paper studies the comprehensive sunshine sports capacity and proposes an evaluation system 
and a grey clustering [A (2010), Mustansar et al (2014) and Wen et al (2014) reported] evaluation model 
based on whitening weight functions [Ker-Tah (2011) reported].  

2. The Evaluation System of Sunshine Sports of Colleges and Universities 

Based on the scientific principle, the systematic principle, the directing principle and the representative 
principle, this paper evaluates the implementation of sunshine sports of colleges and universities from three 
perspectives, namely hardware capacity, software capacity and implementation and execution capacity. The 
evaluation system of overall sunshine sports capacity of colleges and universities is constructed as Table 1. 
 
 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1546100

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Liu Z.E., 2015, An evaluation system and grey clustering evaluation model of sunshine sports overall capacity of 
colleges and universities based on whitening weight functions, Chemical Engineering Transactions, 46, 595-600  DOI:10.3303/CET1546100

595



Table 1: The evaluation system of overall sunshine sports capacity of colleges and universities 

evaluation system Evaluation criteria Evaluation index 

The evaluation system of 
overall sunshine sports 
capacity of colleges and 
universities U  

Hardware capacity
1

U  

Venues and equipment
11

u  

Capital investment
12

u  

Institutional arrangement
13

u  

Management organs
14

u  

Teaching staff
15

u  

Course design
16

u  

Software capacity
2

U  

Teaching quality
21

u  
Integration of production, academia and research

22
u  

Establishment of key majors
23

u  

Extracurricular activities
24

u  

Sports training and competition 
25

u  

Implementation and 
execution capacity

3
U  

Policy implementation
31

u  

Advertisement
32

u  

Teaching reform
33

u  

Improvement of students’ talent
34

u  

Social satisfaction
35

u  

3. Grey Cluster Evaluation Model Based on Whitening Weight Functions 

3.1 Basic forms of whitening weight functions 
Whitening weight functions is the core of the grey cluster analysis. When analyzing the object, evaluation 
indexes of different grey categories usually have distinct whitening weight functions. If the whitening weight 
function between the object and the i-th grey category about evaluation index j  is marked as  jif u . The 
basic forms of whitening weight functions  jif u  can be summarized into the followings.  
(1) Ladder-shape whitening weight functions  jif u  
The basic structure of ladder-shape whitening weight functions  jif u  is shown in Figure 1. 

Corresponding whitening weight functions  jif u  can be 
expressed as: 
 
 
 
 

 
                 (1) 

 
 
(2) Left-half ladder-shape whitening weight functions  jif u  
The basic structure of left-half ladder-shape whitening weight functions  jif u  is shown in Figure 2. 

Corresponding whitening weight functions  jif u  can be expressed as: 
 
 

     
                                   (2) 

  
 

 
(3) Right-half adder-shape whitening weight functions  jif u  

 

 

 

   
   

 

0

1

j

i

j

ij j j

i i ij j

i i

j

i

u u b

u b u
f u u a u u b

u b u a

u u a

 



  






 

   

 

   
   

 

   
   

   

0

1

j j

i i

j

i j j

i ij j

i ij

i j

i j j

i ij j

i i

j j

i i

u u a or u u d

u u a
u a u u b

u b u a
f u

u d u
u c u u d

u d u c

u b u u c

  



 


 


 

 

  

596



The basic structure of right-half ladder-shape whitening weight functions  jif u  is shown in Figure 3. 

Corresponding whitening weight functions  jif u  can be expressed as: 
 
 

                                                   
                            (3)

 

 
 

(4) Triangle-shape whitening weight functions  jif u   

The basic structure of triangle-shape whitening weight functions  jif u  is shown in Figure 4. 

Corresponding whitening weight functions  jif u  can be expressed as: 
  

       
                       (4) 

 
 
 
 
 

 

 jif u

u

1

0
 jiu a  

j

i
u b  jiu c  

j

i
u d

         

 jif u

u

1

0
 jiu a  

j

i
u b

 
Figure 1: Ladder-shape whitening weight functions  Figure 2: Left-half ladder-shape whitening weight functions 

 jiu a  
j

i
u b

 jif u

u

1

0

                 

 jif u

u

1

0
 jiu a  

j

i
u b  

j

i
u c

 
Figure 3: Right-half ladder-shape whitening             Figure 4: Triangle-shape whitening weight functions 

weight functions 

3.2 Weight of indexes of overall sunshine sports capacity 
In this paper, weights of indexes of overall sunshine sports capacity are allocated on the basis of Delphi  
Method. Assume m  experts are invited to score n  evaluation indexes. If the score of evaluation index j  
from expert i  is

ij
v , the judgment matrix V  is: 

 
   

                    
         
                              (5)

 

 
 

 
Thus, the column vector and its value 

j
w

  of evaluation index j  is obtained: 

 

 

 

   
   

 

0

1

j

i

j

ij j j

i i ij j

i i

j

i

u u a

u u a
f u u a u u b

u b u a

u u b

 



  






 

   

 

   
   

 

   
   

 

0

1

j j

i i

j

i j j

i ij j

i ij

i j

i j j

i ij j

i i

j

i

u u a or u u c

u u a
u a u u b

u b u a
f u

u b u
u b u u c

u c u b

u u b

  



 


 


 

 

 

11 12 1

21 22 2

1 2

n

n

m m mn

v v v

v v v

v v v

 
 
 
 
 
 

V

597



1

m

j ij

i

w v




 
                       (6) 

Consequently, the weight of evaluation index j  is: 

1

/
n

j j j

j

w w w
 



 
                      (7) 

3.3 The grey cluster analysis of overall sunshine sports capacity 
Based on actual implementation of sunshine sports of colleges and universities as well as the distribution of 
indexes values in the evaluation system, overall sunshine sports capacity is categorized into five levels, 
namely excellent (level 1), good (level 2), mediocre (level 3), quali fied (level 4) and unqualified (level 5). The 
whitening weight functions corresponding to each level are shown in Figure 5. 

 jif u

u

1

0
0.4 0.5 0.8 0.90.70.6

 5f u  4f u  1f u 3f u  2f u

 
Figure 5: Whitening weight functions of overall sunshine sports capacity 

According to the whitening weight functions in Figure 5, whitening weight functions of different evaluation 
levels can be expressed by the followings: 

 5

0 0.6

0.6
0.4 0.6

0.2

1 0.4

u

u
f u u

u





  




                    (8) 

 4

0 0.5 0.7

0.5
0.5 0.6

0.1

0.7
0.6 0.7

0.1

1 0.6

u or u

u
u

f u
u

u

u

 



  


 
  






                    (9) 

 3

0 0.6 0.8

0.6
0.6 0.7

0.1

0.8
0.7 0.8

0.1

1 0.7

u or u

u
u

f u
u

u

u

 



  


 
  






                  (10) 

 2

0 0.7 0.9

0.7
0.7 0.8

0.1

0.9
0.7 0.9

0.1

1 0.8

u or

u
u

f u
u

u

u





  


 
  






                 (11) 

 1

0 0.8

0.8
0.8 0.9

0.1

1 0.9

u

u
f u u

u





  




                  (12) 

Therefore, it can be obtained the grey clustering coefficient  1Uif u  of hardware capacity 1U  of sunshine 
sports evaluation of colleges and universities is: 

    11
6

1

1

juU

i j i

j

f u w f u


 
                    (13) 

598



The grey clustering coefficient  2Uif u  of software capacity 2U  of sunshine 1U  sports evaluation of colleges 
and universities is: 

    11
6

1

1

juU

i j i

j

f u w f u


 
                   (14) 

The grey clustering coefficient  3Uif u  of implementation and execution capacity 3U  of sunshine sports 
evaluation of colleges and universities is: 

    33
5

3

1

juU

i j i

j

f u w f u


 
                   (15) 

So the comprehensive grey clustering coefficient  3Uif u  of sunshine sports evaluation of colleges is: 

       31 21 2 3
UU UU

i i i i
f u w f u w f u w f u                                     (16)

 

And the overall sunshine sports capacity of colleges and universities is at level p , and it satisfies: 

            1 2 3 4 5, , , ,
U U U U U U

p
f u max f u f u f u f u f u                  (17) 

4. Case Study 

Based on the evaluation index system, the overall sunshine sports capacity of a key university in West China 
is studied and analyzed. Through questionnaire, consultation with experts and statistical analysis, index 
values of overall sunshine sports capacity of this university is known. And according to whitening weight 
functions and grey clustering model, grey clustering coefficients of indexes of different levels are obtained, as 
shown in Table 2. 

Table 2: The grey clustering coefficient of sunshine sports evaluation 

Evaluation 
criteria 

Evaluation 
index 

Weight Value 
Grey clustering coefficient 
Level 1 Level 2 Level 3 Level 4 Level 5 

1
U  

11
u  0.20 0.85 0.500 0.500 0 0 0 

12
u  0.20 0.60 0 0 0 1.000 0 

13
u  0.15 0.70 0 0 1.000 0 0 

14
u  0.15 0.75 0 0.500 0.500 0 0 

15
u  0.15 0.70 0 0 1.000 0 0 

16
u  0.15 0.80 0 1.000 0 0 0 

2
U  

21
u  0.25 0.80 0 1.000 0 0 0 

22
u  0.10 0.50 0 0 0 0 0.500 

23
u  0.15 0.50 0 0 0 0 0.500 

24
u  0.25 0.80 0 1.000 0 0 0 

25
u  0.25 0.85 0.500 0.500 0 0 0 

3
U  

31
u  0.20 0.90 1.000 0 0 0 0 

32
u  0.15 0.95 1.000 0 0 0 0 

33
u  0.15 0.60 0 0 0 1.000 0 

34
u  0.25 0.75 0 0.500 0.500 0 0 

35
u  0.25 0.80 0 1.000 0 0 0 

 
Similarly, the grey clustering coefficient and the comprehensive weighted grey clustering coefficient of indexes 
under different evaluation criteria of overall sunshine sports capacity are obtained, as shown in Table 3.  
 
 

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Table 3: The comprehensive weighted grey clustering coefficient of sunshine sports evaluation 

Evaluation criteria Weight 
Grey clustering coefficient 
Level 1 Level 2 Level 3 Level 4 Level 5 

1
U  0.30 0.100 0.325 0.375 0.200 0 

2
U  0.30 0.125 0.625 0 0 0.100 

3
U  0.40 0.350 0.375 0.125 0.150 0 

Comprehensive grey clustering coefficient 0.208 0.435 0.163 0.120 0.030 
 
From Table 3, it is known that the overall sunshine sports capacity of this key university is at level 2 or defined 
as “good”. 

5. Conclusions 

This paper analyzes evaluation indexes of sunshine sports of colleges and universities and proposes an 
improved evaluation index system, making the evaluation more reasonable and more reliable. At the same 
time, whitening weight functions corresponding to different levels of indexes are established on the basis of 
the grey system theory. And a grey clustering coefficient is put in place, making the result even more 
convincing. Last but not the least, the model is verified through case study. The study contributes to the 
evaluation of the implementation effect of sunshine sports with theoretical and practical values. 

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