CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-43-3; ISSN 2283-9216 

Research on the Model of Public Project Performance Evaluat
ion-A Case Study of Water Environment Project 

Hongbo Xu 
School of Economics and Management, Nanjing Institute of Industry Technology.  Nanjing 210000, China.  
xuhongbo2011@163.com 

In order to improve urban water environment project investment benefit, it is necessary to evaluate the 
performance of the project systematically and comprehensively. The paper takes advantage of Dempster-
Shafer (D-S) evidential theory and triangle whitening function in data processing and data integration to 
construct the evaluation model. Firstly, the triangular fuzzy number is used to determine the indicator weight. 
Then the grey clustering matrix is constructed to determine the level of each criterion of the urban water 
environment project. Finally, the paper identifies the grey class of project performance evaluation based on D-
S evidence theory and determines the integrated performance level of project. 

1. Introduction 

Quite a number of pollutants have been discharged into water bodies and have accumulated in company with 
economic growth in recent years in China(Miao and Fan,2012). As a result, most waters in China are suffering 
different degrees of pollution. From a national perspective, the pollution is extending from the tributaries to the 
master streams, spreading from urban areas to rural areas, permeating from earth surface to underground 
layers, and diffusing from areas to basins Wu,2010;Lv , et al.,2014).. Water environment has turned into one 
of the key bottle necks to the economic and social development in China. 
Water environment has turned into one of the key bottle necks that severely restrict the economic and social 
development in China. In order to control urban water pollution, improve the urban sewage treatment capacity, 
and assure drinking water security, the governments at all levels made heavy investment in engineering 
construction, and the number and size of urban water environment improvement projects are growing. 
However, project performance assessment is still a difficulty. With this fact as a starting point, this paper 
probes into the method for urban water environment improvement project performance evaluation. 
In order to control urban water pollution and improve the urban sewage treatment capacity to protect the 
security of drinking water, the Chinese government have made heavy investment in water environment 
improvement project since 2005. In this background, the project performance assessment is necessary and 
has been researched by many scholars : Ma and Weng(2011)constructed a performance  evaluation  index  
system  of  urban  water  environment  treatment  including  function,  benefit and  potential  indexes. Zhang 
(2006) established an index system for urban water environment improvement performance evaluation using 
analytic hierarchy process and presented the fuzzy comprehensive evaluation method based on indicators. 
Bai and Wang (2010) established the fuzzy synthetic evaluating model for assessing pollution control 
performance. Xu and Song (2005) brought forward the concept of "guarantee rate" for quantitative 
assessment of water environment for urban environmental & hydraulic works and the hydraulic calculation 
method based on the predictive evaluation and mathematical statistics theory of water environment.  
The present studies have focused on the indexes of the performance evaluation of urban water environment 
project from different perspectives. As the information of the project is always little and ambiguity in the 
performance evaluation, the paper tries to takes advantage of Dempster-Shafer (D-S) evidential theory and 
triangle whitening function in data processing and data integration to construct the evaluation model. The 
reminder of this paper is organized as follows. In Section 2, the general knowledge for the methodology is 
described. In Section 3, the improved performance evaluation model for urban water environment project is 
described in detail. Finally, some concluding remarks are drawn in Section 5. 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651044

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Xu H.B., 2016, Research on the model of public project performance evaluation-a case study of water environment 
project, Chemical Engineering Transactions, 51, 259-264  DOI:10.3303/CET1651044   

259



2. Establishment of Urban Water Environment Improvement Project Performance Evaluation 

Index System.  

Urban water environment improvement project performance evaluation index system is essential for project 
performance evaluation; scientific and rational index system enables evaluators to get the whole picture of the 
performance and existing problems of urban water environment improvement project, thus being a means 
necessary for performance evaluation. An evaluation index system is developed in this paper to objectively 
reveal the level of consistency of project with national policy and physical needs, rationally determine the 
project implementing efficiency, accurately reflect the project effectiveness, completely indicate the project 
sustainability, while assuring the independence between indicators. 
The urban water environment improvement project performance evaluation index system developed in this 
paper consists of three layers, i.e. the objective layer, the criteria layer, and the indicator layer, as shown in 
table 1. 

Table 1: Urban water environment improvement project performance evaluation index system 

Objective layer  Criteria layer  Indicator layer  

Urban water environment 
improvement project 
performance evaluation   

Level of consistency x1 
  

Degree of correlation of project with 
development strategy x11 
Degree of agreement of project with physical 
need x12 

Process efficiency x2 
 

Level of consistency of practical and expected 
cycles x21 
Degree of agreement of the use of fund with 
budget x22 
Sewage treatment plant project completion 
ratio x23 
Sewage interception project completion ratio 
x24 

Output effect x3 
 

Ratio of new sewage treatment capacity x31 
New sewage treatment rate x32 
New sewage household connection rate x33 
BOD reduction x34 
COD reduction x35 
Beneficiaries' satisfaction x36 

Sustainability x4 
 

Soundness of operating equipment x41 
Degree of the adequacy of funds x42 

 
The first layer is objective layer, namely the urban water environment improvement project performance 
evaluation. 
The second layer is criteria layer, which defines the perspective and content of urban water environment 
improvement project performance evaluation. Based on the distinctive features of urban water environment 
improvement project and its performance evaluation, as well as the existing research findings of urban water 
environment improvement project performance evaluation, this paper ascertains four evaluation criteria, i.e. 
the level of consistency, the process efficiency, the output effect, and the sustainability. The level of 
consistency refers to the degree of conformity of urban water environment improvement project with national, 
regional and industrial policies and physical local needs; process efficiency means the economic efficiency of 
the conversion from input into output; output effect indicates the immediate effect and social impact of urban 
water environment improvement project; sustainability refers to the possibility of project outputs to operate 
sustainably and generate benefits upon the completion of project. 
The third layer is indicator layer; in response to the four criteria of criteria layer, this paper sets up the urban 
water environment improvement project performance evaluation indicator layer composed of 14 indicators 
using literature review method and frequency statistics method by taking into account the distinctive features 
of urban water environment improvement project and its performance evaluation. 

3. Dempster–Shafer theory and triangular fuzzy number 

Some scholars have link grey system theory up with D-S evidence theory; for example, Wang Yuhong and 
Dang Yaoguo carried out studies on comprehensive evaluation method for project through the combination of 

260



grey fixed weight grey clustering evaluation model and D-S evidence theory. An evaluation model is built in 
this paper based on grey system theory and D-S evidence theory by taking into account the complexity of 
urban water environment improvement project and the considerable difficulties in data collection for 
performance evaluation. The polar triangle whitening weight function-based grey evaluation method and D-S 
evidence theory are combined for rational, comprehensive and systematic evaluation of urban water 
environment improvement project by borrowing the domestic and foreign experience in urban water 
environment improvement project performance evaluation and making use of the more objective selection of 
extreme point by polar triangle whitening weight function based on the objective, function and characteristics 
of urban water environment improvement project performance evaluation on the basis of the predecessors' 
research findings regarding the method for combining grey theory and D-S evidence theory. 
D-S evidence theory-based development of urban water environment improvement project performance 
evaluation model is realized in the following four steps: (1) The collection and processing of basic data through 
desk research, face-to-face interview, expert consulting, panel discussion, and field research; (2) The 
determination of indicator weight by triangular fuzzy number method; (3) Identify evaluation grey class, 
compute grey integrated clustering matrix, and determine each criterion level; (4) Identify the grey class of 
project performance evaluation using D-S evidence theory, and determine the integrated performance level of 
project. 
Dempster–Shafer theory is a generalization of the Bayesian approach. The Dempster–Shafer theory was first 
developed by Dempsterin the 1960s. His work was later extended and refined by Shafer in the 1970s. This 
theory can deal with incomplete data by managing ignorance (Shafer, 1976). It is based on Dempster’s works 
on the lower and upper limits of probabilities. 
Definition 1.  Let m (A) denote the basic probability assignment (BPA) to the subset A, which measures the 
extent to which the evidence supports A. The BPA is a function. 

Definition 2. The function : 2 [0,1]Bel

  is the belief function should satisfy the following: 

1) =Bel （ ）0 , 
2) =Bel （ ）1, 

3)
1 2
, ,

N
A A A  , ， 1

11 1

( ) ( ) ( ) ( 1) ( )
N NN

N

i i i j i

i i ji i

Bel A Bel A Bel A A Bel A


  

       . 

Definition 3. Assume that a= (al, am, au) is a triangular fuzzy number, the membership function is a(x): R [0, 
1], so we can get, 

( )

0

0

l

l
l m

m l

a x
m

m u

m u

u

x a

x a
a x a

a a

x a
a x a

a a

x a




















 


  





  



 

                                                                                                                   (1) 

Where x∈R, al, au stands for the lower bound and the upper bound of the triangular fuzzy number. 
Definition 4. Assume that a= (al, am, au) and b= (bl, bm, bu) are two triangular fuzzy numbers, we can obtain 
the possibility degree of a≥b through: 

( ( 0)) ( ( 0))
( ) (1 )

m l m l m l u m u m u m

m l m l u m u m

min a a b b max a b max a a b b max a b

a a b b a a b b
p a b  

           

     
   

            
(2) 

The value of λ depends on the decision maker's attitude towards risk. When λ>0.5, the decision-maker is 
willing to take risks. When λ=0.5, decision-maker is risk neutral. When λ<0.5, the decision-maker is averse to 
risk. 

4. The model  

The evaluation model for the performance of urban water environment improvement project is realized in the 
following three steps. Firstly, determine the indicator weight by triangular fuzzy number. Secondly, identify 

261



evaluation grey class to determine each criterion level based on gray system theory. At last, identify the grey 
class of project performance evaluation using D-S evidence theory and determine the integrated performance 
level of project. 
4.1 Determine the indicator weight.  

The evaluators build a judgment matrix that determines the importance of urban water environment 
improvement project performance indicators through triangular fuzzy number. Based on (1)and (2) , we can 
get the weights of evaluation indicators. 
4.2 Determine the criterion level through the grey clustering evaluation  
In the principle of "maximum clustering factor", grey integrated clustering matrix can help to identify the grey 
class of each criterion at criteria layer in urban water environment improvement project index system and 
obtain the performance evaluation result for each criterion at criteria layer. Based on gray system theory, the 
calculation for each grey integrated clustering matrix is realized in the following three steps: 
(1) Determine the evaluation grey class 
According to the requirements on urban water environment improvement project evaluation, we need to 
cluster the value range of each indicator j into s grey classes. Suppose that xij is the observed value of object j 
with respect to indicator s , and that the value range is [a1 ij ,as+1 ij ], it could be defined as follows: 

1 1 2 2 2 3 1
, , ,

s s s

ij ij ij ij ij ij ij ij ij
a x a a x a a x a


     

                                                                                                    
 (3) 

Where ak ij ,i=1,2,…,n, j=1,2,…,m, k=1,2,…,s+1. The value of ak ij  is determined based on the practical situation 
of the indicators for urban water environment improvement project. 
(2) Calculate the degree of grey class membership 
According to gray system theory, we suppose that the whitening weight function value of the k  grey class is 
1, connect (k ij ,1), the starting point (ak-1 ij,0) of the k-1 grey class and the ending point (ak+2-1 ij,0) of the k+1 grey 
class to achieve the triangle whitening weight function fk ij ().  
Where k ij =(ak ij + ak+1 ij )/2

 
, i=1,2,…,m, k=1,2,…,s. 

For indicator xij, we can get its the degree of grey class membership fk ij (xij) according to the  following equation: 

1 2

1

1

1

2

2

2

0,                  [ , ] ;       

,     [ , ];

,     ( , ].

k k

ij ij

k

ij ijk k k

ij ij ijk k

ij ij

k

ij ij k k

ij ijk k

ij ij

x a a

x a
f x a

a

a x
x a

a







 




















 





 
     (4) 

                                                                                                          

 

(3) Calculate the whitening weight synthetic clustering factor matrix of each indicator 

Based on equation  
1

m
k k

i j ij j

j

f x 


  , we can get the synthetic clustering factor 
k 

i  of object i in relation to 

grey class k. Where j, j=1,2,…,m is the indicator weight determined with triangular fuzzy number method. 
Based on the above steps, we can obtain the whitening weight synthetic clustering factor of each affecting 
factor for urban water environment improvement project performance evaluation. The clustering factor matrix 
can be composed as the following: 

1 2

1 1 1

1 2

2 2 2
=( )=

s

s

k

i

s s s

n n n

  

  


  

 
 
 
 
 
                                                                                                                             

 (5) 

The grey class of each indicator at criteria layer is identified in the principle of "maximum clustering factor". 

Since 
*

1
max{ }

k k

i i
k s

 
 

 , the object i  should be of grey class k*. If there are many objects belong to grey 

class k*, they could be sorted by synthetic clustering factor, and thereby determine the advantages and 
disadvantages of each object of grey class k*. 

262



4.3 Determine the integrated performance level of the urban environment project 

(1) Determine the assigned value of basic probability 
Assume that   is the identification framework, and that Ai is the single-point set in  ; make 

1

( )    
k

i

i k s
k

i

k

m A








                                                                                                                                             (6) 

Where i=1,2,…,n, k=1,2,…,s. Suppose that as a minimum, there should be an i0 that makes 
0

0
k

i
   for any 

k,k=1,2,…,s. 
Matrix M1 is obtained through computation based on the n s  basic credit assignment functions in the same 

identification framework  : 

1 1 2 1 1

1 2 2 2 2

1

1 2

( ) ( ) ( )

( ) ( ) ( )
=

( ) ( ) ( )

n

n

s s n s

m A m A m A

m A m A m A
M

m A m A m A

 
 
 
 
 
                                                                                                                 (7) 

(2) Make belief function by Dempster rule 
1) Make belief function for the first time 
Assuming that m1, m2,…,mn are  n basic credit assignment functions on the same identification framework 
 ,and the focal elements are ( 1, 2, , )

i
A i s . According to the D-S composition rule (Jia , et al., 2013): 

1 1

1 2 3 4

( )

( ) ( )( ) ,            
1

0 ,                                       

n

n

i i

A A A i

i i

m A

m A m m m m A A
K

A

   





      


  

 

                                                         (8) 

Where, 
1 1

( )
n

n

i i

A A i

K m A
   

    reflects the degree of conflict between evidences. 
i j

A B    means that the 

two evidences assign the credibility respectively to two antagonistic propositions. The bigger the K value, the 
more intensive is the conflict. 
Make belief function according tothe Dempster rule, we can obtain 1 1 1

1 2
( ( ), ( ), , ( ))

s
m A m A m A  based on 

Equation (8). 
2) Make belief function for the second time 

If 
0 0 0 0
( ) 0,  , {1, 2, , }

j i
m A i j n  , 

0 0

1
( )= min{ ( )}

10
j i j i

m A m A , the value could be obtained by 

splitting from basic belief assignment value 
0 0

max{ ( )}
j i

m A . Where 
1

min{ ( )}
10

j i
m A  is called the 

permissible minimum set function value(Shafer,1976) . 
The following equation is obtained through the appropriate adjustment of values assigned to the set functions 
with a basic belief assignment value of 0 in M1: 

1 1 2 1 1

1 2 2 2 2

2

1 2

( ) ( ) ( )

( ) ( ) ( )
=

( ) ( ) ( )

n

n

s s n s

m A m A m A

m A m A m A
M

m A m A m A

 
 
 
 
 
     (9)  

Make belief function following the Dempster rule to obtain * * *
1 2

( ( ), ( ), , ( ))
s

m A m A m A . 

263



3) Determine the result of performance evaluation in the principle of maximum informatively. 
Determine the urban water environment improvement project performance evaluation result using the grey 
class that corresponds to the maximum focal element of belief function in the principle of "maximum 
informatively". Then check whether the result from the first belief function is consistent with that from the 
second belief function. If the result is consistent, the performance can be evaluated the good.  

5. Conclusions  

In this paper, the performance evaluation model for urban water environmental project based on D-S theory 
and gray clustering. In the model, the triangular fuzzy number is used to determine the indicator weight and 
the clustering factor matrix is transformed based on the obtained grey clustering factor of evaluation object to 
determine the level of each criterion. The combination of grey system theory and D-S evidence theory for 
handling the uncertainties in the performance evaluation model for urban water environmental project is 
practically feasible. 

Acknowledgments  

The work was supported by the Project of Philosophy and Social Science Research in Colleges and 
Universities in Jiangsu (2015SJB261). 

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