A TOPSIS Method Based on Triangle Fuzzy Number for Trust Evaluation in Ecommerce System
Dan Li
Business School, East China University of Political Science and Law, Shanghai, China
( huazhengld@126.com)
Abstract - As a new technological environment and
cooperation platform, e-commerce system provides the new
opportunities for sharing and transferring information,
knowledge and provides the new services for enterprises to
participate in business interactions in the era of e-commerce.
But there also exist kinds of risk in operation process. One
kind of risk is lack of trust, and trust is the major barrier to
the successful operation of e-commerce system. So it is
necessary for enterprises to find out the influencing factors
and the methods how to evaluate trust of e-commerce
systems. It can help enterprises to enable better design and
management of e-commerce system. Basing on TOPSIS and
triangle fuzzy number, this research aims to propose an
extended approach for assessing trust in e-commerce system.
It is a multiple criteria evaluation problem under fuzzy
environment. And then an example is given.
Keywords - trust evaluation, e-commerce system,
TOPSIS, linguistic variables, triangular fuzzy number
I. INTRODUCTION
The notion of trust has been examined under various
contexts such as bargaining, industrial buyer-seller
relationship, cooperation relationship in alliances,
economics and market research and even computer
science [1-2].
With the continuous exploration and the support of
emerging advanced information technologies, electronic
commerce develops rapidly and causes a shift in business
simulation is conducted. Electronic commerce, commonly
known as e-commerce, refers to the transaction of
products or services over the internet and other computer
networks. The new technological environment and
cooperation environment also provides the new
opportunities for sharing and transferring information and
knowledge, and provides the new services to participate in
business interactions. However, there also exist different
levels of risk in operation process. With the existence of
risk comes the need for trust [3]. In the era of e-commerce,
trust has been identified as a key for successful
transaction and knowledge transferring. The lack of trust
is cited as a major barrier to the successful operation of
electronic commerce system. So it is necessary for
enterprises to find out the influencing factors and the
methods how to evaluate trust in order to improve the
____________________
Supported by the Science Research Program of East China
University of Political Science and Law (11H2K013)
Capability of building trust of e-commerce system.
The evaluation problems are the process of finding the
best candidate or making the best choice from all of the
feasible alternatives. Trust evaluation in e-commerce
system is a multiple criteria evaluation problem under
fuzzy environment. It is suitable for organizations to
adopt multiple criteria evaluation method to evaluate trust
in e-commerce system.
Technique for order performance by similarity to ideal
solution (TOPSIS) is one of the classical multiple criteria
evaluation method. The concept of the method can be
described that the best candidate should have the shortest
distance from the positive ideal solution and the farthest
from the negative ideal solution. The performance ratings
and the weights of the criteria are given as crisp values [4].
This paper tries to propose an extended method basing on
TOPSIS and triangle fuzzy number to evaluate trust of ecommerce system. The rating of each unit for
participating in evaluation and the weight of each
criterion are described by linguistic variables in triangular
fuzzy numbers. Then, it is needed to calculate the distance
between two triangular fuzzy numbers, and to determine
the ranking order of all candidates according to the
closeness coefficient. This paper aims to provide a
method for deeply analyzing and measuring the capability
of building trust in e-commerce system. The proposed
method can also be applied to solve the problems such as
project selection, partners’ selection and other
management decision problems.
II. THE PROPOSED METHOD
For evaluating trust of e-commerce system, the
extended method basing on TOPSIS and triangle fuzzy
number in the fuzzy environment is proposed in this
paper. It can solve the group decision-making or
evaluation problem under fuzzy environment. In this
paper, we assume that A  {A1 , A2 ,, An } is a set of all ecommerce systems participating in trust evaluation. And
then form a committee of assessment experts. Assumed
R  {R1 , R2 ,, Rm } is a set of given evaluation index, it
includes policy orientation, credit of system, the quality of
service, the quality of information, customer participation,
customer satisfaction, the quality of system and so on [5-8].
And then choose the appropriate linguistic variables for
the importance weight of each criteria and the linguistic
rating for all alternatives. The weight of criterion cannot
completely certain, but it is clear that the importance
weights of various criteria are considered as linguistic
variables, it can be expressed as i   i ,  i ,  i  ,
0   i   i   i  1 . In Table I the linguistic variables
can be expressed in triangular fuzzy numbers.
evaluation matrix denoted by F can be obtained. I 1
and I 2 represent the set of benefit criteria and cost
criteria, respectively, that is
LINGUISTIC VARIABLES FOR THE IMPORTANCE WEIGHT
OF EACH CRITERION AND THE RATINGS
Linguistic
variables
of weight
very low (VL)
Low (L)
Medium low
(ML)
Middling (M)
medium high
(MH)
High (H)
very high (VH)
x ji  (
corresponding
triangle
fuzzy numbers
(0,0,0.1)
(0,0.1,0.3)
Linguistic variables
of index
Very bad (VB)
Bad (B)
Worse than middling
(WM)
Middling (M)
  imax
(0.1,0.3,0.5)
(0.3,0.5,0.7)
better than middling (BM)
(0.5,0.7,0.9)
Good (G)
very good (VG)
(0.7,0.9,1.0)
(0.9,1.0,1.0)
Assume that there are K persons in the evaluation
group, the importance of the criteria and the rating of all
alternatives can be calculated as:
1 ~ 1 ~ 2
~
x ji 
x ji () x ji ()  ~
x ji K
K
(1)


~
x ji K and ~i K are the rating and the importance weight
A j ( j  1,2,n)
Ri for alternative

1
2
m

2) Construct the normalized fuzzy evaluation matrix
It is necessary for using the linear scale
transformation to transform the various criteria scales
into a comparable scale without using the complicated
normalization formula. Then the normalized fuzzy
,
 ji
 
,
 ji

), i  I1
 imax
 imin
), i  I 2 
 ji
 max j  ji ,  imin  min
j
 ji 
~x12
~x22

~x
~x1m 
~x2 m 

n2
 

~xnm 
y12

4) Determine the positive ideal alternative X  and
the negative ideal alternative X 

)  
y  j  ( min  ji , min  ji , min  ji )   i  ,  i  , i 
1i  m
1i  m
1i  m
y  j  ( max  ji , max  ji , max  ji
1i  m
in
triangular fuzzy numbers. Aggregate the weight of criteria
to get the aggregated fuzzy weight i of criterion Ri , and
pool the evaluators’ opinions to get the aggregated fuzzy
rating of all alternatives according to the result of
evaluating the criterion. The fuzzy multi-criteria
evaluation problem which can be expressed in matrix
format as
~
x11 ~
x12
x1m 
~
~

~
~
x
x
x
~
22
2m 
(3)
F   21
    
~

~
~
x nm 
 x n1 x n 2
~
W  ~ , ~ ,  ~
(4)
 imax
 imin
y1m 
y 22
y 2 m 
  

yn2
y nm 
y ji  i x ji  ( ji ,  ji , ji )
(2)
of criterion
 ji
,
 ji
,
x11
~
~
x
B    F   21
 
 ~
xn1
 y11
y
  21


 y n1

of the Kth evaluator.
The algorithm of the multi-person multi-criteria
evaluation with extended TOPSIS approach is given in
the following [4,9-11].
1) Construct the fuzzy evaluation matrix in
triangular fuzzy numbers
~
x ji  (  ji ,  ji ,  ji ) (i=1,2,…,m) is the targeted value
 imax
 imin
The normalization method is to guarantee that the
ranges of normalized triangular fuzzy numbers belong to
[0,1] .
3) Construct the weighted normalized fuzzy evaluation
matrix
Considering the different importance of each criterion,
the weighted normalized fuzzy evaluation matrix can be
constructed as

1
~i  ~i 1 ()~i 2 () ~i K
K
 ji
 x ji  (
TABLE I
The
positive


1i m

1i  m
ideal

i
,  i  , i 
alternative


is

X  ( y1 , y2  yn ) , the negative ideal alternative
is X   ( y1 , y2   yn  ) .
5) Calculate the distance of each alternative
Now calculate the distance of each alternative
from X j and X  , it can be described as


n
D j  D X j , X  
i

 
 

     2      2     2
ji
i
ji
i
 ji i

3

Calculate the distance of each alternative from X j
and X  , it can be described as
D j



n
 D X j, X 
i

 
 

     2      2     2
ji
i
ji
i 
 ji i

3

6) Calculate the closeness coefficient of each
alternative
A closeness coefficient can determine the ranking
order of all alternatives according to the Dj+ and Dj- of
each alternative. We can calculate the closeness
coefficient of each alternative, it can be described as
D j

Cj  
D j  D j
R3
R4
According to the closeness coefficient, the ranking
order of all alternatives can be determined.
R5
III. ILLUSTRATIVE EXAMPLE
The example is given for explaining the process and
method that how to measure the degree of trust in ecommerce system and the evaluation method is described.
Suppose there are three e-commerce systems A1 , A2
and A3 need to be evaluated the capability of building
trust. A committee of three evaluators, M 1 , M 2 and
M 3 has been formed to conduct the interview. During the
process of trust evaluation, five benefit criteria are chosen
as evaluation criteria: credit of system ( R1 ), the quality of
service ( R 2 ), the quality of information and knowledge R1
( R3 ), customer satisfaction ( R 4 ) and the quality of R2
R3
system ( R5 ).
R4
The linguistic weighting variables (shown in Table I)
are used by evaluators to assess the importance of the R5
criteria following as Table II.
TABLE II
THE IMPORTANCE WEIGHT OF THE CRITERIA
M1
M2
M3
A2
M
BM
G
A3
G
VG
BM
A1
M
WM
G
A2
BM
VG
G
A3
G
M
BM
A1
WM
BM
G
A2
M
G
VG
A3
BM
G
M
A1
G
VG
WM
A2
VG
M
BM
A3
WM
VG
G
The linguistic evaluation can be described by
triangular fuzzy numbers to construct the fuzzy evaluation
matrix. The fuzzy weight of each criterion can be
determined as Table IV.
TABLE IV
THE FUZZY EVALUATION MATRIX AND FUZZY WEIGHTS OF THREE ECOMMERCE SYSTEMS
A1
weight
A3
A2
(0.7,0.87,0.97)
(0.77,0.93,1)
(0.5,0.7,0.87)
(0.77,0.9,1)
(0.54,0.93,1)
(0.5,0.7,0.87)
(0.5,0.7,0.87)
(0.7,0.87,0.97)
(0.34,0.8,0.93)
(0.37,0.57,0.73)
(0.7,0.87,0.97)
(0.5,0.7,0.87)
(0.63,0.8,0.9)
(0.43,0.63,0.8)
(0.63,0.8,0.9)
(0.57,0.73,0.83)
(0.63,0.8,0.9)
(0.57,0.73,0.8
7)
(0.5,0.7,0.87)
(0.57,0.73,0.8
3)
Then the weighted normalized fuzzy evaluation
matrix can be constructed as Table V.
TABLE V
THE FUZZY WEIGHTED NORMALIZED EVALUATION MATRIX
R1
MH
H
VH
R2
H
VH
H
R3
MH
MH
VH
R1
(0.54,0.81,0.97)
(0.35,0.61,0.84)
(0.54,0.78,0.97)
R4
VH
H
M
R2
(0.28,0.67,0.9)
(0.28,0.67,0.9)
(0.39,0.84,1)
R5
M
H
VH
R3
(0.13,0.47,0.7)
(0.24,0.72,0.93)
(0.18,0.58,0.84)
R4
(0.3,0.56,0.8)
(0.44,0.71,0.9)
(0.35,0.62,0.87)
R5
(0.42,0.67,0.86)
(0.42,0.67,0.9)
(0.42,0.67,0.86)
The linguistic rating variables can be used by
evaluators to evaluate the rating of alternatives with
respect to each criterion. It can be described in Table III.
TABLE III
THE RATINGS OF THREE E-COMMERCE SYSTEMS BY EVALUATORS
UNDER ALL CRITERIA
Evaluators
Criteria
R1
R2
Candidates
M1
M2
M3
A1
G
VG
G
A2
BM
G
M
A3
BM
VG
VG
A1
G
M
BM
A1
A3
A2
The positive ideal alternative can be determined as
X   0.54,0.81,0.970.39,0.84,10.24,0.72,0.93
0.44,0.71,0.90.42,0.67,0.9
The negative ideal alternative can be determined as
X   0.35,0.61,0.840.28,0.67,0.90.13,0.47,0.7 
0.3,0.56,0.80.42,0.67,0.86
The distance of each e-commerce systems from the
positive ideal alternative and the negative ideal alternative
can be calculated, respectively, as
D1  D A1 , X   0.4914
D1
 
 DA , X   0.1761
1

 
D  DA , X   0.3513
D3  DA3 , X    0.2180
D  D A , X   0.4629
D2  D A2 , X   0.3065

2
2

3
3


The closeness coefficient of each e-commerce systems
can be calculated as
C1=0.2638, C2=0.5341, C3=0.6798
According to the closeness coefficient, the ranking
order of the e-commerce systems is A3 , A2 and A1 .
Obviously, A3 has the strongest capability of building
trust.
IV. CONCLUSIONS
The study is mainly focused on the trust evaluation of
e-commerce system. Trust evaluation in e-commerce
system is a multiple criteria evaluation problem under
fuzzy environment. In this paper, an extended TOPSIS
evaluation method is used for trust evaluation in ecommerce system. An illustrative example is provided to
demonstrate and explain how it operates. Results of this
study can help enterprises to evaluate trust of e-commerce
system and improve the rate of successful transaction and
the system service performance.
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