J. Software Engineering & Applications, 2008, 1: 44-52
Published Online December 2008 in SciRes (www.SciRP.org/journal/jsea)
An Evaluation Approach of Subjective Trust Based on
Cloud Model
Shouxin Wang
1
, Li Zhang
1
, Na Ma
2
, Shuai Wang
1
1
Software Engineering Institute Beihang University Beijing, China,
2
Logistics R&D Center North China Institute of Computing
Technology Beijing, China
Received November 17
th
, 2008; revised November 24
th
, 2008; accepted November 27
th
, 2008.
ABSTRACT
As online trade and interactions on the internet are on the rise, a key issue is how to use simple and effective evaluation
methods to accomplish trust decision-making for customers. It is well known that subjective trust holds uncertainty like
randomness and fuzziness. However, existing approaches which are commonly based on probability or fuzzy set theory
can not attach enough importance to uncertainty. To remedy this problem, a new quantifiable subjective trust
evaluation approach is proposed based on the cloud model. Subjective trust is modeled with cloud model in the
evaluation approach, and expected value and hyper-entropy of the subjective cloud is used to evaluate the reputation of
trust objects. Our experimental data shows that the method can effectively support subjective trust decisions and
provide a helpful exploitation for subjective trust evaluation.
Keywords: Subjective Trust, Cloud Model, Trust Decision-Making
1. Introduction
With the expansion of the Internet, applications based on
the internet, such as electronic commerce, online trading
and networked communities are going from a closed
mode to open and open mode. People and services or
services providers are interacting with each other
independently. Because the parties are autonomous and
potentially subject to different administrative and legal
domains, traditional security mechanisms based on
registry, authorization and authentication have not been
able to satisfy numerous web applications [1,2]. A party
might be authenticated and authorized, but this does not
ensure that it exercises its authorizations in a way that is
expected [3]. Therefore it is important that customers be
able to identify trustworthy services or service providers
with whom to interact and untrustworthy ones with
whom to avoid interaction. Just like Sitkin points that it is
widely agreed that electronic commerce can only become
a broad success if the general public trusts the virtual
environment, and this means that the subject of trust in
e-commerce is an important area for research [4]. Trust
between the participants involved has equal importance
for the nonprofit network community. It is important that
we research subjective trust evaluation based on trust
relation in order to ensure the customers’ satisfaction in
the public-oriented distributed network environment.
At present, there are two trust relations in the area [5,6],
namely objective trust and subjective trust. Hypothesis-
based reasoning argumentation is a basic method in
object trust research, such as BAN Logic [7] in security
protocols. Subjective trust‘s principal component is an
estimate of specific character or specific behavior level of
trust objects, namely people. Trust from the principal part
A to the object B means that A believes that B will
definitely act in a predined or expected way under a
specific circumstance [6]. This paper researches the trust
decision-making of subjective trust relationships, and
provides a quantitative evaluation method for subjective
trust.
Many researchers have done studies on modeling and
subjective trust reasoning. Papers [8,13] provide some
trust evaluation and reasoning methods for probability
models. Those methods don’t consider fuzziness of trust
itself, and their reasoning is based on pure probability
models. As a result, they tend over formalize subjective
trust quantification. Literatures [5,6] consider fuzziness of
subjective trust, constructing subjective trust management
models based on fuzzy set theory. Fuzzy set membership
is a precise set description of the fuzziness but does not
take the randomness into account. So, these methods lack
flexibility [15]. Aiming at subjective uncertainty like
randomness and fuzziness of subjective trust relationship,
Beihang University advanced an approach to express
trust based on a cloud model, which describes the
fuzziness and uncertainty of trust [16].
Based on [16], we consider the impact of an object’s
reputation change with time to trust decision-making and
Thanks to the support by National Basic Research Program of China
(973 project) (N
o. 2007CB310803)

An Evaluation Approach of Subjective Trust Based on Cloud Model 45
exploited a subjective trust quantitative evaluation based
on the subjective trust cloud, which preferably solves
internet trust decision-making by means of analyzing
historical reputation.
The remainder of this paper is organized as follows:
Section 2 introduces the issue of internet trust decision-
making. Section 3 describes the basic knowledge of cloud
model involved in this paper. Section 4 specifies subjective
trust evaluation based on cloud model and formalizes
quantitatively the trust score. Section 5 shows a
simulation experiment of the approach exploited in the
paper and validates its validity and rationality. Finally we
summarize the paper and discuss further research
directions.
2. Trust Decision-making
The online trading and network communities need a set
of entities providing services that they can trust. It is
significant how users make a trust decision as presented
in this paper. Here we call trust decision users trust
subjects or subjects, entities evaluated trust objects or
objects. Some large web application system, such as
Amazon.com, eBay, AllExperts provide evaluation
mechanisms for the reputation of subjects and objects.
For objects, reputation is the evaluation of their capability,
estimating intention, and capability of meeting subjects’
services demands, also called objects’ service satiability.
In the context of this paper, we assume there is no
difference in describing the trust relationship between
objects trust or reputation and service satifaction
capability.
A commonly used trust decision solution is based on
ratings by users, including collaborative filtering [15,16],
associative retrieval [19,20],association rules [21], and
Horting graphs [22]. Of these methods, collaborative
filtering is the most successful. It supposes that if users
grade some items similarly, they will also grade the
others similarly. The basic idea of the algorithm is that
the score of un-graded items given by one user are similar
to ones given by the nearest neighbors of that user [17].
Recommendation system of web application provides a
valuable reference for subjects’ trust decision. However,
the general public prefers estimation based on an object’s
historical reputation. Even though supported by a
recommendation system, subjects are still challenged by
making trust decision(s) among many recommended
objects. Because the essence of subjective trust is based
on subjective belief [7,8], it is random and uncertain. In
addition, reputation of trust objects changes with time,
which should also be quantitatively taken into account.
Therefore, it is essential that Web Application Systems
provide subjects with objects to select from in order to
improve subject satisfaction by analyzing subjective
evaluation data of the objects’ history reputation.
The paper suggests a subjective trust evaluation based
on cloud model, which uses history grade of reputation
from subjects to objects for selecting proper objects. Our
hypothesis of business environment in the paper is listed
below:
1) There are many subjects and objects in web application
systems.
2) Web Application Systems provide rating mechanism
for evaluating objects at least.
3) Web Application Systems provide mechanisms for
avoiding vicious and illusive evaluation.
4) For convenience, we use rating mechanism of five
levels to explain and validate trust decision approach
proposed.
3. Introduction to Cloud Model
In the reasoning process, randomness and fuzziness are
usually tightly related and hard to separate [23]. Based on
random and fuzzy mathematics, a cloud model can
uniformly describe randomness, fuzziness, and their
relationship. This chapter introduces basic knowledge of
the cloud model.
DEFINITION 1: Cloud and cloud drops [24]: Assume
that U is a quantitative numerical universe of discourse
and C is a qualitative concept in U. If x∈U is a random
implementation of concept C, and µ(x)∈[0,1], standing
for certainty degree for which x belongs to C, is a random
variable with stable tendency.
µ:U→[0,1] ∀x∈U x→µ(x)
Then distribution of x in universe of discourse U is
called cloud and each x is called a cloud drop.
According to definition 1, cloud has the important
qualities as follows.
1) Cloud is the distribution of random variable X in the
quantitative universal set of U. But X is not a simple
random variable in the term of probability, for any x∈U,
x has a certainty degree and the certainty is also a random
variable not a fixed number.
2) Cloud is composed of cloud drops, which are not
necessarily in any order. A cloud drop is the singular
implementation of the qualitative concept. The character
of concept is expressed through all drops, the more drops
there are, the better the overall feature of the concept is
represented.
3) The certainty degree of cloud drop can be understood
as the extent to which the drop can represent the concept
accurately.
4) Qualitative concept described in cloud model is reflected
by many quantitative concept values and binary pairs
from <x, µ> of their certainty degree.
The general concept of a cloud model can be expressed
by its three numerical characteristics: Expected value
(Ex), Entropy (En) and Hyper-Entropy (He). In the
discourse universe, Ex is the most representative for
qualitative concept. En is a randomness measure of the
qualitative concept, which indicates its dispersion on the
cloud drops, and the measurement of “this and that” of
the qualitative concept, which indicates how many
elements could be accepted to the qualitative linguistic
concept. He is a measure of the dispersion on the cloud
drops, which can also be considered as the entropy of En

46 An Evaluation Approach of Subjective Trust Based on Cloud Model
and is determined by the randomness and fuzziness of
En.
DEFINITION 2: One-dimension normal form cloud
[24]: Assume that U is a quantitative numerical universe
of discourse and C is a qualitative concept in U. If x∈U
is a random implement of concept C, x satisfies: x～
N(Ex,En’2), En’～N(En,He2), and certainty of x for C
satisfies the following rule:
2
2
)(2
)(
nE
Exx
e
′
−
−
= µ (1)
Then x can be called normal form cloud in the
discourse U. The paper [25] thoroughly analyzes and
discusses the universe of normal form cloud in applying
uncertainty representation. The cloud models involved in
this paper are one-dimension normal form cloud and
Figure 1 shows the graph of one-dimension normal form
cloud whose numerical characteristics are Ex= 3, En= 3,
and He is 0.01.
As defined earlier, the quantitative value of cloud
drops is determined by the standard normal form
distribution function. Their certainty degree function
adopts a bell-shaped membership function used broadly
in fuzzy set theory. As a result, normal form cloud model
is a brand new model based on probability theory and
fuzzy set theory, and concurrently holds randomness in
the former and fuzziness in the latter.
4. Subjective Trust Evaluation Based on
Cloud Model
It is important to understand and distinguish the
difference of alternative trust objects from which trust
decisions are made. Trust decisions in the internet
environment are a process where trust subjects can
distinguish the difference of reputation of alternative
objects using decision constraints. Subjects choose some
objects from an object set Objs={obj
1
,obj
2
,…,obj
n
}. It
can generate a smaller alternative trust object set Objs’=
{obj
1
,obj
2
,…,obj
m
} (m<n) and reduce the selection range.
Decision constraints are the focus of the decision process
and provide rules for distinguishing potential differences
of objects’ trust reputation. The formal description of
trust decision process is given below as expression (2).
Figure 1. Cloud graph of one-dimension normal form cloud
ObjsconstraObjsTransform int)( (2)
A trust decision method means, subjects describe
decision constraints qualitatively or quantitatively in the
process of selecting objects based on analysis of potential
differences in their trust reputation. In this paper, we use
subjective trust cloud based on the cloud model to
quantitatively describe decision constraints, and to
distinguish the average level of trust reputation between
multiple objects.
4.1 Subjective Trust Cloud
With a simple subjective grade mechanism and average
value to calculate trust reputation, i.e., Amazon.com and
OnSale and so on, evaluate a seller’s trust reputation
[26]
.
Table 1 displays five evaluation information of objects’
trust reputation from Amazon.com which provides same
services. Amazon provides the overall reputation of every
object. The other four objects have the same overall
evaluation value except A. Therefore, without other
supporting information, it is difficult for subjects to make
a trust decision reasonably and effectively. Statistical
methods can effectively reflect randomness of subjective
grade, but can’t express the significance of subjective
uncertainty, namely, fuzziness. As a result, it is rational
to express the qualitative concept of subjective trust in a
cloud model. In addition randomness and fuzziness are
correlated in cloud model expression, which provides
support for trust decisions more reasonably and
effectively.
In this paper, we give definitions which are correlated
with subjective trust cloud as follows:
DEFINITION 3: Subjective trust degree (STD) is an
ordered set of number in an universal set [0, n], STD=[0,
n]. STD is composed of sequential or discrete numbers
which represent a trust object’s reputation and n is any
positive integer. 0 and n represent the lower and upper
limit of the reputation.
DEFINITION 4: Subjective trust space (STS) is an
ordered set of qualitative concepts which represent the
qualitative degree of trust. There can be 0 or more than
one trust level standard for one STS.
DEFINITION 5: Subjective trust cloud (STC) is a
subjective trust concept represented by cloud model and
composed of many cloud drops. STD=[0, n] is the
universal set of STC, for any e ∈STS is a qualitative
trust concept of STS, and any x ∈STD is a implement of
e. The certainty degree of x for e, i.e., µ(x) ∈ [0, 1] is a
random value with stabilization tendency.
Table 1. Reputation of objects from amazon.com
object 1 2 3 4 5 Aggregation
A 17 77 89 154 589 4
B 55 29 46 90 732 4.5
C 14 20 62 137 788 4.5
D 16 26 49 121 734 4.5
E 58
60 161 380 234 4.5
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
u(x)
-12 -7 -2 3 8 13 18

An Evaluation Approach of Subjective Trust Based on Cloud Model 47
µ:STD→ [0, n] ∀ x ∈ STD x →µ(x)
Then the distribution of x on STD is defined as STC(x),
and every x is called subjective trust cloud drops.
The subjective trust cloud is extensible, and when the
discourse space of STD is [0, 1], it is equal to the trust
cloud in [16]. Quantitative reputation of subjective trust
cloud can be ordered value composed of any value of [0,
n]. For STD, ordered value is composed of a set of
sequential or discrete values reflecting reputation, which
makes subjective trust evaluation based on cloud more
pervasive. Firstly, without extra data processing, it is
applicable to discrete or sequential value reputation grade
mechanism. Secondly, it can effectively reflect
qualitative-quantitative transformation of cloud and
climbing-up of qualitative concepts. If reputation is
continuous values, it reflects qualitative-quantitative
transformation between subjective qualitative trust
concepts and quantitative discourse. If reputation is
discrete value space, it reflects climbing-up of fine
granularity of concept, namely, qualitative concepts and
values in discourse space form hierarchical construct of
concepts.
The other characteristic of subjective trust cloud means
that it doesn’t necessarily require qualitative concept in
trust space, namely, regulating trust grade. It evaluates
overall objects’ reputation by just comparing < Ex, He >
which is called subjective trust character vector. It is
necessary to endow its numerical characteristic with
rational and significant physical meanings in the context
when cloud model expresses qualitative knowledge. In
this paper, we take Ex as typical value of objects’
reputation, namely, average reputation level of objects. In
addition, we use He to reflect decentralization degrees
from objects’ reputation to the average, namely, He
reflects the stability of an objects’ reputation. If Ex is big,
then an object’s ability to satisfy a subject’s need is big
and vice versa. If He is small, then the stability of
reputation for an object is good and vice versa.
Subjective trust cloud design
The first step for a quantitative evaluation of an object’s
reputation is to design the STD, confirm the upper/lower
limit of reputation space, and select discreteness or
continuity of reputation. In this paper, we give a possible
STD design, with five-grade-mechanism of Amazon.com
serving as an example. When STD is a discrete space,
every discrete reputation virtually can be considered as
qualitative concept. STD is designed to be[1, 2, 3, 4, 5] in
this paper.
Generation of numerical character value of STC
Object reputation varies with time, and it associates
closely with its historical reputation and time [27].
Therefore, evaluation data of subjective reputation is only
effective for a given period of time. This means the
further away the evaluation time from the trust decision,
the lower the effectiveness of its object reputation. In
order to correctly evaluate that, we extend the cloud
generation algorithm backward without certainty degree
in [24], and design a weighted backward cloud generation
algorithm. Based on the distance from reputation
evaluation time to current trust decision time, this
algorithm assigns different weights to reputation data of
different times. The basic weight rule of this algorithm is,
the newer the reputation data is, the bigger its weight and
vice versa. We first explain the time model of reputation
and basic rules for weighting.
Suppose the time model of reputation M=<X, t
c
, t
b
, T>.
1) X={x
1
,x
2
,…,x
n
} is the full set of historical reputation
data of an object. For any x
i
, Time(x
i
) denotes the time of
reputation evaluated.
2) t
c
denotes the current time of trust decision and
serves as time origin. t
b
denotes certain time of forward
direction of time axis, and serves as time threshold for
judging effectiveness of reputation.
3) T={t
1
,t
2
,…,t
m-1
} is an ordered set composed of m-1
time values between t
c
and t
b
. For any t
i
, d
i
=|t
i
-t
c
| is called
time distance from t
i
to t
c
, and satisfies following
constraint.
1)
bcii
ttdmid −≤→−≤≤∀ )11(
2) idd
ji
≤∀ 1(, ＜
i
dmj →−≤ )1 ＜
j
d
Based on Time(x
i
), t
b
can separate X into two subsets,
X
1
’ and X
2
’, and they satisfy the conditions below.
1) X= X
1
’∪X
2
’,且 X
1
’∩X
2
’=Φ
2) ))(()1(1
bcci
i
x
tttxTimeniX −≤−→≤≤
′
∈∀
3) ))(()1(
2cii
txTimeniXx −→≤≤
′
∈∀ ＜ )
bc
tt −
As mentioned above, t
c
serves as time origin, and |t
c
-t
b
|
serves as time threshold for judging effectiveness of
reputation evaluation data. The set of X is separated
based on the difference of |Time(x
i
)-t
c
| and |t
c
-t
b
|. Time
distance from any element in X
1
’ to t
c
is less than or
equal to the threshold, and that of X
2
’ is more than the
threshold. Therefore, we consider evaluation time of
reputation data in X
2
’, to be far away from current
decision time, which can’t correctly reflect the object
reputation of current time. Evaluation data of object
reputation is all included in X
1
’.
The set T separates time interval between t
c
and t
b
into
m sub-areas called temporal windows and marked as W
t
.
Temporal windows make X
1
’ m subsets of reputation
evaluation data, Xt
1
, Xt
2
, …, Xt
m
. They satisfy
following conditions:
For any temporal window, =
ti
Win <
ii
low
tt
sup
,>,
i
low
t,
is the lower time limit of W
ti
, and
i
t
sup
is the upper time
limit of Win
ti
which satisfy
c
i
low
tt − ＜
c
i
tt −
sup
.
=
ti
Win
i
low
i
tt −
sup
is called window length of Win
ti
X
1
’=Xt
1
∪Xt
2
∪,…,∪Xt
m
, and
φ =∩→≤≤≤≤∀ )()1,1(,
XtXtXtXt jiji
mjmi
ttXtXt
ccji
zTimeyTimemjizy −<−→≤<≤∈∈∀ )()()1(,

48 An Evaluation Approach of Subjective Trust Based on Cloud Model
When we design the set of T, we should consider the
time span of |t
b
-b
c
|, and quantity of reputation data in the
span. T further separates X
1
’ into m subsets, and based on
whose subject temporal windows, there is strict time
sequence in Xt
1
, Xt
2
, …, Xt
m
. There is equivalent weight
of effectiveness for some reputation data whose time
value is in the same temporal window. For any subset Xt
i
(1<=i<=m) of X
1
’, we can assign a weight wt
i
, which
denotes the reputation influence extent from data in Xt
i
to
that of overall results of the objects. Weights should
satisfy the constraints of expressions (3) and (4). Based
on these expressions, we provide a simple weight
assignment method satisfying the expression (5), which is
based on that, as the time distance of t
i
from t
c
increases,
its effectiveness for a period of time fades, and we
express that fading trend in the mode of descent with the
same difference which is indicated by the variable inter.
)()1(,
wtwtXtxXtx
lkljKi
mlk <→≤<≤∈∈∀
(3)
1)(
1
=
∑
=
m
ii
wt
(4)
)11(int
1
−≤≤−=
+
mier
w
w
titi
(5)
After calculating the weights we can apply the
weighted backward generation cloud algorithm, to
calculate the subjective trust cloud values of Ex, En, He.
The weighted backward generation cloud algorithm is
described as follows.
Input: a set of N cloud drops, X
1
’={x
1
,x
2
,…,x
N
}, and a
set of cloud drops’ weight, W
t
={ w
t1
,w
t2
,…,w
tm
}. m
indicates the number of temporal windows.
Output: (Ex, En, and He) representative of qualitative
concept of N cloud drops.
Steps:
1) Calculate the weight w
i
of x
i
with the equation i.e.,
)1,1( mjNi
numWin
w
w
j
tj
i
≤≤≤≤= . Win
j
is the jth
temporal window and w
tj
is the weight of it. num (Win
j
)
is a function which computes the number of drops in
Win
j
.
2) On the basis of x
i
and its weight, calculate sample
mean, first-order absolute central moment, and sample
variance of x
i
, i.e.,
∑
=
=
N
iii
xwX
1
,
∑
=
−
N
iii
Xxw
1
, and
∑−
=
=
N
ii
X
x
wS
i
1
2
2
)(
3) XxE =
ˆ
4)
∑
=
−=
N
iii
xEnE
xw
1
|
ˆ
|
2
π
)
5)
| ˆ
|
2
2
eH
S
eH −=
)
4.2 Trust Decision-making
After we compute three numerical values of the subjective
trust cloud, we can make trust decisions based on the
foundation of its character vector. For the physics
meaning of < Ex, He >, we should pick objects whose Ex
is big and He is small. A formal description of the trust
decision, based on the subjective trust cloud, is expressed
by equation (6).
ObjsHeExObjsTransform >< ,)( (6)
But the character vectors may not accurately represent
the things the trust subjects care about because they only
pay attention to the result of selecting a trust objects
based on some reasonable and simple rules. Therefore,
similar to some existing methods
[2, 28, 29, 30]
, it is very
necessary to provide one certain approach, which can
combine the Ex with He to obtain certain simple result of
reputation, for trust subjects. Relying on the simple result,
the most suitable object would be selected for trust
subjects. Here we provide a reputation scoring method to
address the issue.
As stated as above, Ex expresses the average reputation
level, and He describes the decentralization degrees from
reputation to the average, namely, stability of uncertainty
of reputation. Hereby, for calculating quantitatively, we
consider the Ex as the master value and He slave value.
Reputation score is a function of Ex and He and increases
with Ex and decreases with He. The formalized function
of reputation score (hereafter RS) is described as
He
eExRS
−
×= (7).
Expression 7 can represent the basic function
relationship among RS, Ex and He. But in some special
situations, expression 7 may have inaccurate results. To
analyze these special situations, some typical cases of Ex
and He are listed in Table 2.
According to expression 7, the RS is clearly better in
case1 than case3. However, if there exists object A with
high Ex and He, and object B with low Ex and He. Then
the Ex of A may be higher than B’s, but object A and B
may have the same RS. In this situation, RS can not tell
the fine difference of object A and B. To overcome the
issue, expression 8 is introduced to amend the function of
expression 7.
)1( +=+×=
−
bcEx
c
b
eExRS
He
(8)
c
b
is an impact factor to adjust the computing result
of RS. Expression 8 with the impact factor can
distinguish the RSs among objects in case2 and case4.
We can prove the validity of expression 8 as follows:
Proof: Suppose RS
a
and RS
b
are the reputation scores
of objects A and B.
ExExRs
aaa
c
b
He
e
a
+×=
−
,
ExExRs
bbb
c
b
He
e
b
+×=
−, and Ex
a
>Ex
b
.
Table 2. Table 1 four cases of EX and HE
Ex He
Case1 High Low
Case2 High High
Case3 Low High
Case4 Low Low

An Evaluation Approach of Subjective Trust Based on Cloud Model 49
1) If RS
a
=RS
b
then
ExExExEx bbaa
c
b
He
e
c
b
He
e
ba
+×=+×
−−
and
c
b
He
e
c
b
He
e
b
a
Ex
Ex
a
b
+
+
=
−
−
(9)
2) Because 1<e<1 and He>0, so 0<
e
He a −
<1 and
0<
e
He
b
−
<1
3) As the result, 1＜
a
b
Ex
Ex
＜
b
b
bc1
+
=
4) From the initial assumptions and the sequence of
deduction steps, we can conclude that if RS
a
=RS
b
then
Ex
a
approximately equals to Ex
b
.
Similarly, let α =
a
b
Ex
Ex
, then
c
b
He
e
c
b
He
e
ab
+=+
−−
αα
(10). Applying natural logarithm
and equation transformation to equation 8, we can get a
new equation )
1
(
2
α
LnHeHe
ba
=− (11). Since α is close
to 1, He
a
is approximately equivalent to He
b
.
Computing the RS of objects by the equation 8, can
limit the error into acceptable range.
c
b
is used to adjust
the precision of reputation score. More small the inverse
of
c
b
, more fine difference among reputation score of
objects can be distinguished.
5. Experiment and Discussion
5.1 Maintaining the Integrity of the Specifications
Because most Web Sites can’t provide time of reputation
and the intention of the experiment is evaluating the
effectiveness of the approach in the paper, we simulated
the time of reputation based on real reputation data from
Amazon.com. We collected 14 objects which provide a
similar service, with ratings of each service greater than
700. Table 3 shows three typical original reputation data
of objects.
The simulation steps are described as follows.
1) Assume the basic time unit is a week and all
reputation data has been given in past ten weeks, this
means t
b
=10 weeks.
2) Designate several different ways to divide the
temporal windows
3) Calculate time weight for each temporal window
based on the equation (4) and (5)
Table 3. The original reputation data of three objects
objects 1 2 3 4 5
A 264 519 496 649 967
B 571 533 504 680 363
C 424 604 903 579 756
Firstly, we divide the ten weeks into three temporal
windows. The number of weeks of each window is 1, 4,
and 5 respectively. Applying the weighted backward
generation cloud algorithm, we can obtain the numerical
characteristics of the subjective trust cloud for objects A,
B, and C depicted in Table 4.
From table 4, the Ex of B is lower than that of A and C.
But the Ex of A is similar to C, and their difference is
only 0.07. However, the He of A is smaller than that of C.
Therefore, we can say that the basic level of reputation of
B is lower than others, and the stability of reputation of A
is higher than B. The result shows not only that the cloud
model can express the uncertainty of subjective trust, but
the numerical characteristics can be used as the decision
constraints for subjective trust decision-making, and
indicate fine differences among objects.
Next we validate the effect of temporal window on the
result of reputation evaluation based on our approach.
Actually, customers or owners of web site have many
optional ways to define different temporal windows.
They can choose two, three, or more temporal windows,
and decide the number of basic time units of each one.
Table 5 gives some possible methods to divide temporal
windows.
Temporal windows depicts the number of temporal
windows whereas the column of Basic time unit indcates
the partition of each temporal window. For example, (1, 4,
5) means the first window should contain one week, and
the second and third should contain four and five weeks.
The curves of Ex and He of A, C under different
partitions are shown in Figure 2 below.
The red curves represent object A, and blue ones
represent object C. According to the partitions of Table 5,
the Ex of A is always higher than that of C, and the He of
Table 4. Reputation ranking and the numbers of STC
objects Ex En He
A 3.60 1.45 0.62
B 3.13 1.51 0.62
C 3.53 1.46 0.88
Table 5. The instances of temporal windows
Serial
number
Temporal
windows The number of basic time unit
1 2 (10, 0)
2 2 (1, 9)
3 2 (2, 8)
4 2 (3, 7)
5 2 (4, 6)
6 2 (5, 5)
7 2 (6, 4)
8 2 (7, 3)
9 2 (8, 2)
10 2 (9, 1)
11 10 (1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
12 3 (1, 4, 5)
13 3 (1, 2, 7)

50 An Evaluation Approach of Subjective Trust Based on Cloud Model
Figure 2. Ex and He curves of A and C
Figure 3. Curves of difference of Ex and He for A and C
A is smaller than C. Therefore, we can conclude that
different partition methods don’t change the result of
reputation evaluation based on the subjective trust cloud.
But different partitions can affect the precision of
reputation evaluation. To exhibit this, the curves showing
the difference of Ex and He of A, and C are depicted in
Figure 3.
In Figure 3, the difference of Ex reaches the
maximal value at the tenth partition, and the minimum at
the second partition. However, the maximum and
minimum of He are achieved at the first and third
partition. So the trend of the two curves is not absolute
consistent. We believe the distribution of reputation data
may be what causes the difference under different
partitions. Additionally, from Figure 2 and 3, the
difference of Ex of A and C is more than zero, while their
He difference is less than zero. Although different
partitions may result in dissimilar evaluation, we can
obtain the same conclusion which is consistent with that
from Figure 2. That is the result of reputation evaluation
does not change with the partition method.
5.2 Reputation Scoring Function
Based on the values of Ex and He in table 4, we apply the
reputation scoring function mentioned in section 4.2 to
compute the quantitative reputation scores of trust objects.
Then the RSs can be calculated and the graphs of the RSs
under different
c
b
is shown in Figure 4.
Figure 4. Reputation scores of trust objects A, B and C
There are ten groups of columniations in Figure 4. The
value of c of each group from left to right is 3, 5, 8, 7, 21,
31, 41, 51, 101, 1001. The RS changes clearly from 3 to
21, but these ones between 31 and 1001 are very similar.
So it is not necessary to give c a high value. On the other
hand,
c
b
can control the precision to tell difference of
RSs. Actually RS of reputation may be in the range from
c
Ex
to Ex. At the same time, we could find that different
c would not affect the order of reputation scores for
objects A, B, and C. From the view of reputation scores,
object A may be the final one selected by trust subjects.
The choice result based on reputation score is consistent
4
3.5
3
2.5
2
1.5
1
0.5
0
Reputation score
A
B
C
1
2 3 4
5 6
7 8 9
10
Objects

An Evaluation Approach of Subjective Trust Based on Cloud Model 51
with that one based on Figure 2 and 3, but more simple
and suitable to trust subjects.
6. Conclusions
Cloud model overcomes the limit of fuzzy set theory
which represent fuzzy concept with an accurate and sole
membership degree. We proposed an evaluation approach
of subjective trust based on subjective trust cloud. The
approach combines Ex with He of subjective trust cloud
to evaluate the randomness and fuzziness of subjective
reputation. We validated our approach with a simulation
experiment and showed the effectiveness of the approach.
Our approach needs time of reputation. However, most
Web Sites don’t provide this data. But with development
of business and cooperation on the Internet, especially
with more attention put on satisfaction of general public,
we believe that the evaluation of reputation change will
be a novel and effective approach to assist end-users in
trust decision-making. Furthermore there is still a need
for significant research in this field, such as how to
extend the approach to apply in the other related field,
how to design and validate other weighting methods of
reputation, how to combine subjective with objective
trust data to make trust decisions, find the reasonable law
and rules to design temporal windows and so on.
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