Content uploaded by Weimin Li
Author content
All content in this area was uploaded by Weimin Li on Aug 16, 2017
Content may be subject to copyright.
J Supercomput (2014) 69:1154–1165
DOI 10.1007/s11227-014-1084-2
Recommendation of location-based services based
on composite measures of trust degree
Weimin Li ·Mengke Yao ·Xiaokang Zhou ·
Shoji Nishimura ·Qun Jin
Published online: 4 February 2014
© Springer Science+Business Media New York 2014
Abstract As more and more users use the mobile terminals of high computing power,
the location-based services (LBS) recommendations for mobile users have become an
important and interesting topic. Mobile users are eager to get their interested and reli-
able services quickly. A considerable number of research works have been dedicated
to service recommendation based on users’ preferences and locations. In this paper,
we study the credibility of recommended services, and propose a set of composite
measures on how to provide more reliable services. We further propose the trustwor-
thy Skyline of LBS recommendation in terms of the trust degree based on the newly
introduced composite measures to achieve more credibility to provide recommenda-
tion services. Experimental results show that our method can recommend desired and
trusted services to users.
Keywords Location-based services (LBS) ·Credibility ·Skyline ·Recommendation
1 Introduction
With the popularity of the global positioning system (GPS) and the rapid develop-
ment of mobile terminal technology, the location-based services (LBS) have been
widely provided in our work and daily life environments in recent years. Based on the
W. Li ·M. Yao
School of Computer Engineering and Technology, Shanghai University, Shanghai, China
e-mail: wmli@shu.edu.cn
W. Li ·X. Zhou ·S. Nishimura ·Q. Jin
Graduate School of Human Sciences, Waseda University, Tokorozawa, Japan
Q. Jin (B)
College of Information Engineering, China Jiliang University, Hangzhou, China
e-mail: jin@acm.org
123
Recommendation of location-based services 1155
specific location of mobile users, suitable information services and timely decision-
making support can be provided to the users who need it. With the help of a gyroscope
of smart phones and the basis of the GPS co-ordinates, people could gain the time
spent in jogging, walking and traveling [1]. Most of service recommendation systems
are currently focused on the location where a user queries. Faced with a large number
of similar location-based services, mobile users have no idea about choosing the ser-
vices that they need. Although some services are recommended based on the user’s
preferences and interests, it is difficult to identify the real value of the recommended
services by the users themselves. One of the important reasons is considered to be that
the trust factor that a user may concern about the potential services has not been well
taken into account. Therefore, it is still a great challenge to meet each user’s preference
and ensure the reliability of the service for location-based service recommendation.
As many research works have clarified, there exist trust relationships in online social
networks. In real life, the concept of trust covers sociology, psychology, economics,
history, philosophy, and so on. It is obvious that the real trust cannot be easily modeled
in a computational system. It is important to find the trust relationship through the
social relation in online social networks. How can we use the data provided by social
networks and find the trust relationship between the users? The trust relationship may
help recommend the services to the users. Such a kind of service recommendation
should have higher reliability than that of not considering the trust between the users.
As we know, a user’s trust is a subjective concept. However, this subjective concept
that every user may have his/her credible criterion is difficult to be described, because
different people have distinct subjective feelings and expectations even on the same
service. Recently, the scores about the services given by the users have been used in
some of the recommendation systems. The scores reflect the users’ judging criterion of
the services to some extent. Through using these scores, similar users or their similar
preferences can be chosen according to the users’ selected analogous services, and
related services that the users used can be recommended to the target users. Under this
condition, the quality of historical evaluation information has not been considered.
Though the scores might not be right in some aspects, it becomes an important part of
the recommendation. How can we avoid incorrect scores caused by personal tendency
arbitrariness or prejudice? How can we provide reliable services? This is a great
challenge to the LBS recommendation.
In this study, we propose an integrated approach to trustworthy location-based
service recommendation based on the trust degree, which is represented by a set of
composite factors, such as correlation and similarity of the users and trustworthy
dominance between the users and items (the targets of the services). As we know, the
trust of users to a specific service is a subjective concept. Different users may have a
different credible criterion for the same service. On the other hand, the users may be
more concerned with the service evaluation and remarks given by their closest friends
or some others having similarities with them. Therefore, based on the introduction
of several quantitative measures on trust degree, we further make our effort to find
evaluation criteria based on the high similarity of users to achieve enough credibility
to provide recommendation services, by introducing several quantitative measures on
trust degree.
123
1156 W. Li et al.
The remaining part of this paper is organized as follows. We overview related work
in Sect. 2and introduce the trustworthy Skyline in Sect. 3. Section 4describes how
to measure the trust degree. In Sect. 5, we show experimental results to evaluate our
algorithm based on the synthesized data. Finally, we conclude this study in Sect. 6.
2 Related work
Personalized recommendation is used to solve the information overload. Its basic
approach is to infer and discover a user’s interests and preferences from his/her
demands. Many effective methods have been introduced into the recommendation
systems. Jeong et al. [5] suggested a movie recommendation system, based on the
selection of optimal personal propensity variables and the utilization of a secure col-
laborating filtering system. Balabanovic and Shoham [6] proposed a content-based
Fab System to recommend web pages to users, and a similar technique was used for
the Syskill and Webert System [7]. In addition to the content-based method, collabo-
rative filtering is the most mature recommendation method which is widely used in the
e-commerce field. Gallego and Huecas [8] designed a model that took into account
social, mobile and ubiquitous requisites to generate personalized recommendations
in the banking environment. Breese et al. [9] studied memory-based algorithms that
gained rating predictions based on the entire collections of previously rated items by the
users. Cortes et al. [10] proposed a probabilistic approach to collaborative filtering, and
the common probability model contains clustering model [11] and maximum-entropy
model [12]. On the other hand, model-based algorithms [13] use the collection of rat-
ings to train a specific model, which can be used to make predictions later. Besides the
user scores’ prediction, the user feedback information is important. Zhu and Jin [14]
proposed an adaptively emerging mechanism (AEM) that considers the user feedback
including the user satisfaction degree after using the services.
Most of the current recommendation systems assume a single score per item. How-
ever, an item may be rated on several attributes in some specific applications. We can-
not find out a user’s individual preferences on any distinctive attributes if we simply
return the overall scores (or average scores), especially in a mobile environment. For
multi-criteria ratings recommendation problems, Skyline queries (also called Pareto)
which return those non-dominated data can provide a good solution for the multi-
criteria decision-making problems. BNL algorithm [2] avoids simple pairwise com-
parison method, while the SFS algorithm [15] sorts all the data based on it. Recently,
Skyline query as a basic function of LBS has attracted a lot of attention. Location-
Dependent Skyline Query (LDSQ) [16] returns all these not location-dependently
dominant points. Huang et al. [17] studied continuous Skyline query on moving objects
in the context of LBSs, in which the query point moves continuously in the Skyline
set. All these Skyline queries in the context of LBSs using different preferences at
the same location return the same results. Kazuki [18] presented for the first time a
useful approach to taking into account both user preferences and locations, but a user
preference profile should be provided in advance.
Maximilien et al. [19] described a framework to select a service in a manner that
considers the preferences of service consumers and the trustworthiness of providers.
They explored the idea of adding explorer agents to the framework to achieve better
123
Recommendation of location-based services 1157
self-adjusting trust, so that as bad services correctly behave they are reconsidered.
Aikebaier et al. [20] proposed a P2P system, in which each group member peer has to
be trustworthy so that malicious behavior of a member peer cannot affect the overall
outcomes of the whole group in the group cooperation. The authors considered the
trustworthiness of each group member as a base of an agreement procedure in the
distributed environment. By taking advantage of the trustworthiness concept of each
peer, they proposed a novel approach to composing a trustworthy group in the distrib-
uted agreement protocols. Al-Oufi et al. [21] extended the Advogato trust metric in a
way that can be incorporated with the strength of social relationships and discovered
a group of reliable users associated with each individual user. Their approach is of
significant advantage both in finding a trustworthy group of people and potentially
minimizing the negative impact of unreliable users. Although many research works
considered multi-attribute factors so that better personalized recommendation can be
achieved, most of the current works ignored users’ subjective biases and trustworthi-
ness of the services. Furthermore, the reliability of the recommended results needs to
be guaranteed. In this study, we propose a composite measure based on correlation
and similarity to ensure that a service is reliable.
3 Trustworthy Skyline
To query on a trustworthy and reliable service with multi-dimensional location infor-
mation, Skyline is widely applied as a promising method [2–4]. The basic Skyline
computation is finding all the points not dominated by any other points. That is, object
pdominates an object qif pis not worse (better or worse depends on the specific
application) than qwith respect to all attributes and there exists at least one attribute
where pis better than q. Skyline queries are also called Pareto and maximum vector
set [2], which have given rise to great interest in its wide applications including multi-
criteria decision making, data mining, and database visualization. A large number
of algorithms have been proposed to more efficiently handle location-based Skyline
query problems, from one-shot [3] to fuzzy query based on a range of positions [4].
Let us consider a typical example: a car owner wants to find the nearest hotel which
is cheap and good. Here, we cannot simply consider the distance factor. We can use
the Skyline query method to find a hotel with a short distance and good reputation. In
general, some people want to stay at hotels with the lowest price, while others may
put the quality of service in the first place. However, whether comments about a hotel
are credible is also a critical factor. For two hotels with equal distance and similar
comprehensive evaluation, it will still be difficult for the users to determine which one
to choose. However, it will be easier for them to select one if their friends have made
valuable remarks about it.
Figure 1shows an example of trustworthy Skyline. We assume the Skyline of a set
Rof multi-dimensional records consisting of all the points of Rnot dominated by
any other services. A point riis said to dominate another record rj(rirj),ifriis
better than or equal to rjin the trustworthy measuring of all dimensions. We can see
from Fig. 1that the distance from the user to r2and r4is the same. However, the user
who gives rates on r4is closer to the test user than another user who give rates on r2.
So that r4’s trustworthy value is higher than that of r2. This is to say that r4r2.
123
1158 W. Li et al.
Fig. 1 Example of trustworthy Skyline
For r2and r3, although the distance from the user to r3is farther than r2, the relation
between the user and r3is closer than that of r2. In this paper, r3’s trustworthy value is
higher than that of r2and r3r2.FromFig.1and the two examples, we can see that
the relation is an important factor in selecting services. If a user is not familiar with the
situation and related services, the user’s trustworthiness on the service relies on the
evaluation rates of service from friends, and not the rates themselves. Though there
are different choices for a user based on the defined distance on selecting services, the
user generally tends to select the service that has high trust values.
4 Composite measures of trust degree
In this section, we consider not only whether there is a similar preference between the
users, but also a very important factor in the relationship between the users to better
reflect the credibility of the service. We can get credible services domination relations
and provide the trusted service to users.
Similarity: U is defined as a set of users. We assume the similarity between umand
unsim(um,un)must be in the range [0, 1], which can be represented as follows.
sim(um,un)=1+corr(um+un)
2(1)
where
corr(um,un)=
ri∈Rm∩R
n(Si,m−¯
Sm)(Si,n−¯
Sn)
ri∈Rm∩R
n(Si,m−¯
Sm)2
ri∈Rm∩R
n(Si,n−¯
Sn)2
(2)
123
Recommendation of location-based services 1159
Si,jdenotes a user uirating on a record rj. In many applications, the score Si,jinvolves
multi-dimensional attributes (Si,j[1],Si,j[2],...,Si,j[k]). As we know, most people
enjoy a service with shorter distance in LBS environments. Rmand Rnare defined as
the set records rated by umand un,respectively. Rm∩Rnstands for the set of records
that both users umand unhave assessed, while ¯smand ¯smdenote the average scores of
umand unon all records of Rmand Rn,respectively. In addition, Pearson correlation
coefficient corr (um,un)is normalized in the range [−1,1].
On the other hand, social networking can provide a better means to analyze the
incident relation between different people. As we know, people’s behavior is more
or less affected by other people with interpersonal relation. In this study, we employ
friendship as the most direct relation.
Relation: We can compute the relationship with the aid of relational tree, and the
direct children in the tree mean the direct friendship. We assume that their relation is 1.
The relation between the root and the second layer child nodes is lower than the first
layer children, and we define their relation is 1/√2(=0.7071); and so on. If the layer
is lower than the second layer, their relation is less than 0.5. Therefore, their relations
depend on the layer and can be expressed as follows.
Re(um,un)=1
√l(3)
where Re(um,un)indicates the relationship between umand un, and lis the layer of
child node umin the relational tree whose root node is un.
Composite coefficient of similarity and relation: It is defined as follows.
CCSR(um,un)=ωSim(um,un)+σRe(um,un)(4)
which denotes the composite values of similarity and relation between umand un.ω
and σare the weight of similarity and relation respectively, and ω+σ=1.
Trustworthy rate: We define the trustworthy rate that a user ulrates on record ras
follows.
TWR(ul,ri)=k∗
v∈Top (ul,k)
Sv,r×CCSR(ul,v) (5)
where Top(ul,k)is expressed as the set users who have the highest degree with the
user uand the multiplier kserves as a normal factor and is usually selected as follows.
k=1
v∈Top (ul,v) |CCSR(ul,v)
|(6)
Trustworthy dominance: In the context of LBS, the distance between the user and
the item must be taken into consideration. To simplify the computation, dist(u,r,L)is
expressed as the Euclidean distance between user uand record rwhen uis at location
L. If an active user uis under ri
u
Lrj, the record riis said to trustworthily dominate
the record rj, which can be expressed as follows.
123
1160 W. Li et al.
TrSKY (active user u, location L, parameter k )
1 TrSky(u,L)=
2 For each record ri {
3 For each record rirj {
4 if // trustworthy dominate for u at L
5 break and goto 2
6 } Insert ri into TrSky(u,L)
7 } return TrSky(u,L)
Fig. 2 TrSKY algorithm
TWR(u,ri)TWR(u,rj)dist(u,ri,L)dist(u,rj,L)(7)
Trustworthy Skyline: All the records that are not trustworthily dominated by other
records for an active user uat location Lcan be considered in the trustworthy Skyline,
which is represented as follows.
TrSky(u,L)=r|¬∃t∈(R−{r})∧tu
Lr(8)
We propose a basic algorithm TrSKY based on trustworthy dominance and trustworthy
Skyline as shown in Fig. 2.
TrSKY computes the Skyline not only considering the trustworthy rate based on
composite coefficient of similarity and relation, but also taking related location infor-
mation into account. Every record riis a candidate for the trustworthy Skyline and
should compare against every other record rjfor the active user u, if there is no other
record to trustworthily dominate it. Then the trustworthy Skyline should contain the
record. The worst case cost of the algorithm is O(|R|2), where |R|is the number of
effective records, since it has to consider all pairs of records before breaking a loop.
5 Evaluation experiment and result analysis
In this section, we show the effectiveness of our methods by the experiment. Our
experiment was run on the machine with Intel core i5 processor, 4G main memory
and Linux operating system, and the programming language is Java and the IDE is
Eclipse.
As there are no public test data sets for the recommendation in the mobile environ-
ment, our dataset was crawled from www.dianping.com/shanghai and contains three
parts:
1. Hotel Table: we screened 150 popular hotels which have been rated at least 200
times a year in Shanghai. The table also contains other information such as loca-
tion, telephone number and tags.
2. User Table:we selected 1,000 users with high contribution value in this community
and simply considered the following users as his/her direct friends.
123
Recommendation of location-based services 1161
00.2 0.4 0.6 0.8 1
0.6
0.65
0.7
The value of σ
CCSR(u
m
,u
n
)
TrSKY
CF
Fig. 3 Trusted similarity at the different σlevel (under Sim(um,un)=0.65,l=2)
0.4 0.5 0.6 0.7 0.8 0.9 1
0.4
0.5
0.6
0.7
0.8
0.9
1
The value of RE
CCSR(um,un)
TrSKY
CF
Fig. 4 Trusted similarity at the same σlevel (under σ=0.5,Sim(um,un)=0.65)
3. Rating Table: it saved the scores with respect to a user rating on a hotel in the past,
but the score is a multi-dimensional rating (from 1 to 5) for the rooms, environment
and service.
The results are shown in Figs. 3,4,5and 6. The ordinate is the value of
CCSR(um,un). It reflects the trusted degree between umand un.Thevalueof
CCSR(um,un)is linear to the value of the number of layer and the relation according
to Formula (4). The value of CCSR(um, un) has an effect on trust degree. In this paper,
the higher value of CCSR(um,un)will be chosen in the TrSKY algorithm based on
123
1162 W. Li et al.
7 6 5 4 3 2 1
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
The number of layer
CCSR(um, un)
TrSKY
CF
Fig. 5 Trusted degree under σ=0.5, Sim(um,u
n)=0.5
7 6 5 4 3 2 1
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
The number of layer
CCSR(um, un
)
TrSK Y
CF
Fig. 6 Trusted degree under σ=0.5, Sim(um,u
n)=0.35
supplying appropriate number of services to users. If the value of CCSR(um,un)is
high and there is not any service to be recommended, it is meaningless to introduce
the trust degree.
Let Sim(um,un)=0.65 and l=2, we can see the relation between σ
and CCSR(um,un)from Fig. 3. If a user has a close relation with another user,
they would have similar preference and the higher trusted views on services. The
CCSR(um,un)would have a higher value, when the value of σincreases. Let
σ=0.5 and Sim(um,un)=0.65, we can get the relation between the friendship
and the CCSR(um,un)from Fig. 4. If the number of layers is lower than the sec-
ond layer, the trusted degree of TrSKY is better than CF (collaborative filtering).
Otherwise, though the similarity is higher, the trusted degree is not given a higher
value.
123
Recommendation of location-based services 1163
Tab le 1 Services score errors
between the two methods The top number of recommendation TrSKY CF
MAE 5 0.6440 0.6734
10 0.6153 0.6556
20 0.6021 0.6437
RMSE 5 0.8529 0.9286
10 0.8172 0.8969
20 0.8010 0.8875
MAPE 5 0.2038 0.2132
10 0.1955 0.2087
20 0.1923 0.2072
We can see from Figs. 5and 6that the value of CCSR(um,un)is higher than 0.45
if the number of layers is lower than the third layer. If Sim(um,un)is low even to
0.35 and have a direct friendship, the value of CCSR(um,un)is higher than 0.65. As
a result, the closer friendship that a user has with another one, the more trustworthy
we can model for a user, thereby leading to a better recommendation.
We use the trusted method proposed in this study to compare with the original
collaborative filtering methods in multi-dimensional ratings for a user. There exists
score error that is the error between the prediction value by using the TrSKY or CF
and real value. In this study, we use three indices, namely mean absolute error (MAE),
root mean square error (RMSE) and mean absolute percent error (MAPE) to measure
the scores forecasting the accuracy of the two methods. These indices are represented
as follows.
MAE =1
N
N
t=1|Xt−Yt|(9)
RMSE =
1
N
N
1
(Xt−Yt)2(10)
MAPE =1
N
N
t=1
Xt−Yt
Yt
(11)
The results are shown in Table 1. In Table 1, we empirically analyze the services
score errors of room, environment and service between the trustworthy method and
CF by using MAE, RMSE and MAPE indices. It can be observed that the services
score errors indeed have a great effect on the performance of the two methods. The
results show that our proposed method is more precise and able to supply high-reliable
recommendations than the CF method.
Figure 7shows the relation between the number of services and trusted users for
the CF and TrSKY methods. The more the services are provided, the more the user
rating’s indicators are. The trustworthy user proportion in CF increases according to
the number of services. The proportion of trustworthy users is reduced in our TrSKY
method. However, the percentages of credible users in TrSKY are superior to CF
123
1164 W. Li et al.
5 10 15 20
20%
30%
40%
50%
60%
70%
80%
Number of services
The percent of Trusted users
CF
TrSKY
Fig. 7 The relation between the number of services and trusted users
overall. Moreover, the highest value of CF is less than the minimum of TrSKY. In
particular, when fewer services are provided, the effect is more apparent.
6 Conclusion
In this study, we have proposed a trustworthy service-recommended method, which is
mainly based on friendships to establish a credible recommendation of location-based
services, especially for social websites in the mobile environment. We have provided
the definitions and a framework of LBS recommendation based on the trust degree. To
improve the credibility of services, we have introduced a set of quantitative measures
based on composite factors. Our goal is to recommend the trusted services based on the
user’s preferences, and location of nearest relations as well. We have further developed
a TrSKY algorithm based on the trust degree. Our experiment has demonstrated that
our method can provide an efficient LBS recommendation and achieve credibility to
the user’s satisfaction.
Although we have formulated the trustworthy services for the location-based ser-
vices, proposed and developed TrSKY algorithms to supply credibility services to
users and defined the trust metric based on friendship, there are still many factors
that may influence the trust metric between the users, and between the user and ser-
vices. As for our future work, we will study these factors and incorporate them for
the improved computation model of trust in more dimensions and further consider the
dynamic situation between them, so that we can supply more personalized and reliable
services to the users.
Acknowledgments This work has been supported by the National Natural Science Foundation of China
(NSFC) under Grant No. 71061001 and No. 71061005/G0112, Japan Society for the Promotion of Science
(JSPS), China Jiliang University, and Shanghai Leading Academic Discipline Project (Project Number:
J50103).
123
Recommendation of location-based services 1165
References
1. Kiss G (2011) Using smartphones in healthcare and to save lives, internet of things (iThings/CPSCom).
In: Proceedings of 4th international conference on cyber, physical and social computing, pp 614–619
2. Borzsonyi S, Kossmannand D, Stocker K (2001) The Skyline operator. In: Proceedings of international
conference on data engineering, Heidelberg, Germany, pp 421–430
3. Lee M-W, Hwang S-w (2009) Continuous skylining on volatile moving data. In: Proceedings of IEEE
25th international conference on data engineering, pp 1568–1575
4. Lin X, Jianliang X, Haibo H (2013) Range-based skyline queries in mobile environments. IEEE Trans
Knowl Data Eng 25(4):835–849
5. Jeong W-h, Kim S-j, Park D-s, Kwak J (2013) Performance improvement of a movie recommendation
system based on personal propensity and secure collaborative filtering. J Inf Process Syst 9(1):157–172
6. Balabanovic M, Shoham Y (1997) Fab: content-based, collaborative recommendation. Comm ACM
40(3):66–72
7. Pazzani M, Billsus D (1997) Learning and revising user profiles: the identification of interesting web
sites. Mach Learn 27:313–331
8. Gallego D, Huecas G (2013) An empirical case of a context-aware mobile recommender system in a
banking environment. J Converg 49–56
9. Adomavicius G, Tuzhilin A (2005) Toward the next generation of recommender systems: a survey of
the state-of-the-art and possible extensions. IEEE Trans Knowl Data Eng 17(6):734–749
10. Breese JS, Heckerman D, Kadie C (1998) Empirical analysis of predictive algorithms for collaborative
filtering. In: Proceedings of 14th conference on uncertainty in artificial intelligence pp 43–52
11. Xue GR, Lin C, Yang Q, Xi WS, Zeng HJ, Yu Y, Chen Z (2005) Scalable collaborative filtering using
cluster-based smoothing. In: Proceedings of the 28th annual international conference on research and
development in information retrieval (SIGIR ’05). New York, NY, USA, pp 114–121
12. Pavlov DY, Pennock DM (2002) A maximum entropy approach to collaborative filtering in dynamic,
sparse, high-dimensional domains. In: Proceedings of 16th annual conference on neural information
processing systems (NIPS ’02), pp 1441–1448
13. Kim TH, Park SI, Yang SB (2008) Improving prediction quality in collaborative filtering based on clus-
tering, In: Proceedings of IEEE/WIC/ACM international conference on web intelligence and intelligent
agent technology, pp 704–710
14. Zhu Y, Jin Q (2012) An adaptively emerging mechanism for context-aware service selections regulated
by feedback distributions. Hum Centric Comput Inf Sci 2–15
15. Chomicki J, Godfrey P, Gryz J, Liang D (2003) Skyline with presorting. In Proceedings of the inter-
national conference on data engineering, pp 717–719
16. Zheng B, Lee KCK, Lee WC (2008) Location-dependent skyline query. In: Proceedings of 9th inter-
national conference on mobile data management, pp 148–155
17. Huang Z, Lu H, Ooi BC, Tung AKH (2006) Continuous skyline queries for moving objects. IEEE
Trans Knowl Data Eng 18(12):1645–1658
18. Kodama K, Iijima Y, Guo X, Ishikawa Y (2009) Skyline queries based on user locations and preferences
for making location-based recommendations. In: Proceedings of the 2009 international workshop on
location based social networks (LBSN ’09). ACM, New York, USA, pp 9–16
19. Michael EM, Singh MP (2004)Toward autonomic web services trust and selection. In: Proceedings of
the 2nd international conference on service oriented computing, pp 212–221
20. Aikebaier A, Enokido T, Takizawa M (2011) Trustworthy group making algorithm in distributed
systems. Hum Centric Comput Inf Sci 1–6
21. Al-Oufi S, Kim H-N, El Saddik A (2012) A group trust metric for identifying people of trust in online
social networks. Expert Syst Appl 39(18):13173–13181
123
