An analytic network process and trapezoidal interval-valued fuzzy technique for order preference by similarity to ideal solution network access selection method

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS
Int. J. Commun. Syst. (2014)
Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/dac.2833
An analytic network process and trapezoidal interval-valued fuzzy
technique for order preference by similarity to ideal solution
network access selection method
Emmanouil Skondras1,2, Aggeliki Sgora1,2, Angelos Michalas2 and
Dimitrios D. Vergados1,*,†
1Department of Informatics, University of Piraeus, 80, Karaoli and Dimitriou St., GR-18534, Piraeus, Greece
2Department of Informatics Engineering, Technological Educational Institute of Western Macedonia, GR-52100,
Kastoria, Greece
SUMMARY
Next generation wireless networks consist of many heterogeneous access technologies that should support
various service types with different quality of service (QoS) constraints, as well as user, requirements and
provider policies. Therefore, the need for network selection mechanisms that consider multiple factors must
be addressed. In this paper, a network selection method is proposed by applying the analytic network process
to estimate the weights of the selection criteria, as well as a fuzzy version of technique for order preference
by similarity to ideal solution to perform the ranking of network alternatives. The method is applied to a
heterogeneous network environment providing different QoS classes and policy characteristics. Each user
applies the method to select the most appropriate network, which satisﬁes his or her requirements in respect
of his or her service-level agreement (SLA). Performance evaluation shows that when the user requests only
one service, the proposed method performs better compared to the original technique for order preference by
similarity to ideal solution, as well as the Fuzzy AHP-ELECTRE method. Moreover, the proposed method
can be applied in cases where a user requires multiple services simultaneously on a device. The sensitivity
analysis of the proposed method shows that it can be properly adjusted to conform to network environment
changes. Copyright © 2014 John Wiley & Sons, Ltd.
Received 9 January 2014; Revised 17 June 2014; Accepted 18 June 2014
KEY WORDS: network selection; vertical handover; MADM; ANP; TOPSIS; interval value fuzzy numbers
1. INTRODUCTION
Next generation wireless access networks are growing rapidly integrating multiple network tech-
nologies aiming to support multimedia services in addition to voice and data with high data rates
and guaranteed QoS [1]. In this context, end users devices (such as mobile phone or netbook) are
equipped with multiple radio interfaces allowing connectivity to the most suitable network envi-
ronment based on users requirements and operators policies [2, 3]. According to the always best
connection principle of the fourth generation wireless networks, users of mobile services should be
provided with connectivity to the best access technology at anytime [4, 5]. Therefore, there is a need
for efﬁcient vertical handover (VHO) mechanisms to be applied.
The handover process is supposed to be successful, infrequent, and imperceptible to enable
telecommunication providers meet the QoS requirements of the users [6]. Especially, in the case
*Correspondence to: Dimitrios D. Vergados, Department of Informatics, University of Piraeus, 80, Karaoli and Dimitriou
St., GR-18534, Piraeus, Greece.
†E-mail: vergados@unipi.gr
Copyright © 2014 John Wiley & Sons, Ltd.

E. SKONDRAS ET AL.
of heterogeneous networks, seamless interworking among the different technologies is also needed
[7]. Thus, special attention to the VHO process should be given [8].
The VHO procedure consists of three main steps including the handover initiation, the net-
work selection, and the handover execution. The initiation step contains the required procedures to
identify the available access networks and select the time of handover in respect of network condi-
tions and user mobility. The network selection step is related to the selection of the most appropriate
network alternative based on the available network characteristics, user preferences, and applications
requirements. Finally, the execution step completes the handover process by seamlessly connect-
ing the terminal to the selected network. This paper deals with the network selection step of the
VHO process.
Existing handover network selection schemes employ multi attribute decision-making methods
(MADM), fuzzy logic, neural networks, and utility functions [9]. However, because the selection
of an access network depends on several parameters with different relative importance, the access
network selection problem is usually looked at from the aspect of multi-criteria analysis and more
specifically by applying different MADM algorithms. In this paper, a network selection method is
proposed by employing two MADM algorithms: the analytic network process (ANP), which is an
extension of the analytic hierarchy process (AHP) for criteria weights calculation, and a fuzzy ver-
sion of the technique for order preference by similarity to ideal solution (TOPSIS) for accomplishing
the ranking of the candidate networks. The proposed method considers network QoS characteristics
and policies, application requirements and different types of users service-level agreements (SLAs)
to provide advanced connection services. Linguistic values are used to characterize the performance
of selection criteria, which are represented by interval-valued trapezoidal fuzzy numbers.
Our approach provides the following main contributions:
It allows complex relationships within and among clusters (in our case, the network QoS char-
acteristics and the network policies characteristics) of selection criteria by applying the ANP
method, which does not use an hierarchical framework as AHP but a network model of depen-
dencies. Additionally, ANP eliminates the index consistency requirement of AHP (i.e., in AHP
the relative importance of decision factors need to be redefined in case index consistency value
is more than 0.1).
It can better express imprecise information of performance selection criteria for different
application types and users SLAs by applying linguistic values and interval-valued fuzzy num-
bers. Interval value fuzzy numbers are adopted because they can efficiently present uncertain
information by minimum maximum membership intervals rather than by single membership
values.
It performs the selection of the best network access technology by considering contradictory
selection criteria, facilitating the provision of high quality services and at the same time satis-
fying different types of users SLAs. This is achieved through a fuzzy version of TOPSIS, the
trapezoidal interval-valued Fuzzy TOPSIS (TFT), introduced in this study. Because TFT uses
fuzzy logic, it resolves the case of having several services of different QoS constraints running
simultaneously on a terminal. Therefore, network selection is performed in a way satisfying
multiple groups of criteria per user. Furthermore, the ranking abnormality problem experienced
in the original TOPSIS is discarded in a way similar to [10] to avoid inconsistencies when a
new network is available or an existing network is removed from the alternatives.
The remainder of the paper is organized as follows: In Section 2, the MADM-related research
literature is revised. Section 3 presents the proposed network selection method followed in this study
including the AHP, the ANP, and the TFT. Section 4 describes a scenario that applies the proposed
method to accomplish the network selection process. Moreover, a performance evaluation of the
proposed method is presented, and its results are discussed compared with the TOPSIS as well as the
Fuzzy AHP-ELECTRE (FAE) results. Finally, Section 5 concludes our work and presents possible
future extensions and plans.
Copyright © 2014 John Wiley & Sons, Ltd. Int. J. Commun. Syst. (2014)
DOI: 10.1002/dac

NETWORK ACCESS SELECTION SCHEME BASED ON ANP AND TI-VALUED FUZZY TOPSIS
2. RELATED WORK
Multi attribute decision-making methods are used to select the best alternative among candidate
networks given a set of criteria with different importance weights. Specifically, MADM algorithms
are able to evaluate criteria of different value ranges, sometimes even contradictory, using multi-
criteria analysis. Widely used methods include AHP [11, 12], simple additive weighting (SAW)
[12, 13], TOPSIS [12–14], FAE [15], gray relational analysis (GRA) [12, 13], multiplicative expo-
nent weighting (MEW) [12, 13], distance to ideal alternative [12], and ANP [16]. Furthermore,
various weighting methods are used to provide suitable criteria weights for each alternative. Several
research studies use MADM methods for network selection.
Sharma and Khola [14] presented a network selection algorithm based on the TOPSIS algorithm.
The proposed algorithm besides the usual parameters (i.e., QoS, bandwidth, and cost) it also takes
a prediction of the Received Signal Strength (RSS) into account for the network selection.
Shi and Zhu [11] employed two MADM methods combined with the group decision-making algo-
rithm to perform network selection. The proposed procedure defines two types of weights, namely
the objective weights, which consider the current attributes of candidate networks and the subjective
weights specified according to the subscribers and traffic class preferences. The objective weights
vector is determined using the entropy weighting method while the subjective weights vector is
evaluated using the AHP. Then, the group decision-making method employs both vector types to
produce a synthesized vector, whereas the ranking of alternatives is the sum of the product of the nor-
malized attribute values with their respective weights. The compatibility of the integrated decision
is finally checked to ensure the effectiveness of the proposed solution. Results showed that the pro-
posed method reduces the number of handoffs and improves QoS characteristics of conversational
and interactive traffic flows compared with entropy weighting and GRA approaches.
Lassoued et al. [13] described an evaluation framework of VHO mechanisms, which emulates
application characteristics, mobile terminals context, and user and operators preferences. The model
provides user traces containing information about the location of the users and the QoS performance
of the networks. Current network characteristics are obtained from a mobility simulator emulating
network access technologies, location of access points, and user mobility. The proposed method-
ology is used to compare the efficiency of various MADM network selection algorithms including
SAW, TOPSIS, GRA, MEW, and their own proposed scheme called Ubique [17] in a dynamic envi-
ronment. Simulation results showed that the examined algorithms achieve good performance, while
Ubique is less flexible to changes of delay and cost criteria weights than the other approaches.
Lahby et al. [12] proposed a network selection scheme, which is based on the AHP method and
the Mahalanobis distance. Mahalanobis distance is used to measure the distance of alternatives from
the correlation of criteria so that the optimal network satisfying the QoS, security, and cost criteria is
selected. According to simulation results, both the ranking abnormality problem and the number of
handoffs in the proposed method are reduced compared with the decision algorithms SAW, MEW,
TOPSIS, and distance to ideal alternative.
Lahby et al. [16] proposed a technique for network selection using ANP to estimate the weights
of selection criteria and GRA to rank the alternative networks. Selection criteria include network
related attributes while the preference of users is expressed by evaluating different criteria weights
through the ANP for each access network. Accordingly, the ANP evaluates the criteria weights of
each access network separately based on users preferences; in that way, unique criteria weights exist
for each network. Simulation results indicated that this method reduces both the ranking abnormality
problem and the number of handoffs compared with other method variants.
Sheng-mei et al. [18] presented a network selection algorithm making use of the AHP and the
entropy weight method to evaluate the weights of network and user related criteria. The candidate
access networks are identified on the basis of their signal-to-interference-plus-noise ratio (SINR)
values. TOPSIS is used for the final ranking of the network alternatives. The proposed method
achieved higher throughput and reduced number of vertical handoffs for various traffic classes com-
pared with combined SINR-based vertical handoff [19] and multi-dimensional adaptive SINR-based
vertical handoff [20] algorithms.
DOI: 10.1002/dac

E. SKONDRAS ET AL.
Alkhawlani et al. [21] proposed a VHO decision system, which integrates fuzzy logic and TOP-
SIS method. Network and user related criteria are each processed by parallel fuzzy logic control
(FLC) subsystems, and consequently, TOPSIS is applied to perform the selection of the best network
choice. Simulation results showed that the proposed solution reduces handover rate and handover
failure while it increases the percentage of users assigned to networks of their preference, as well
as, the utilization of inexpensive networks.
Alkhawlani and Mohsen [22] presented a network selection system suitable for tightly coupled
wireless network environments consisting of two modules. The user software module evaluates the
best network alternative based on selection criteria set by the user including reliability, security, bat-
tery power, and price. The operator software module resides at the coordinator of the radio access
technologies and performs the final selection decision. It takes into account the network choice
proposed by the user as well as criteria imposed by the operator such as network policies, QoS
characteristics, system capacity, and utilization. The operator module initially uses the FLC subsys-
tems of [18] to evaluate the performance of criteria and finally the AHP method to assess the FLC
subsystems outputs and select the best possible network. Simulation results show that the proposed
network selection scheme achieves better performance in terms of user preferences satisfaction, QoS
fulfillment, and operator benefits improvement, than four different reference algorithms performing
(i) random selection, (ii) selection based on terminal speed, (iii) selection based on service type, and
(iv) selection based on the availability of resources, respectively.
Vasu et al. [23] proposed a fuzzy rule based decision algorithm for vertical handoff in wire-
less heterogeneous networks. The algorithm uses QoS performance values as decision parameters,
while triangular fuzzy membership functions are used for the fuzzification of the input parameters
and the defuzzification of the output result. For the evaluation of the proposed model, a non-birth
Markov chain with states corresponding to available access networks is used. Simulation experi-
ments comparing the proposed approach against various MADM methods demonstrated that the
method presented improves the performance of delay sensitive applications.
The use of fuzzy logic for network selection requires the definition of logic rules from specialists
with thorough knowledge of the behavior of the available access networks in various conditions.
Furthermore, as the number of selection criteria and the available networks increase, rules become
more complex, struggling to define effective policies and evaluate the best alternative. Accordingly,
the use of fuzzy logic based solutions is limited to handover decision schemes with reduced number
of networks and selection criteria.
Some network selection methods combine fuzzy logic with neural networks to rate the alternative
access networks. Accordingly, Gowrishankar et al. [24] created an artificial neural network multi-
criteria decision analysis system, which performs network selection using network related attributes
expressed either in crisp or in fuzzy linguistic values. Sensitivity analysis among the proposed solu-
tion, the TOPSIS and the SAW methods, is carried out in a network environment consisting of
four overlaid networks, where weights of different criteria change and connections of four traffic
types exist. Results show that the proposed method is less stable than TOPSIS but more stable than
SAW in respect to criteria weights changes. Neural network approaches replace the complex logic
rules of fuzzy logic approaches, but they still suffer from scalability issues because of the required
large number of the processing elements at their hidden layers as the complexity of criteria and the
number of networks increase.
Several network selection schemes make use of utility/cost functions to provide performance
metrics for different types of criteria. Rodriguez et al. [25] use a cost function for the network
selection that includes the rules and policies for selecting the best candidate network or for adapt-
ing ongoing session parameters. Wu et al. [26] used a set of utility functions to quantify selection
criteria including the link quality (RSS), battery power, average throughput, network delay, mone-
tary cost, and application type. The relative weights of criteria are calculated according to the AHP
method. Consequently, the candidate networks are ranked using the weighted product method. Sim-
ulation results show that the proposed scheme improves network performance and reduces power
consumption of users terminals. In the approach of Wang et al. [27], the concepts of fuzzy logic,
neural network, and utility functions are combined to perform network selection. The proposed
method uses a fuzzy neural network, which obtains network, user, and terminal related input crite-
DOI: 10.1002/dac

ria and evaluates the performance of each access network. Attributes of criteria are defined through
utility functions and processed through the fuzzification, interference, and defuzzification layers
of the neural network. A fuzzy version of the particle swarm optimization is used for neural net-
work training; however, it is not clear how expected network performance degrees are specified
during the learning process. Simulation results show that the proposed method achieves better per-
formance in terms of access blocking probability, packet drop probability, and average throughput
of access networks compared with other network selection algorithms including GRA, AHP, and
game theoretic.
Generally, there is a rate of uncertainty in characterizing performance measurements as well as
rates of influence of performance metrics. Therefore, fuzzy MADM methods expressing uncertain
quantities by fuzzy numbers have received the interest of many researchers in decision theory. In
particular, several fuzzy MADM network selection methods are suggested utilizing linguistic vari-
ables, triangular fuzzy numbers, trapezoidal fuzzy numbers, etc. to model network attributes and
their respective weights.
Chamodrakas and Martakos [10] proposed a method that considers network conditions, QoS
constraints, and energy consumption requirements for network selection criteria. User preferences
indicating the relative importance of criteria in different applications are expressed using linguis-
tic expressions, which are transformed to triangular fuzzy numbers. The graded mean integration
method is used for the defuzzification of fuzzy numbers into crisp values. Furthermore, utility
functions are used to model QoS requirements and energy consumption characteristics of different
applications. The fuzzy set representation version of TOPSIS is used to combine selection crite-
ria and weights to perform the rating of the available networks. The fuzzy set representation of
TOPSIS resolves possible inconsistencies because of conflicting criteria such as bandwidth and
energy consumption. Simulation results show that the proposed method accomplishes a trade-off
between QoS requirements and energy consumption.
Sasirekha and Ilanzkumaran [28] described two methods to perform network selection. Initially,
both methods use a fuzzy version of the AHP technique to obtain the weights of selection crite-
ria specifying networks performance. The relative importance matrix resulting from the pairwise
comparison of criteria is fuzzified using triangular fuzzy numbers with membership functions rep-
resenting the scale of importance of five levels. Then, the relative importance values are turned into
crisp values using the geometric mean operator while the rest of the steps of the AHP method follow.
Subsequently, the former network selection method uses TOPSIS to evaluate the best alternative
network based on the weights from AHP and the criteria values of each alternative network. The lat-
ter method combines the fuzzy AHP with VIKOR method, which has less complexity and performs
equally well as TOPSIS. Evaluation examples are given illustrating that both methods succeed to
select the best network alternative.
Kaleem et al. [29] presented a VHO decision algorithm, which is based on network performance
measurements to evaluate, firstly, the necessity of making a handoff and, secondly, the best network
alternative in case that handoff is required. To determine the handoff decision, a handoff factor
is evaluated and compared with a constant threshold. Network selection is performed using fuzzy
TOPSIS. User preferences are defined in the form of criteria weights, while ratings of selection
criteria and criteria weights are expressed as trapezoidal or triangular fuzzy numbers. Numerical
examples and simulation experiments present the competence of the proposed approach for various
traffic classes in heterogeneous network access technologies.
Lahby et al. [30] compared the weighting algorithms of AHP, fuzzy AHP, ANP, and fuzzy ANP
for assigning weights to network dependent criteria used by MADM algorithms performing network
selection. To evaluate the effects of the weighting algorithms, the TOPSIS method is used. Results
show that all algorithms achieve similar results concerning the network selected. However, the rank-
ing abnormality of TOPSIS is reduced, when the ANP weighting method is used for background,
conversational, and interactive traffic classes, as well as for streaming traffic.
Zhang [31] performed an analysis of MADM methods for handover decision. Uncertain linguistic
terms of decision criteria such as sojourn time and seamlessness are converted to fuzzy data which
in turn are converted to crisp values. SAW and TOPSIS are suggested to perform the final ranking
of the candidate networks while results from the sensitivity analysis of these methods conclude
DOI: 10.1002/dac

E. SKONDRAS ET AL.
that TOPSIS is more sensitive to the criteria performance and their weights. Moreover, the paper
identifies the handover decision case in which several applications are running simultaneously on a
terminal as a group decision problem, although its solution is not being addressed.
3. THE PROPOSED NETWORK SELECTION METHOD
Our proposed method consists of two MADM algorithms: the ANP to calculate the relative impor-
tance of the selection criteria and the TFT to accomplish the ranking of the candidate networks. It
should be noted that the TFT represents the performance of selection criteria using interval-valued
trapezoidal fuzzy numbers. The following of this section presents the algorithms that this method
employs, as well as an overview of the interval-valued trapezoidal fuzzy numbers that TFT algorithm
utilizes.
3.1. The analytic network process
The ANP was also introduced by Saaty [32] to deal with decision problems that criteria and alter-
natives depend on each other. ANP is actually the generalization of the AHP. A decision problem
that is analyzed with the ANP can be designed either as a control hierarchy or as a nonhierarchical
network. Nodes of the network represent components (or clusters) of the system while arcs denote
interactions between them. All interactions and feedbacks within clusters are called inner depen-
dencies, while interactions and feedbacks between clusters are called outer dependencies. The ANP
is composed of four major steps [33]:
Step 1. Model construction and problem structuring: During this step, the problem is analyzed
and decomposed into a rational system, such as a network.
Step 2. Pairwise comparison matrices and priority vectors: During this step, the pairwise
comparison matrix, as in AHP, is derived using Saaty’s nine-point importance scale
(Table I).
Step 3. Supermatrix formation: During this step, the supermatrix of the ANP model is con-
structed to represent the inner and outer dependencies of the network. It is actually a
partitioned matrix, where each matrix segment represents a relationship between two
clusters in the network. To construct the supermatrix, the local priority vectors obtained
in step 2 are grouped and placed in the appropriate positions in a supermatrix based on
the flow of influence from one cluster to another, or from a cluster to itself, as in the
loop. Then, the supermatrix is transformed to a stochastic one, the weighted superma-
trix. Finally, the weighted supermatrix is raised to limiting powers until all the entries
converge to calculate the overall priorities, and thus, the cumulative influence of each ele-
ment on every other element with which it interacts is obtained [34]. At this point, all the
columns of the new matrix, the limit supermatrix, are the same, and their values show the
global priority of each element of network.
For example, if we assume a network with n clusters, where each cluster Ck; k D
1; 2; ; n; and has mn elements, denoted as ek1; ek2; ; ekmk
, then the standard form for a
supermatrix can be expressed as
Table I. Analytic hierarchy process.
Importance Definition
1 Equal importance
3 Moderate importance
5 Strong importance
7 Very strong importance
9 Extreme importance
2, 4, 6, 8 Intermediate values
DOI: 10.1002/dac

W D
C1 : : : Ck : : : Cn
e11 : : : e1m1
: : : ek1 : : : ekmk
: : : en1 : : : enmn
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
e11
C1
::: W11 : : : W1k : : : W1n
e1m1
:::
:::
:::
:::
:::
:::
ek1
Ck
::: Wk1 : : : Wkk : : : Wkn
ekmk
:::
:::
:::
:::
:::
:::
en1
Cn
::: Wn1 : : : Wnk : : : Wnn
enmn
(1)
Step 4. Selection of the best alternatives: If the supermatrix formed in step 3 covers the whole
network, then the priority weights of the alternatives can be found in the column of alter-
natives in the normalized supermatrix. Otherwise, additional calculations are required in
order to obtain the overall priorities of the alternatives. The alternative with the largest
overall priority should be selected, as it is the best alternative as determined by the
calculations made using matrix operations.
3.2. The trapezoidal interval-valued fuzzy numbers
The concept of fuzzy logic was introduced by Zadeh [35] and is used to make a decision from
indeterminate and approximate information. A fuzzy number is represented by a set of real values
representing an uncertain quantity and a convex normalized continuous function, which estimates
the degree of membership for each value in the subset. Triangular or trapezoidal fuzzy numbers are
frequently used to represent uncertain information. A trapezoidal fuzzy number can be defined as a
vector x D .x1; x2; x3; x4; v OA
/ with membership function:
.x/ D
8
ˆˆˆˆ<
ˆˆˆˆ:
x x1
x2 x1
; if x1 6 x < x2I
v OA
; if x2 6 x 6 x3I
x x4
x3 x4
; if x3 < x 6 x4I
0; otherwise.
(2)
where x1 < x2 < x3 < x4 and v OA
2 Œ0; 1.
An interval-valued fuzzy number (IVFN) introduced by Sambuc [36] is defined as ADŒAL
; AU

consisting of the lower AL
and the upper AU
fuzzy numbers. IVFNs replace the crisp membership
values by intervals in Œ0; 1. They were proposed because fuzzy information can be better expressed
by intervals than by single values. Liu and Jin [37] and Cornelis et al. [38] suggest that IVFNs
are useful in multiple criteria decision-making problems and particularly in cases where attribute
values are in the form of linguistic expressions. Therefore, Ashtiani et al. [39] propose an extension
of the fuzzy TOPSIS method using interval-valued triangular fuzzy numbers. Moreover, Liu and
Jin [37] propose a decision-making method using weighted geometric aggregation operators on
attribute values expressed in the form of interval-valued trapezoidal fuzzy numbers. According to
the definition in [39], an IVFN A is defined as follows:
A D
®
x; L
A.x/; U
A .x/
¯
(3)
L
A.x/; U
A .x/ W X ! Œ0; 18x 2 X; L
A.x/ < U
A .x/ (4)
DOI: 10.1002/dac

E. SKONDRAS ET AL.
Figure 1. The interval-valued trapezoidal fuzzy numbers.
O A.x/ D L
A.x/; U
A .x/ (5)
A D ¹.x; O A.x//º; x 2 . 1; 1/ (6)
In particular, the interval-valued trapezoidal fuzzy number deﬁned in [40] is the most general form
of fuzzy number (Figure 1) and can be represented as A D ŒAL
; AU
D xL
1 ; xL
2 ; xL
3 ; xL
4 ; vAL ;
xU
1 ; xU
2 ; xU
3 ; xU
4 ; vAU , where 0 6 xL
1 6 xL
2 6 xL
3 6 xL
4 6 1, 0 6 xU
1 6 xU
2 6 xU
3 6 xU
4 6 1,
0 6 vAL 6 vAU 6 1 and AL
AU
. The operational rules of the interval-valued trapezoidal fuzzy
numbers are deﬁned in [40].
3.3. The trapezoidal interval-valued fuzzy TOPSIS algorithm
The Technique for order preference by similarity to ideal solution (TOPSIS) introduced by Hwang
and Yoon [41] is based on the concept that the best alternative should have the shortest distance from
the positive ideal solution and the longer distance from the negative ideal solution. In the present
work, network selection is performed using a proposed fuzzy version of TOPSIS, namely TFT. This
method assumes that the linguistic values of criteria attributes are represented by interval-valued
trapezoidal fuzzy numbers.
Suppose A D ¹A1; A2; : : : ; Anº is the set of possible alternatives, C D ¹C1; C2; : : : ; Cnº is the
set of criteria, and w1; w2; : : : ; wm are the weights of each criterion. The steps of the method are
as follows:
Step 1. Construction of the decision matrix: Each xij element of the n m decision matrix
D is an interval-valued trapezoidal fuzzy number, which expresses the performance of
alternative i for criterion j . Thus,
D D
C1 : : : Cm
A1 x11 : : : x1m
:::
:::
:::
:::
An xn1 : : : xnm
(7)
where xij D
h
xL
ij1; xL
ij 2; xL
ij 3; xL
ij 4; vL
ij
Á
; xU
ij1; xU
ij 2; xU
ij 3; xU
ij 4; vU
ij
Ái
In case there are Q decision makers, the decision matrix and the criteria weights
include the average of the performance values and weights, respectively, of the decision
makers. Hence, assuming that for the k-th decision maker, xijk is the performance of
alternative i for criterion j , and wjk is the importance weight for criterion j ; the average
of the performance values and weights are given by
DOI: 10.1002/dac

xij D
1
Q
QX
kD1
xijk
D
2
4
0
@ 1
Q
QX
kD1
xL
ijk1;
1
Q
QX
kD1
xL
ijk2;
1
Q
QX
kD1
xL
ijk3;
1
Q
QX
kD1
xL
ijk4; vL
ijk
1
A ;
0
@ 1
Q
QX
kD1
xU
ijk1;
1
Q
QX
kD1
xU
ijk2;
1
Q
QX
kD1
xU
ijk3;
1
Q
QX
kD1
xU
ijk4; vU
ijk
1
A
3
5
(8)
and
wj D
1
Q
QX
kD1
wjk: (9)
Step 2. Normalization of the decision matrix: Consider that ˝b is the set of beneﬁts attributes
and ˝c is the set of costs attributes. Then, the elements of the normalized decision matrix
are computed as
(a)
rij D
"
xL
ij1
bj
;
xL
ij 2
bj
;
xL
ij 3
bj
;
xL
ij 4
bj
; vL
ij
!
;
xU
ij1
bj
;
xU
ij 2
bj
;
xU
ij 3
bj
;
xU
ij 4
bj
; vU
ij
!#
(10)
where bj D maxi xU
ij 4 for each j 2 ˝b.
(b)
rij D
"
cj
xL
ij 4
;
cj
xL
ij 3
;
cj
xL
ij 2
;
cj
xL
ij1
; vL
ij
!
;
cj
xU
ij 4
;
cj
xU
ij 3
;
cj
xU
ij 2
;
cj
xU
ij1
; vU
ij
!#
(11)
where cj D mini xL
ij 4 for each j 2 ˝c.
Step 3. Construction of the weighted normalized decision matrix: The weighted normalized deci-
sion matrix is constructed by multiplying each element of the normalized decision matrix
rij with the respective weight wj according to the formula.
uij D rL
ij1 wj ; rL
ij 2 wj ; rL
ij 3 wj ; rL
ij 4 wj ; vL
ij ;
rU
ij1 wj ; rU
ij 2 wj ; rU
ij 3 wj ; rU
ij 4 wj ; vU
ij
(12)
Step 4. Determination of the positive and negative ideal solution: The positive ideal solution is
deﬁned as
XC
D
h
xCL
ij1 ; xCL
ij 2 ; xCL
ij 3 ; xCL
ij 4 ; vCL
ij
Á
; xCU
ij1 ; xCU
ij 2 ; xCU
ij 3 ; xCU
ij 4 ; vCU
ij
Ái
D
"
^
i
uL
ij1;
^
i
uL
ij 2;
^
i
uL
ij 3;
^
i
uL
ij 4; vL
ij
!
;
^
i
uU
ij1;
^
i
uU
ij 2;
^
i
uU
ij 3;
^
i
uU
ij 4; vU
ij
!#
(13)
where
V
i
Á maxi in case j 2 ˝b and
V
i
Á mini in case j 2 ˝c.
DOI: 10.1002/dac

E. SKONDRAS ET AL.
The negative ideal solutions are deﬁned accordingly as
X D x L
ij1 ; x L
ij 2 ; x L
ij 3 ; x L
ij 4 ; v L
ij ; x U
ij1 ; x U
ij 2 ; x U
ij 3 ; x U
ij 4 ; v U
ij
D
"
_
i
uL
ij1;
_
i
uL
ij 2;
_
i
uL
ij 3;
_
i
uL
ij 4; vL
ij
!
;
_
i
uU
ij1;
_
i
uU
ij 2;
_
i
uU
ij 3;
_
i
uU
ij 4; vU
ij
!#
(14)
where
W
i Á mini in case j 2 ˝b and
W
i Á maxi in case j 2 ˝c.
Step 5. Measurement of the distance of each alternative from the ideal solutions: The distances
of each alternative from the positive ideal solution are evaluated as follows:
dC
i1 D
mX
j D1
²
1
4
Ä
uL
ij1 xCL
ij1
Á2
C uL
ij 2 xCL
ij 2
Á2
C uL
ij 3 xCL
ij 3
Á2
C uL
ij 4 xCL
ij 4
Á2
³1
2
(15)
dC
i2 D
mX
j D1
²
1
4
Ä
uU
ij1 xCU
ij1
Á2
C uU
ij 2 xCU
ij 2
Á2
C uU
ij 3 xCU
ij 3
Á2
C uU
ij 4 xCU
ij 4
Á2
³1
2
(16)
Likewise, the distances of each alternative from the negative ideal solution are estimated
di1 D
mX
j D1
²
1
4
h
uL
ij1 x L
ij1
2
C uL
ij 2 x L
ij 2
2
C uL
ij 3 x L
ij 3
2
C uL
ij 4 x L
ij 4
2
i³1
2
(17)
di2 D
mX
j D1
²
1
4
h
uU
ij1 x U
ij1
2
C uU
ij 2 x U
ij 2
2
C uU
ij 3 x U
ij 3
2
C uU
ij 4 x U
ij 4
2
i³1
2
(18)
Consequently, similar to [39], the distance of the alternatives from the positive and nega-
tive ideal solutions are expressed by intervals such as ŒdC
i1 ; dC
i2 and Œdi1; di2, instead of
single values. In this way, less information is lost.
Step 6. Calculation of the relative closeness: The relative closeness of the distances from the
ideal solutions are computed as
RCi1 D
di1
dC
i1 C di1
(19)
and
RCi2 D
di2
dC
i2 C di2
(20)
The compound relative closeness is obtained from the average of the aforementioned
values
RCi D
RCi1 C RCi2
2
(21)
Step 7. Alternatives ranking: The alternatives are ranked according to their RCi values. The best
alternative is the one with the highest RCi value.
DOI: 10.1002/dac

TableII.QoSclassmappingandservice-levelagreements.
LTEQCIWiMAXIEEE802.11eRequiredRequiredRequiredRequired
(type/priority)QoSclassQoSclassthroughputpacketlossdelay(ms)jitter(ms)Services
1(GBR/2)UGS/ertPS(802.16e–802.16m)AC_VO200Kbps10210050VoIP,CVideo,BStreaming,RTGaming,Web
3(GBR/3)UGSAC_VO250Kbps1035040CVideo,BStreaming,RTGaming,Web
2(GBR/4)UGSAC_VI8Mbps1036550CVideo,BStreaming,Web
4(GBR/5)rtPSAC_VI8Mbps1056560CVideo,BStreaming,Web
6(Non-GBR/6)nrtPSAC_BE2.5Mbps105200N/ABStreaming,Web
7(Non-GBR/7)nrtPSAC_BE2Mbps105160100BStreaming,Web
8(Non-GBR/8)BEAC_BE1.5Mbps103300N/A
Web
9(Non-GBR/9)BEAC_BE1.5Mbps105300N/A
LTE,long-termevolution;QCI,QoSclassindicator;UGS,unsolicitedgrantservice;GBR,guaranteedbitrate.
DOI: 10.1002/dac

E. SKONDRAS ET AL.
4. SIMULATION SETUP AND RESULTS
In our experiments, we consider a heterogeneous network environment consisting of a number of
long-term evolution (LTE), WiMAX, and WiFi networks. Each network can provide at least one of
the following ﬁve service types: Voice-over-Internet protocol (VoIP), conversational video (CVideo),
buffered streaming (BStreaming), real time gaming (RTGaming), and Web browsing. In order to
allow service continuity, QoS mapping among the QoS classes of the different access technologies
is required. Table II shows this mapping relation among the different technologies.
Four SLAs are deﬁned, with SLA1 having the highest service priority and SLA4 having the lowest
service priority. SLA1 supports all service types, as well as provides the best values for QoS and
policy decision criteria. SLA2 supports less service types, by not providing support for the VoIP and
real time gaming services. Additionally, it provides slightly worse decision criteria values than those
offered by the SLA1. SLA3 supports only the buffered streaming and the Web browsing services
and satisfactory QoS characteristics and policies. Whereas the low price SLA4 supports only the
Web browsing service while providing acceptable decision criteria values.
Network selection weights
per service & SLA
Network QoS
Characteristics
Network Policy
Characteristics
Throughput
Delay
Jitter
Packet Loss
Service Reliability
Security
Price
Goal
Criteria Groups
Criteria
Figure 2. The analytic network process network model.
Throughput
Delay Jitter
Packet loss
Service
Reliability
Price
Security
Figure 3. Relations of criteria.
Table III. The analytic network process supermatrix for SLA1 Voice-over-Internet protocol service.
Throughput Delay Jitter Packet loss Price Reliability Security
Throughput 0.015625 0.015625 0.015625 0.015625 0.015625 0.015625 0.015625
Delay 0.328125 0.328125 0.328125 0.328125 0.328125 0.328125 0.328125
Jitter 0.328125 0.328125 0.328125 0.328125 0.328125 0.328125 0.328125
Packet loss 0.328125 0.328125 0.328125 0.328125 0.328125 0.328125 0.328125
Price 0.05 0.05 0.05 0.05 0.019607 0.05 0.0625
Reliability 0.95 0.95 0.95 0.95 0.759804 0.95 0
Security 0 0 0 0 0.220588 0 0.9375
DOI: 10.1002/dac

The ANP method is applied in order to estimate the weights of network selection criteria per
service type and SLA. Figure 2 depicts the ANP network model. Criteria are classiﬁed into two
groups, namely the QoS and the policy characteristics. The QoS characteristics group contains net-
work performance related criteria including throughput, delay, jitter, and packet loss while the policy
characteristics group contains operator deﬁned rules such as price, security, and service reliabil-
ity. Service reliability determines the ability for service constraints satisfaction and optimization of
performance when a network is congested. Pairwise comparison decision matrices are created on
Table IV. The analytic network process weighted supermatrix for SLA1 Voice-over-Internet protocol service.
Throughput 0.0078125 0.0078125 0.0078125 0.0078125 0.0078125 0.0078125 0.0078125
Delay 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062
Jitter 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062
Packet loss 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062
Price 0.025 0.025 0.025 0.025 0.00980392 0.025 0.03125
Reliability 0.475 0.475 0.475 0.475 0.379902 0.475 0
Security 0 0 0 0 0.110294 0 0.46875
Table V. The analytic network process limit supermatrix for SLA1 Voice-over-Internet protocol service.
Throughput 0.0078125 0.0078125 0.0078125 0.0078125 0.0078125 0.0078125 0.0078125
Delay 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062
Jitter 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062
Packet loss 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062 0.164062
Price 0.0246573 0.0246573 0.0246573 0.0246573 0.0246573 0.0246573 0.0246573
Reliability 0.470224 0.470224 0.470224 0.470224 0.470224 0.470224 0.470224
Security 0.0051191 0.0051191 0.0051191 0.0051191 0.0051191 0.0051191 0.0051191
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
VoIP Conversational Video Buffered Streaming Real Time Gaming Web
Weight
SLA1
Throughput
Delay
Jitter
Packet Loss
Price
Reliability
Security
Figure 4. Criteria weights for SLA1.
DOI: 10.1002/dac

E. SKONDRAS ET AL.
the basis of relations among the seven selection criteria depicted in Figure 3. Then, these pairwise
comparison decision matrices are used to evaluate the priority vectors of criteria and form the super-
matrix per service type and SLA. Subsequently, the weighted supermatrices and, ﬁnally, the limit
supermatrices are obtained. Indicatively, for the SLA1 VoIP service, the initial, the weighted, and
the limit supermatrices are presented in Tables III–V, respectively.
The criteria weights per service and SLA obtained by the limit supermatrices are presented in
Figures 4–7. As illustrated, the weights are proportional to the constraints of each service as well
as to the agreements of each SLA. In particular, the weight of the price criterion is low for SLA1,
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Conversational Video Buffered Streaming Web
Weight
SLA2
Throughput
Delay
Jitter
Packet Loss
Price
Reliability
Security
0
0.1
0.2
0.3
0.4
0.5
WebBuffered Streaming
Weight
SLA3
Throughput
Delay
Jitter
Packet Loss
Price
Reliability
Security
Figure 6. Criteria Weights for SLA3.
DOI: 10.1002/dac

0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Web
Weight
SLA4
Throughput
Delay
Jitter
Packet Loss
Price
Reliability
Security
Table VI. Linguistic terms and the corresponding interval-valued trapezoidal
fuzzy numbers.
Linguistic term Interval-valued trapezoidal fuzzy number
Absolutely poor [(0.0, 0.0, 0.0, 0.0, 0.8), (0.0, 0.0, 0.0, 0.0, 1)]
Very poor [(0.01, 0.02, 0.03, 0.07, 0.8), (0.0, 0.01, 0.05, 0.08, 1)]
Poor [(0.04, 0.1, 0.18, 0.23, 0.8), (0.02, 0.08, 0.2, 0.25, 1)]
Medium poor [(0.17, 0.22, 0.36, 0.42, 0.8), (0.14, 0.18, 0.38, 0.45, 1)]
Medium [(0.32, 0.41, 0.58, 0.65, 0.8), (0.28, 0.38, 0.6, 0.7, 1)]
Medium good [(0.58, 0.63, 0.8, 0.86, 0.8), (0.5, 0.6, 0.9, 0.92, 1)]
Good [(0.72, 0.78, 0.92, 0.97, 0.8), (0.7, 0.75, 0.95, 0.98, 1)]
Very good [(0.93, 0.98, 1, 1, 0.8), (0.9, 0.95, 1, 1, 1)]
Absolutely good [(1, 1, 1, 1, 0.8), (1, 1, 1, 1, 1)]
Table VII. Relation of the network QoS characteristics and linguistic terms for Voice-over-Internet protocol.
Linguistic term Throughput range (Kbps) Delay range (ms) Jitter range (ms) Packet loss range
Absolutely poor 6 164 > 116 > 65 > 0:4
Very poor 165–174 111–115 55–64 > 0:2–0.4
Poor 175–184 106–110 45–54 >10 1–<0.2
Medium poor 185–194 100–105 40–44 10 1
Medium 195–204 95–99 35–49 10 2
Medium good 205–214 86–94 30–34 10 3
Good 215–224 66–85 25–29 10 4
Very good 225–239 41–65 20–24 10 5
Absolutely good > 240 6 40 6 20 6 10 6
in which the service reliability and the network QoS characteristics are considered as the most
important factors. In SLA2, the price criterion is more important than in SLA1, thus the respective
weight is greater than that of SLA1. Consequently, the weights of the service reliability and QoS
characteristics criteria in SLA2 are lower compared to the relative weights of SLA1. In SLA3,
DOI: 10.1002/dac

E. SKONDRAS ET AL.
Table VIII. The available networks of SLA1 and SLA2.
SLA Service Network Throughput Delay Jitter Packet loss Price Service reliability Security
SLA1 VoIP LTE 1 MG AG VG VG VP AG VG
LTE 2 AG MG AG MG VP VG AG
WiMAX 1 M M MP AG P VG AG
WiMAX 2 G G G G P AG VG
WiFi 1 VG VG MG AG MP G G
WiFi 2 MG M MG VG MP MG MG
WiFi 3 M MP M AG MP G G
CVideo LTE 1 MP MG VG G AP AG VG
LTE 2 AG AG AG VG AP VG AG
WiMAX 1 MP M MG AG AP VG AG
WiMAX 2 MG MG G AG VP AG VG
WiFi 1 M MG M VG P G G
WiFi 2 VG VG VG AG P MG MG
WiFi 3 G G M VG P G G
BStreaming LTE 1 M G VG VG AP AG VG
LTE 2 VG VG AG AG AP VG AG
WiMAX 1 M MG MG VG VP VG AG
WiMAX 2 MG G MG G P AG VG
WiFi 1 VG G M AG P G G
WiFi 2 AG AG G VG P MG MG
WiFi 3 G VG VG AG MP G G
RTGaming LTE 1 G AG AG VG VP AG VG
LTE 2 G MG VG AG VP VG AG
WiMAX 1 MP MG G AG P VG AG
WiMAX 2 VG AG AG VG VP AG VG
WiFi 1 AG VG VG VG VP G G
WiFi 2 M M MG AG MP MG MG
WiFi 3 P M M AG MP G G
Web LTE 1 AG AG AG AG VP AG VG
LTE 2 MG M G VG MP VG AG
WiMAX 1 G M G AG P VG AG
WiMAX 2 VG G VG AG P AG VG
WiFi 1 MG MP MG VG MP G G
WiFi 2 VG G M VG MP MG MG
WiFi 3 AG VG AG AG MP G G
SLA2 CVideo LTE 1 MG G VG AG MP G G
LTE 2 MP M MG VG M G G
WiMAX 1 M MG G AG MP MG MG
WiMAX 2 MP M M AG M MG MG
WiFi 2 G VG VG AG MG G M
WiFi 3 MP G M VG MG P M
BStreaming LTE 1 M G G VG MP G G
LTE 2 MG MG AG G MP G G
WiMAX 1 M MG MP AG MP MG MG
WiMAX 2 G G MG VG MP MG MG
WiFi 1 G VG MG AG MP MP MP
WiFi 2 AG AG VG VG MP M M
WiFi 3 MG VG VG AG M P M
Web LTE 2 M MP MG VG M G G
WiMAX 1 MG M G AG MG MG MG
WiMAX 2 VG G AG AG M MG MG
WiFi 1 MG MP M VG MG MP MP
WiFi 2 MG M G VG MG M M
WiFi 3 VG VG AG AG MG P M
AG, absolutely poor; VP, very poor; P, poor; MP, medium poor; M, medium; MG, medium good; G, good; VG,
very good; AG, absolutely good; SLA, service-level agreement; LTE, long-term evolution.
DOI: 10.1002/dac

the weights of price and service reliability criteria are balanced as they are almost of equivalent
importance. Finally, in SLA4, the price is the most important criterion resulting in a high estimated
weight value.
Ranking of the networks alternatives is performed using the TFT algorithm described in Section 3.
The weights of network selection criteria are obtained from Figures 4–7. The linguistic terms for
the criteria attributes are represented by interval-valued trapezoidal fuzzy numbers as shown in
Table VI. Network policy specifications are expressed directly using linguistic terms. Additionally,
crisp values of network QoS characteristics are converted into linguistic terms, which correspond to
specific ranges of values per service type. Specifically, Table VII presents a relative example for the
VoIP service, illustrating the correspondence between ranges of network QoS characteristics values
and linguistic terms.
The available-candidate networks in our simulations at the time of network selection per service
and SLA, as well as, their specifications expressed by linguistic terms, are depicted in Tables VIII
and IX.
The case of having several services of different QoS constraints running at the user site is being
addressed, and network selection is performed in a way satisfying multiple groups of criteria per
user. Specifically, we consider the case where nine users need to select a network that satisfies
the requirements of their services as presented in Table X and at the same time comply with their
respective SLA agreements. To achieve this goal, the proposed TFT algorithm is applied for each
user, and the available networks are ranked as shown in Figure 8. The positive and negative ideal
solutions are represented by unary and null trapezoidal fuzzy numbers, respectively, to eliminate the
ranking abnormality problem.
From the obtained results, it is clear that the ranking of the network alternatives is in accordance
with the users expectations. For example, user 1 requiring increased QoS provisioning selects LTE 1
network, which guarantees the best QoS characteristics and service reliability. As Figure 8 depicts,
LTE 1 achieves higher ranking than the other networks, because of the high values of the QoS
characteristics and service reliability factors bearing higher importance according to the relative
ANP weights in SLA1. On the contrary, user 9, whose prior selection criterion is the price of the
Table IX. The available networks of SLA3 and SLA4.
SLA Service Network Throughput Delay Jitter Packet loss Price Service reliability Security
SLA3 BStreaming LTE 1 M MG G VG MG MP MP
LTE 2 G G M AG MG M M
WiMAX 1 M G MP VG MG M M
WiFi 1 G G MG AG G VP P
WiFi 2 G AG G VG MG VP P
WiFi 3 MG VG MG AG G VP P
Web LTE 1 MG MP M G G MP MP
LTE 2 M M G VG G M M
WiMAX 1 MG M M AG G M M
WiMAX 2 VP M AG AG VG P MP
WiFi 1 MG MP M AG G VP P
WiFi 2 AP AP VP G VG VP P
SLA4 Web LTE 1 MP M M VG VG P P
LTE 2 M M G MG VG P MP
WiMAX 1 VP P M AG AG VP VP
WiMAX 2 P MP MP G VG VP P
WiFi 1 MG G M G AG AP AP
WiFi 2 AP AP VP G AG AP VP
WiFi 3 AP VP P AG AG AP VP
AG, absolutely poor; VP, very poor; P, poor; MP, medium poor; M, medium; MG, medium good; G, good; VG,
very good; AG, absolutely good; SLA, service-level agreement; LTE, long-term evolution.
DOI: 10.1002/dac

E. SKONDRAS ET AL.
Table X. The required services per user.
User SLA Required services
1 SLA1 -VoIP
2 SLA1 -VoIP,-RTGaming, -BStreaming, -Web
3 SLA1 -VoIP, -RTGaming
4 SLA1 -RTGaming
5 SLA2 -CVideo
6 SLA2 -BStreaming
7 SLA3 -BStreaming, -Web
8 SLA3 -Web
9 SLA4 -Web
SLA, service-level agreement; VoIP, Voice-over-Internet protocol.
0
0.05
0.1
0.15
0.2
User 1 User 2 User 3 User 4 User 5 User 6 User 7 User 8 User 9
NetworkScore
Trapezoidal Fuzzy Topsis Results
LTE 1
LTE 2
WiMAX 1
WiMAX 2
WiFi 1
WiFi 2
WiFi 3
Figure 8. The TFT results.
service, selects the WiFi 1 network, which satisfies his or her requirements in respect of his or her
SLA agreement.
4.1. Performance evaluation of the TFT algorithm
The performance of TFT algorithm was evaluated against the original TOPSIS method, as well as,
the method presented in [15], the FAE method. The FAE method calculates the criteria weights
using the fuzzy AHP and performs the network selection by applying the ELECTRE algorithm. We
consider the scenario of the nine users of Table X. A critical weakness of the TOPSIS and FAE
is that they do not support users with more than one service. In these cases, the TOPSIS and FAE
methods consider only the most demanding service of the user. Specifically, for users 2 and 3, they
applied only for the VoIP service; for user 7, it is applied only for the BStreaming service; and for
the rest of the users, the methods are applied, respectively, for each single user service defined in
Table X.
Table XI presents the networks classification performed by the proposed TFT, the TOPSIS, and
the FAE algorithms, respectively. From the analysis of the results, we conclude that when a user
has only one service, the methods usually provide similar results. However, when a user requires
multiple services, the TFT accomplishes more reliable results than the TOPSIS and FAE, because
DOI: 10.1002/dac

TableXI.Networksclassiﬁcationinrespectoftrapezoidalinterval-valuedFuzzyTOPSIS(TFT),techniquefororderpreferencebysimilaritytoidealsolution(TOPSIS)
(T),andFuzzyAHP–ELECTRE(FAE)results.
NetworksUser1User2User3User4User5User6User7User8User9
MethodTFTTFAETFTTFAETFTTFAETFTTFAETFTTFAETFTTFAETFTTFAETFTTFAETFTTFAE
LTE1111211111211422425425214464
LTE2333333333442236114131325334
WiMAX1555555555554343547214131673
WiMAX2224124224121554232———553554
WiFi1462462462333———663353442111
WiFi2646746646675111351542666744
WiFi3776676776766665776——————222
Theboldvaluesrepresentthebestalternativeprovidedbyeachmethod.
DOI: 10.1002/dac

E. SKONDRAS ET AL.
Figure 9. TFT’s networks ranking in case of networks environment changes.
DOI: 10.1002/dac

it considers the weights of each service. For example, the results concerning user 1 using only the
VoIP service are similar for TFT and TOPSIS methods with the exception of the evaluation sequence
of the WiFi 1 and WiFi 2 networks. Also, FAE accomplishes quite similar network rates with the
TFT and TOPSIS methods for this user. Nevertheless, TFT succeeds more reliable results for user
4, compared with TOPSIS and FAE methods. In this case, only the RTGaming service is used, and
the most important criteria are service reliability, throughput, and delay. TFT selects the WiMAX 2
network, which provides AG for service reliability, VG for throughput, and AG for delay criterion.
On the other hand, TOPSIS selects the LTE 1 network, which has similar values with the WiMAX 2
for service reliability and delay criteria but worse performance for throughout criterion by providing
G instead of VG. Moreover, FAE does not provide a clear choice for user 4 and results to equal
evaluation sequence for both WiMAX 2 and LTE 1 networks. Finally, the classification of networks
obtained from the three methods is quite different for user 7 who requests both BStreaming and
Web browsing services, and the TFT accomplishes more reliable results by taking into account the
weights of both services.
4.2. Sensitivity analysis of the TFT
In this section, the sensitivity of the TFT is evaluated when the number of the available access net-
works changes frequently. Particularly, we consider three different network configuration scenarios
for the users defined in Table X. In the first scenario, all networks defined in Tables VIII and IX are
available. In the second and third scenarios, the LTE 1 and the WiFi 2 networks, respectively, are
not reachable. The graphs of Figure 9 include three column types of different pattern indicating the
ranking of network alternatives in each case. Particularly, in the first case, user 1 selects the LTE 1
network. In the second case, the remaining networks improve their ranking order thus user 1 selects
the WiMAX 2 network. Furthermore, in the third case, only the last rated WiFi 3 network increases
its rank, because the WiFi 2 network preceded WiFi 3 in the other two cases. Similar behavior is
observed in the ranking of network alternatives for the other users. From the aforementioned analy-
sis, we conclude that ranking results of the proposed method are normally adjusted with respect to
the heterogeneous network environment changes, highlighting thus the methods sensitivity.
5. CONCLUSIONS
Network selection in heterogeneous networks is a complex task because it takes into account
different parameters with different relative importance, such as the network and the application
characteristics, the user preferences, and the service cost. This paper presents a network selection
method that takes into account the network QoS characteristics policies, application requirements,
and different types of users SLAs to select the optimal network that will satisfy simultaneously all
the applications’ requirements and user’s preferences running on a mobile user’s device.
More specifically, the proposed method employs two MADM algorithms: the ANP for criteria
weights calculation and the TFT for accomplishing the overall rating of the network technologies.
The ANP is selected to determine the relative importance and the dependence of the criteria. As
selection criteria, we consider the network QoS parameters, service constraints, user requirements,
and provider policies. These criteria are easily configured and represented by interval-valued trape-
zoidal fuzzy numbers. Then, the TFT algorithm is applied to calculate the overall rating of the
available networks.
Performance evaluation of the TFT showed that when a user has only one service, it provides
similar results to the original TOPSIS and FAE methods. However, when a user requires multiple
services, the TFT performs better by satisfying multiple groups of criteria per user because the
original TOPSIS and FAE methods cannot support more than one services. Furthermore, according
to the sensitivity analysis of results, it is showed that the described method does not suffer from the
ranking abnormality problem; thus, the results are normally adjusted to the heterogeneous network
environment changes.
Our future work will be focused on the design of a complete solution for the VHO process with
the proposed method as the main mechanism for the network selection step.
DOI: 10.1002/dac

E. SKONDRAS ET AL.
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DOI: 10.1002/dac

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