AN INTELLIGENT CALL ADMISSION CONTROLLER FOR GUARANTEED QOS IN 4G MOBILE NETWORKS

International Journal on Soft Computing (IJSC) Vol.8, No. 3/4, November 2017
DOI:10.5121/ijsc.2017.8403 21
AN INTELLIGENT CALL ADMISSION CONTROLLER
FOR GUARANTEED QOS IN 4G MOBILE NETWORKS
Uduak Umoh 1
, Daniel Asuquo2
, Imoh Eyoh3
and Margaret Offisong4
1,2,4
Department of Computer Science, University of Uyo, Akwa Ibom State, Nigeria
3
ASAP Research Group, University of Nottingham Nottingham, United Kingdom
ABSTRACT
Call admission control (CAC), a resource management function, is required to regulate network access to
provide the required levels of QoS to emerging services in Fourth Generation (4G) mobile networks.
However, CAC is one of the challenging issues for quality of service (QoS) due to imprecise, uncertain and
inaccurate measurements of network data. Although type-1 fuzzy system (T1FLS) can handle the
uncertainties related to imprecise data, it cannot adequately handle new problems posed by the complex
nature of data traffic and diversity of the QoS requirements of data users. This is because T1FLS is
characterised by precise membership functions. This study presents an intelligent CAC controller for 4G
network using interval type-2 fuzzy logic (IT2FL) for providing guaranteed QoS requirements. The IT2FLS
with fuzzy membership functions can fully cope with uncertainties associated with such dynamic network
environments by raising its accuracy for a better performance. The Karnik–Mendel (KM) iterative
algorithm and Wu-Mendel (WM) approach are explored for computing the centroid and to derive inner-
and outer-bound sets for the type-reduced set of IT2FS respectively. The study also implements a T1FLS –
CAC for comparison with the KM and WM methods. The empirical comparison is made on the designed
system with synthetic datasets. Simulation and analyses of results indicate that IT2FLS-CAC using WU
approach achieves minimal call blocking probability and provides high performance in CAC decision
making with a more reduced root mean square error (RMSE) than IT2FLS-CAC using KM and IT1FLS
approaches.
KEYWORDS
Interval type-2 fuzzy logic; Admission control system; 4G Mobile Networks; Computational complexity
1. INTRODUCTION
Wireless access has seen exponential growth in past decades and transmission of multimedia
applications and services over wireless networks is gaining popularity. This has brought about the
emergence of different wireless technologies such as second generation (2G), third generation
(3G), beyond 3G (B3G), and 4G networks to satisfy demands for mobile services and internet
access. In 4G networks, different types of wireless networks are interconnected to support
handoff from one technology to another, with the goal of replacing the entire core of cellular
networks with a single worldwide cellular network. These wireless systems are designed
independently and targeting different service types, data rates, and users, and thus require an
intelligent management approach. Effective, secure and efficient operations and resource
management are the major challenges facing 4G Networks. Also, these networks are associated
with much uncertainty and imprecision due to escalating number of access points, constant
change in propagation channels, random mobility of users, etc. Due to the tremendous growth and
complex nature of 4G networks, it is difficult to manage. In order to control and mange such a
complex network, CAC is required [1-5].

22
CAC is an important resource management function required to regulate network access by
restricting access to the network resources to provide the required levels of QoS to emerging
services. CAC accepts a new connection request without disrupting the service quality of ongoing
connections to ensure fair admission control for efficient service delivery to all categories of call
requests. CAC is widely researched in wireless networks as an important tool for QoS
provisioning. QoS evaluation is necessary for determining the efficiency of CAC scheme in
mobile multimedia networks in terms of signal quality, packet delay, jitter and loss rate, call
blocking and dropping probabilities, and transmission rate, etc. The main function of CAC is to
decide, at the time of call arrival, whether or not a new call should be admitted into the network
or not. A new call is accepted only if QoS constraints are fulfilled without affecting the QoS
constraints of the existing calls in the network. Maintaining QoS parameters is necessary for
efficient admission control in mobile multimedia networks. Several methods have been used to
improve QoS across 4G networks. These methods include Markov models, queuing models, and
expert systems, etc. In recent years, type-1 fuzzy logic systems (T1FLS) are widely used to
improve the capability of existing CAC methods in mobile networks [6-13].
Type-1 fuzzy set (T1FS) was introduced by Zadeh [11] in 1965 to tackle uncertainty and
imprecision, which widely exist in real-life problems.T1FLSs have the ability to process
information using linguistic variables and make decision with imprecise, vague, ambiguous,
uncertain data. T1FLSs have achieved great success in many different real world applications
including wireless sensor networks, Asynchronous Transfer Mode (ATM) networks, wireless
cellular networks, and congestion control in 4G Networks [14-21]. However, T1FLS cannot
adequately handle the effect of the uncertainties posed by the complex nature of data traffic and
by the diversity of the QoS requirements of data users. This is because T1FLS is characterized by
precise membership functions. Type-2 fuzzy logic (T2FL), an extension of T1FL, provides
additional design degrees of freedom with membership functions that are themselves fuzzy.
T2FLS can cope fully in situations where lots of uncertainties are present and have the potential
to provide better performance than T1FLS. However, due to computational complexity of using a
general T2FLS, IT2FLS, a simplified version of T2FLS is used. IT2FLS provides very
manageable computation making it quite practical. Recently, T2FLSs and IT2FLSs are applied as
useful techniques to handle all forms of uncertainties both in classification, prediction and control
and the results are promising and very encouraging [22-33]. Consequently, IT2FLSs are widely
applied in various areas because of their abilities to simplify type-2 fuzzy logic controllers
(T2FLCs) [34-36].
An IT2FLS is made up of five components namely, fuzzifier, rule base, inference engine, type-
reduction and defuzzifier. An iterative Karnik-Mendel (KM) algorithm can be explored to
perform type-reduction. An extended version of type-1 defuzzification operation technique is
usually applied on T2FSs case of the IT2FLS to obtain a T1FS at the output. The T1FS so
obtained becomes a type-reduced set which is a collection of the outputs of all of the embedded
T1FLSs [25]. However, Karnik-Mendel (KM) algorithm is computationally complex, time-
consuming with computational overhead which can reduce the real-time performance of the
IT2FLS and also limit their application in industrial embedded controllers. To overcome the
limitations of IT2FLS in order to speed up a T2FLC, Wu and Mendel uncertainty bounds (UB)
technique is employed to approximate the type-reduced set instead of using KM algorithm
[37][23]. This approach is believed to reduce the computation cost of the type-reduction and the
memory required for the IT2FLS implementation.
This paper presents an intelligent call admission controller for 4G network using IT2FL for
providing guaranteed QoS requirements. The IT2FLS with fuzzy membership functions can fully
cope with uncertainties associated with such dynamic network environment by raising its
accuracy for a better performance.The admission decisions are made based on system parameters
like latency, packet loss, load, signal strength, and user mobility. The study employs K-M

23
algorithm to obtain the type-reduced sets, and Wu-Mendel uncertainty bound approach for
approximation of type-reduced set to estimate the uncertainty and crisp output of an IT2FLC. The
remainder of the paper is given as follows; Section 2 presents an overview of interval type-2
fuzzy logic. In section 3, an intelligent call admission controller for guaranteed QoS in a 4G
mobile network is presented. Results and discussion are given in section 4, while conclusion of
the paper is presented in section 5.
2. AN OVERVIEW OF INTERVAL TYPE-2 FUZZY LOGIC
2.1. INTERVAL TYPE-2 FUZZY SETS
According to [38], an interval type-2 fuzzy set (IT2FS) Ã is characterized as in (1):
Ã = x, u , μÃ x, u ∀ x ∈ X, ∀ u ∈Jx ⊆ [0, 1]} (1)
where x, the primary variable, has domain X; u∈U, the secondary variable, has domain Jx at each
x∈X ; Jx is called the primary membership of x and the secondary grades of Ã all equal 1 [39].
Uncertainty about Ã is conveyed by the union of all the primary memberships, which is called the
footprint of uncertainty (FOU) of Ã as shown in (2) and Figure 1.
μÃ x, u = 1, Ã = ⋃ J ∀ ∈ = { x, u : u ∈ Jx ⊆ [0, 1]} (2)
Fig 1: Interval Type-2 Fuzzy set [27]
The upper membership function (UMF) and lower membership function (LMF) of Ã are two type-
1 MFs that bound the FOU as represented in (3) and (4).
UMF = μÃ x ≡ Ã ∀$ ∈ % (3)
LMF = μÃ x ≡ Ã ∀$ ∈ % (4)
J = { x, u : u ∈ [μÃ x , μÃ x ]} (5)
where J is an interval set. We can apply set theory operations of union, intersection and
complement to easily compute for IT2FSs
2.2. INTERVAL TYPE-2 FUZZY LOGIC SYSTEMS
Figure 2 represents an IT2FLS architecture, which is a FLS that uses at least one IT2FS. It is
characterized by five components, viz; a rule-base, a fuzzification unit, an inference-engine unit,
type-reduction (TR) and defuzzification units - that are inter-connected.

24
Fig. 2: Architecture of IT2FLS [27]
The IT2FL architecture updates a T1FS by adding the type reduction component. The fuzzifier
maps a crisp input vector into T1 or IT2FSs using singleton fuzzifier. Input IT2FSs then activate
the inference engine and the rule base to produce output IT2FSs. A TR unit combines the output
sets and then performs a centroid calculation which produces an interval T1FS (type-reduced set).
The TR set is then processed by the defuzzifier to produce crisp outputs. The rules, supplied by
experts or extracted from numerical data can be expressed as a collection of IF–THEN
statements. In IT2FLS, the rule can have m inputs and n outputs or m inputs and one output as the
later is specified as in (6).
+ ' $( )* +,(
-
+./, … , +./ $1 )* +,1
-
234. 5 )* 67-
(6)
where $( , i = 1,…, m are the antecedents, 5 is the consequent of the lth rule of IT2FLS.
The +,(
’s are the MFs 897:
; $( of the antecedent part assigned of the ith input $( , The 6-
is
the MFs 8 <7=
; 5 of the consequent part assigned to the output 5>. The result of the input
and antecedent operations contained in the firing set produces an interval type-1 set as
shown in (7) [26].
(
$?
= [@?
$?
, @? $?
] ≡ [@?
, @′] (7)
where (
$?
is the antecedent of rule i and µF1
i
(xˈ) is the degree of membership of x in F.
8B,:(x) and 8B,:(x) are upper and lower MFs of 8B,:, i = 1to m respectively. The inference
engine combines the fired rules and gives a mapping from input to output in IT2FSs. The
combined output fuzzy set, 8 C7=
; 5> , is obtained by combining the fired output
consequent sets by taking the union of the lth rule fired output consequent sets.
There are two ways to perform type-reduction: firstly, by iterative KM procedure to
calculate the type-reduced fuzzy sets [25], while the second way is by Wu- Mendel
uncertainty bounds method, employed to approximate the type-reduced set [38]. After the
TR process, the type-reduced sets or the approximate type-reduced sets are then
defuzzified to obtain crisp outputs that determine the level of call admittance factor in our
case.
2.3. AN IT2FLS USING KM ALGORITHM
Five different TR techniques are described in [39], where the type-reduced set gives an interval of
uncertainty for the output of an IT2FLS. IT2FS are characterized by their left- and right-end

25
points required to compute the centroid of an IT2FS. An exact KM iterative method of TR is
performed to compute the type-reduced sets of an IT2FS which is a T1FS [23] [25] [41] [42]. TR
center-of-sets (COS) process can all be expressed in [27] [29] as
DEF $?
= [5- $?
, 5G $?
] ≡ [5-, 5G] = H … H H . . H 1/
BK∈[BK,B
K
]BL∈[BL,B
L
]ML∈NM;
K
,MO
KPML∈NM;
L
,MO
LP
∑ B:M:K
:RL
∑ B:K
:RL
(8)
where 5-
(
and 5G
(
are the left and right end points of the centroid of the consequent of the ith rule
while @(
and @
(
are the lower and upper firing degrees of the ith rule and N is the number of fired
rules.
In this paper, KM Algorithms [41] is applied to compute the end-points exactly and are presented
in (9) and (10) and the defuzzified crisp output for each output k is achieved by averaging ylk and
yrk, in (11).
5G =
∑ BO
:MO
:K
:RL
∑ BO
:K
:RL
(9)
5- =
∑ B;
:
M;
:K
:RL
∑ B;
:K
:RL
(10)
DS % =
M;TUMOT
V
(11)
2.4. AN IT2FLS USING WM UNCERTAINTY BOUNDS
The type-reduction (TR) is computationally intensive, time-consuming and associated
with output uncertainty for a real-time application of an IT2FLS. However, to overcome
the limitations of IT2FLS in order to speed up a T2FLC, Wu-Mendel uncertainty bounds
technique is employed to approximate the type-reduced set. The inner- and outer-bound
sets (called minimax uncertainty bounds) are provided for the type-reduced set to
estimate the output uncertainty of IT2FLS and directly perform defuzzification to obtain
output under certain conditions. These uncertainty bounds are 5- $?
, 5-
$?
, 5G $?
,
5G
$′ as expressed in details in [38], where 5- $′ ≤ 5- $′ ≤ 5-
$′ and 5G $?
≤
5G $?
≤ 5G
$?
. The type-reduction sets are approximated in (12) without having to
perform TR. Defuzzification is performed directly in (13) to obtain the output [23][38].
[5- $ , 5G $ ] ≈ [ 5- $ + 5- $ /2, 5G $ + 5G $ /2] (12)
The output of IT2FLS is given as;
5 $ =
[
V
[5- $ , 5G $ ] =
[
V
[ 5- $ + 5- $ /2 + 5G $ + 5G $ /2] (13)
2.5. ADVANTAGES OF IT2FL OVER T1FLC
The advantages T2FS over T1FS in representing the inputs and outputs of a FLC are summarized
as:

26
(i) T2FL applications based on T2FS have the ability to handle the numerical and linguistic
uncertainties associated with the inputs and outputs of a FLC because, T2FSs MFs are
themselves fuzzy with an FOU, thus, can offer a better performance than T1FLC.
(ii) With T2FSs, there is a reduction in the rule base size than using T1FSs due to the
uncertainty represented in the FOU in T2FSs which provides coverage of the same range
as T1FSs with a smaller number of labels. Also, we tend to experience more relative
reduction when there is an increase in FLCs [23] [34].
(iii) In T2FLC, input and output are represented by a large number of T1FSs which are
embedded in the T2FSs [33]. This allows for a detailed description of the analytical
control surface, a much smoother control surface and a response is achieved with the
addition of the extra levels of classification [34].
(iv) Given the same number of MFs, FOU in T2FSs allows a T2FLC to provide provide
outputs that cannot be achieved by T1FLCs in many applications. This is because of the
extra degrees of freedom provided by the T2Fs, thus, allows a T2FLC to model more
complex systems than T1FLC with a better control response [26].
3. AN INTELLIGENT CALL ADMISSION CONTROLLER FOR GUARANTEED
QOS IN 4G MOBILE NETWORKS
3.1. IT2FL-CAC MODEL
The IT2FL-CAC model for improved QoS in 4G mobile networks is shown in Figure 3. Due to
computational intensiveness of general T2FLSs [43], IT2FL controller, as discussed in this work,
is employed to reduce the computational burden of T2FLS and an intelligently control call
admission parameters in order to guarantee an improved QoS in 4G mobile networks. The choice
of this technique lies in its ability of IT2FLS to fully cope with uncertainty associated with
variables used in connection admission decision compared to T1FL model. Based on the impact
of QoS parameters, connection admission factor (CAF) is determined for an effective decision on
call admission and proper management of network’s resources in the 4G mobile environment.
The model in Figure 3 is made up of five components: fuzzification, knowledge engine,
inference, type-reduction and defuzzification. The system makes use of five inputs and one output
variables which include, latency (LA), Packet Loss (PL), Signal Strength (SS), Load (LD), User
Mobility (UM) and Call Admittance Factor (CAF) respectively, where the input parameters are
obtained from the knowledge engine. CAF determines the degree of acceptability or otherwise of
call request.
Fig. 3: The IT2FL-CAC model for call admission control
Type-1 Reduced
Fuzzy sets
Type-2 Fuzzy
Output sets
Fuzzification
Inference
Defuzzification
Knowledge Engine
Knowledge Base
Rule
Processing
Membership
Function
Type
Reduction
Latency
PacketLoss
Load
SignalStrength
UserMobility
Call
Admittance
Factor
Type-2 Fuzzy
Input sets

27
3.2. FUZZIFICATION
In this work, fuzzy inputs are converted and fuzzified into input IT2F sets, and then are mapped
to the linguistic labels of fuzzy sets to determine their degree of membership. Fuzzification is
carried out using five input fuzzy linguistic variables, defined as latency (LA), packet loss (PL),
signal strength (SS), Load (LD), and user mobility (UM). The linguistic terms are also defined for
the five input parameters as; Low (L), Medium (M), High (H), Very Low (VL), Low (L), High (H),
Very High (VH), Weak (W), Moderate (M), and Strong (S) respectively. The MFs of these fuzzy
sets contain five inputs and one output. We explore the use of MATLAB tool in MF plots as
shown in Figures 9(a) – (e). The output variable (CAF) is defined with four linguistic terms; Poor
(P), Fair (F), Good (G,) and Excellent (E), and presented in Figure 4.The MF limits are selected
based on input parameters and applied for reducing footprint of uncertainties. We consider IT2
Gaussian MFs with uncertain width (deviation) in (14) because it is suitable for highly dynamic
random networks such as 4G. The σ ∈ [σ1, σ2] with upper and lower membership functions are
defined in (15) and (16).
@ $ = exp ^−
`ab
Vcde, σ ∈ [σ1, σ2] and c ∈ [c1, c2] (14)
8̅Ã:g
$( = exp h−
`:ab:g
Vcid,:g
d j , 8̅Ã $ = . k, lV; $ (15)
8Ã:g
$( = exp h−
`:ab:g
VcL,:g
d j , 8Ã $ = . k, l[; $ (16)
where c is the center (mean) of the MF, σ is the width (standard deviation) of the MF and x is the
input vector. The variables lV,(1 and l[,(1 are premise parameters that define the degree of
membership of each element to the fuzzy set Ã and FOUs of the IT2IFS. The detail description is
found in [33] [23]. MFs are defined and evaluated for all the input and output linguistic variables.
IT2FSs are explored in the antecedent parts and each MF of the antecedent part is represented by
an upper and a lower MF, denoted by 8̅Ã(x) and 8Ã(x) as described in [33]. Each node output
indicates the lower and upper interval.
3.3. Fuzzy Rules
Fuzzy rules are defined based on (6), typically illustrated as; IF Latency is High and Packet Loss
is Moderate and Load is High and Signal Strength is Strong and User Mobility is Low THEN CAF
is FAIR = [0.32, 0.29]. Rules are defined based on human expert opinion with 243 rules for the
IT2FLC - CAC. For simplicity, parts of the rules are presented in Table 1. In the IT2FLS, the rule
base part are enclosed with five antecedents (LA, PL, SS, LD, UM) which divide the input space
into a set of fuzzy regions and one consequent (CAF) part which describes the system behavior in
those regions. Each MF of the antecedent part is represented by an upper and a lower membership
function.
Table 1: The IT2FL –CAC Fuzzy Rules
S/N Latency Packet Loss Load Signal Strength User Mobility CAF
1 L L VL W H EXCELLENT
2 H H VH S L FAIR
3 H H VH S L FAIR
4 L M VL W H EXCELLENT
5 L H VL W H GOOD
6 L L VL W H EXCELLENT

28
L M VL W H GOOD
8 L H VL W H GOOD
9 M L VL W H GOOD
10 M M VL W H GOOD
11 M H VL W H GOOD
12 H L VL W H GOOD
13 H M VL W H GOOD
14 H H VL W H FAIR
15 H L VL W H GOOD
16 H M VL W H FAIR
17 H H VL W H FAIR
18 L M L M M EXCELLENT
19 L H L M M GOOD
20 L M L M M GOOD
.
.
.
,
.
.
.
.
.
.
.
.
.
.
43 H L VH W H FAIR
44 H M VH W H POOR
45 M M L S L GOOD
3.4. FUZZY INFERENCE
Here, inference engine combines fired rules, maps input IT2FSs and output IT2FSs by computing
unions and intersections of type-2 sets, as well as compositions of type-2 relations. The main
problem is to determine the effect of input parameters in the antecedent part such that a concise
representation of the system’s behavior is produced in the consequent part, i.e. network
connection admission. This paper uses Mamdani fuzzy inference engine to calculate the firing
strengths of the lth rule illustrated in (7). Two firing levels are then computed, including a lower
firing level, @?
$?
, and an upper firing level @? $?
, @?
$?
= min [ 8ÃL
$[ , 8Ãd
$[ ] and
@? $?
= min [8̅ÃL
$[ , 8̅Ãd
$[ ]. The firing interval $ , which is the main observation, is the
result of input and antecedent operation, where q $ = [@ $ , @̅ $ ].
3.4. TYPE REDUCTION AND DEFUZZIFICZTION
Type reducer maps IT2-FS into a T1FS by combining the fuzzy output sets (IT1FS). In our paper,
IT2FLC-CAC employs center-of-sets type-reduction [45] to compute the two end points (yl and yr
) of centroids of the M consequent of IT2FSs using the KM algorithms illustrated in section 2.4 of
this paper, to produce the correct values of type-reduced sets. Defuzzification is carried out by
mapping the T1FS into a crisp number. Here, the interval output for each node present in
computed respectively. The final output of T2FLS-CAC, which is a numeric value, is obtained by
averaging the output of the resultant effect of the four embedded T1FLS using (10).
However, it is observed that KM TR scheme shows a major bottleneck using an interval type-2
FLS in real-time practices. Wu-Mendel uncertainty bounds approximation method is employed,
to estimate the type-reduced sets and determine the output of the FLS directly in order to
eliminate type-reduction. The WM model is described in section 2.5 of this paper.
Next, we present our model experiments and discuss of simulation results. We use the root mean
square error (RMSE) performance criterion for our experiments which is defined as:

29
rst4 = u
[
v
∑ 5` − 5 Vv
(w[ (17)
Where 5`
is the desired output, y is our model output and N is the number of data items.
4. MODEL EXPERIMENT RESULTS
In this paper, an intelligent IT2FL-CAC using KM type-reduction and Wu-Mendel UB methods
are applied to guarantee QoS provisioning in 4G mobile networks. In order to illustrate the
methodology proposed in this paper, we conduct some experiments for CAC in 4G networks
described in this work. The universe of discourse is defined for the linguistic variables as shown
in Table 2. The membership matrices’ for the various levels of crisp inputs for our IT2FLS are
presented in Tables 3-7. 200 datasets are generated based on the input variables LA, PL, SS, LD,
and UM and CAF is the desired output. For each input, Gaussian MFs with fixed mean and
uncertain standard deviation is employed for MF evaluation. For example, given the crisp input
vector v = [20, 2, 50, -94, 2], their degrees of membership are calculated as shown in Table 8.
Evaluating fired rules 20, 22, 30, 32, 45 against the fuzzy set yields the firing level and the results
are presented in Table 9.
Table 2: The Universe of Discourse defined for the linguistic variables
Input Variables and their Universe of Discourse
Latency
(LA)
Packet
Loss (PL)
Signal Strength
(SS) (dBm)
Load
(LA)
User Mobility
( UM) (m/s)
Call Admittance
Factor (CAF)
[0,100] [0,5] [-100,-80 ] [0,100] [0,6] [0,1]
Table 3: Membership matrix for Latency
Table 4: Membership matrix for Packet Loss
Fuzzy
Set[8
V
, 8V
]
Crisp Input
0 1 2 3 4 5
L [1.0,1.0] [0.45,0.24] [0.04,0.003] [0.0,0.0] [0.0,0.0] [0.0,0.0]
M [0.0,0.0] [0.003,0.0] [0.53,0.36] [0.53,0.36] [0.003,0.0] [0.0,0.0]
H [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.043,0.003] [0.45,0.24] [1.0,1.0]
Fuzzy
Set[8
[
, 8[
]
Crisp Input
10 20 40 60 80 100
L [0.3,0.08] [1.0,1.0] [0.008,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0]
M [0.0,0.0 ] [0.01,0.001] [0.6,0.5] [0.6,0.5] [0.01,0.001] [0.0,0.0]
H [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.008,0.0] [1.0,1.0] [0.008,0.0]

30
Table 5: Membership matrix for Load
Fuzzy
Set[8
x
, 8x
]
Crisp Input
10 30 50 70 90
VL [0.36,0.13] [0.36,0.13] [0.0,0.0] [0.0,0.0] [0.0,0.0]
L [0.0,] [0.45,0.24] [0.45,0.24] [0.0,0.0] [0.0,0.0]
H [0.0,0.0] [0.0,0.0] [0.36,0.13] [0.36,0.13] [0.0,0.0]
VH [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.36,0.13] [0.36,0.13]
Table 6: Membership matrix for Signal Strength
Fuzzy
Set[8
y
, 8y
]
Crisp Input
-96 -94 -90 -85 -82
W [0.84,0.70] [0.84,0.70] [0.013,0.0] [0.0,0.0] [0.0,0.0]
M [0.001,0.0] [0.06,0.003] [1.0,1.0] [0.013,0.0] [0.0,0.0]
S [0.0,0.0] [0.0,0.0] [0.013,0.0] [1.0,1.0] [0.21,0.04]
Table 7: Membership function for User Mobility
Fuzzy
Set[8
z
, 8z
]
Crisp Input
1 2 3 4 5
L [0.45,0.24] [0.04,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0]
M [0.01,0.0] [0.36,0.13] [1.0,1.0] [0.3,0.13] [0.01,0.0]
H [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.04,0.0] [0.45,0.24]
Table 8: Fuzzified Values
Linguistic Variable
Latency
[8
[
, 8[
]
PacketLoss
[8
V
, 8V
]
Signal
[8
x
, 8x
]
Load
[8
y
, 8y
]
Mobility
[8
y
, 8y
]
µL[1.0,1.0] µL [0.04,0.003] µVL [0.0,0.0] µW [0.84,0.70] µL[0.04,0.01]
µM[0.01,0.001] µM [0.53,0.36] µL [0.42,0.24] µM [0.06,0.003] µM[0.36,0.13]
µH[0.0,0.0] µH [0.0,0.0] µH [0.36,0.13] µS [0.0,0.0] µH[0.0,0.0]
µVH[0.0,0.0]
Table 9: Rule Evaluation
Rule
No.
Firing Interval Consequent
R20 [ @[
, @
[
] = = [0.000007, 0.00013] [ 5[
, 5
[
] = GOOD[0.3,0.2]
R22 [ @V
, @
V
] = = [0, 0.0] [ 5V
, 5
V
] = GOOD[1.0,1.0]

31
R30 [ @x
, @
x
] = = [0.0012, 0.0016] [ 5x
, 5
x
] = GOOD[0.3,0.2]
R32 [ @y
, @
y
] = = [0, 0.0] [ 5y
, 5
y
] = GOOD[1.0, 0.9]
R45 [ @z
, @
z
] = = [0, 0.0] [ 5z
, 5
z
] = GOOD[0.3,0.2]
We perform type reduction by selecting our leftmost (L) and rightmost (R) points at L=4 and R =
1 and compute the values of 5- and 5G in (18) and (19) and defuzzification is performed as
presented in (20).
5- =
B̅LMLUB̅dMdUB̅{M{UB̅|M|UB}M}
B̅LUB̅dUB̅{UB̅|UB} = 0.33 (18)
5G =
BLM
L
UB̅dM
d
UB̅{M
{
UB̅|M
|
UB̅dM
}
BLUB̅dUB̅{UB̅|UB̅} = 0.32 (19)
DS($) = (0.33 Y 0.32)/2 = 0.325 (20)
We apply Wu-Mendel uncertainty bounds method to compute the TR set by its inner- and outer-
bound sets and approximate [5-($), 5G($)] to estimate the output uncertainty of an IT2FLS for the
end-points of the TR set as shown in (18) – (24). The output of the FLS is calculated in (25).
5-i =
B̅LMqLUB̅dMqdU⋯UB̅€Mq€
B̅LUB̅dU⋯UB̅€ = 0.2 (21)
5- =
B̅LMLUB̅dMdU⋯UB̅€M€
B̅LUB̅dU⋯UB̅€ = 0.3 (22)
5qG =
BLM
L
UB̅dM
d
U⋯UB̅€Mq€
BLUB̅dU⋯UB̅€ = 0.2 (23)
5qG =
BLMLUB̅dMdU⋯UB̅€M€L
BLUB̅dU⋯UB̅€ = 0.3 (24)
[5-($), 5G($)] = D($) X 0.25 (25)
The output of the system is described mathematically by;
‚ƒ„‚ƒ = …
† r: )@ ‡‚ƒ„‚ƒ W 25%
+'r: )@ 25% ‰ ‡‚ƒ„‚ƒ W 50%
Š /: )@ 50% ‰ ‡‚ƒ„‚ƒ W 75%
4%Œ4••4.2: )@ ‡‚ƒ„‚ƒ Ž 75%
• (26)
A threshold of 50% is set in other to constrain the limits of acceptance values. A threshold is a
value of a metric that should cause an alert to be generated or management action to be taken
[46]. A threshold of 50% and above indicates that network resources are available hence; a call
can be accepted into the network.
5. RESULTS AND DISCUSSION
The intelligent IT2FL-CAC is simulated using two controllers: the IT2FL controller using KM
type-reduction method and the IT2FL controller using WM method. Furthermore, we also
implemented a T1FLS-CAC; thus an IT2FLS-AC and T1FLS-AC are implemented for

32
comparison purposes. Fuzzy logic toolbox in Matlab 7.5.0 is used for the input and output MFs
plots and presented in Figures 4(a)-(f). The system is developed using Java software development
toolkit (SDK). The input form accepts fuzzy parameters from the user. These parameters are then
passed to the fuzzification module of the system. The fuzzifier acts on the parameters to produce
an IT2FS which is evaluated against the rules to produce yet another IT2FS. Type reduction and
defuzzification are carried out to produce a crisp output that is displayed using a “TextField”
component of the system. From Figure 5, the result shows a fair call admittance factor of 48% is
achieved based on the level of influence of the inputs on the output. This indicates that the
network does not have enough resources to admit the call i.e, the call is not accepted into the
network. The results obtained from applying different approaches to the admission control
process to guarantee efficient QoS are as shown in Table 10. Table 11 presents the comparison of
IT2FLS-KM, IT2FLS-WM and ITIFLS in admission control in 4G networks and RMSE
performance criterion for our experiment. The graph of the result of IT2FLS- CAC using KM
approach is shown in Figure 6. Figure 7 gives the graph of the result of IT2FLS- CAC using WU
approach, while Figure 8 presents the graph of the result of IT1FL-CAC.
Fig. 4: (a) Latency (b) Packet Loss (c) Load (d) Signal Strength (e) User Mobility (input IT2 Membership
Functions for) and (f) Output membership functions (CAF)
Figure 5: IT2FL-CAC Result
Fig. 5: (a) Latency (b) Packet Loss (c) Load (d) Signal Strength (e) User
(a) (a) (b)
(c)
(f)(e)
(d)

33
Table 10: IT2FL and IT1L CAC Experimental Results
Fig. 6: Graph of the result of Interval Type-2 Fuzzy Logic Admission Control using KM approach
Fig. 7: Graph of the result of Interval Type-2 Fuzzy Logic Admission Control using WU approach
0
0.2
0.4
0.6
0.8
1
1.2
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
161
166
171
176
181
186
191
196
T2FLAC- KM
0
0.2
0.4
0.6
0.8
1
1.2
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
161
166
171
176
181
186
191
196
IT2FL- WU

34
Fig. 8: Graph of the result of Interval Type-1 Fuzzy Logic Admission Control
Table 11: Comparison of IT2FLS-KM, IT2FLS-UM and ITIFLS in Admission Control in 4G Networks
From the results, it generally indicates that IT2FLS-CAC using Wu-Mendel method outperforms
KM on the same set of input parameters. For example, from Table 10, with 35% ‘low’ latency,
0.79 ‘low’ packet loss, 56% ‘low’ load, -91.9 ‘very high‘ signal strength and 2 ‘moderate’ user
mobility factor, 57% ‘good’ CAF is achieved using WU approach as against 55% good CAF
with KM method. From our results, it can be seen that though the KM procedure is proven to
converge in no more than M (number of fired rules, maximum four, if all rules fired) iterations to
find the left endpoint of the type-reduced set and no more than M iterations to find the right
endpoint of the type-reduced sets, then the IT2FLS-CAC would take a maximum of eight
iterations (which is an acceptable number) to finish the TR steps. But in this paper, where as large
as 243 fuzzy rules considered, it is not feasible to employ the M procedure and calculate a better
result of the type-reduced sets. Rather an approximate type-reduced set using the Wu–Mendel
uncertainty bounds method is employed to offer a better performance. However, it is observed
that approximately 100% optimal value in terms of QoS demands and overall network
performance is achieved using both approaches with 44% ‘medium’ latency, 5% ‘high’ packet
loss, 67% ‘high’ load, -85 ‘strong’ signal strength and 5 ‘high’ user mobility factor or 57%
latency, 4.9 packet loss, 57% load, -88.2 signal strength, and 0.1 user mobility factor.
From Table 11, it is observed that IT2FLS-CAC using WM gives 0.0016 RMSE, which
outperforms IT2FLS-CAC using KM with 0.0021 RMSE. This is because the lower the error, the
better the performance of the technique. We also implement a T1FLS in order to comparatively
evaluate the performance of the IT2FLS-CAC with the T1FL model. The result indicates that
IT2FLS-CAC outperforms T1FLS-CAC. This is as a result of the extra degrees of freedom
offered by the FOUs of the IT2FLSs. The overall result shows a 1.62% improvement of IT2FLS-
CAC with WM over IT2FLS-CAC with KM and 87.07% over T1FLS-CAC. This indicates that
there is a significant performance improvement of IT2FLS over T1FLS on system control.
5. CONCLUSION
In this study, an IT2FLS approach to control CAC for guaranteed QoS in 4G mobile networks is
presented. The main problem is to determine the effect of input parameters in the antecedent part
-0.2
0
0.2
0.4
0.6
0.8
1
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
161
166
171
176
181
186
191
196
IT1FL
Models Training/Chk Mean Standard
Deviation
Root Mean Square
Error (RMSE)
IT1FLAC 400/200 0.5123 58.6776 0.0456
IT2FLAC-KM 400/200 0.6789 51.5483 0.0021
IT2FLAC-WM 400/200 0.6876 48.2197 0.0016

35
such that a concise representation of the system’s behavior is produced in the consequent part, i.e.
call connection admission. We have shown that IT2FLS-CAC using WM method outperforms
KM on the same set of input parameters. The study indicates that IT2FLS-CAC outperforms
T1FLS-CAC as a result of the extra degrees of freedom offered by the FOUs of the IT2FLSs. Key
to this work is the ability to show that an IT2FLS-CAC can preserve all the qualities of an
IT1FLS-CAC and still respond to uncertainty in the packet delay measurements in 4G networks.
The IT2FLS can accommodate more imprecision thereby modeling imperfect and imprecise
knowledge better than some T1FLS. In future, we intend to learn and fine tune the parameters of
the IT2FLS using Gaussian membership function with uncertain mean and train the IT2FLS using
hybridized approach by combining neural networks and particle swarm optimization.
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37
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Umoh U. A. had received her Doctor of Philosophy (PhD) degree in Soft Computing
from University of Port Harcourt, Rivers State, Nigeria in the year 2012, Master’s
degree in Database Management System from University of Port Harcourt, Rivers
State, Nigeria in the year 2006 and Bachelor’s degree from University of Uyo, Akwa
Ibom State, Nigeria in 2007. She is currently working as a Senior Lecturer, in
theUniversity of Uyo in the Department of Computer Science. She has published
several articles in her areas in reputable national and international journals and has
written some quality books in Computer discipline. Her area of interest include; Soft
Computing (Fuzzy System, Neural network, Hybrid models), Database System, Data Communications, etc.
She is a member of Nigerian Computer Society (NCS), Member, Computer Professionals Registration
Council of Nigeria (CPN), member, Nigerian Women in Information Technology (NWIT), member,
Organization for Women in Science in Developing World (OWSD), member, Universal Association of
Computer and Electronics Engineers (UACEE), member, Soft Computing Research Group (SCRS),
member, Internet Society (ISOC), etc.
Daniel Asuquo holds a PhD, M.Sc., and B.Sc. in Computer Science from the
University of Port Harcourt, University of Ibadan, and University of Calabar, Nigeria,
respectively. He is a Lecturer in the department of Computer Science, University of
Uyo, Nigeria with research interest in intelligent approach to wireless networks design
and optimization, mobile and web computing. He is a registered member of Nigeria
Computer Society and Computer Professionals (Registration Council of Nigeria).
Imo Eyoh received her B.Sc and M.Sc degrees in Computer Science from the University of Uyo and
Ibadan respectively, all in Nigeria. She is currently a Ph.D student in the Automated Scheduling,
Optimisation and Planning (ASAP) and Laboratory for Uncertainty in Data and Decision Making (LUCID)
research groups, University of Nottingham, UK. Her research interest is in uncertainty modeling using both
classical and intuitionistic type-2 fuzzy logic systems.

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