Application of Mamdani Method on Fuzzy Logic to Decision Support
of Traffic Lights Control System at a Crossing of Malang City
Risna Zulfa Musriroh
1
, Wahyu H. Irawan
2
and Evawati Alisah
2
1
Mathematics Education at State University of Malang
2
Mathematics Department at UIN Maulana Malik Ibrahim Malang
Keywords: Fuzzy Logic, Traffic Light, Mamdani Method.
Abstract: Adaptive traffic management system has been implemented using fuzzy logic control. This study supposed
to design a traffic light system with fuzzy logic using defuzzification Mamdani method on fuzzy logic.
Establishment of fuzzy sets by defining variables are vehicle volume, road capacity, and green light duration
for three fuzzy sets i.e. small, medium, and large. Fuzzy rules are formed to express relation between input
and output which is an implication. Composition between the implication functions using the MAX function
combine the fuzzy sets of each rule and defuzzification with the centroid method. Case study is conducted at
the ITN crossing that was resulted in the timing of a change of traffic light from Department of
Transportation of Malang City cause still was not effective to break down the congestion. This can be seen
from the duration (in seconds) on a leg of the crossing with an incomparable vehicle volume. Plot data of
vehicle volume with green light duration of Transportation Department of Malang that vehicle volume is
larger has shorter duration of green light, and otherwise. Furthermore, the Mamdani method on fuzzy logic
gives solution as control system for the setting of traffic light more effective.
1 INTRODUCTION
Increasing the number of vehicles, especially in the
city of Malang, especially in the city of students to
make jams become one of the important problems
that must be resolved. This situation is usually
observed from a crossroads with many queues of
vehicles going through a crossroads. Traffic flow at
the crossroads in the city of Malang has many that
are set using traffic lights. The use of traffic lights at
intersections is intended to control traffic flow in
order to avoid prolonged congestion. In the
development of complex traffic light control systems
have been applied adaptive traffic management
system by using the control of fuzzy logic or logic
(P. Mahalakshmi and K. Ganesan, 2015). The basic
concept of an adaptive strategy used to manage
membership functions according to traffic conditions
in order to work optimally (Jang, 1997). Adaptive
setting system will take into account the uncertain
traffic conditions to optimize the flow of traffic in
accordance with the circumstances.
The state of traffic under consideration is limited
to the circumstances in an intersection area only. In
fact, traffic conditions on the highway between
intersections with each other are related. Traffic at
an intersection, the number of passing vehicles, can
be used to predict traffic conditions at the next
intersection. In this research will describe the design
of traffic light control system with fuzzy logic
control. This system will consider the prediction of
traffic conditions as inputs or inputs in determining
the duration of the green light on a traffic light. So, it
is expected that this concept can provide the
duration of green time corresponding to the number
of queues of vehicles that will cross the intersection.
In the previous research there is Mamdani Fuzzy
inference system Application Setting for Traffic
Lights (Sumiati et al, 2014) which will develop in
Malang City.
2 RESULTS AND DISCUSSION
2.1 The Establishment of the Fuzzy Set
The traffic control system in Malang City consists of
three input variables namely vehicle, volume and
road capacity and one output variable are duration of
236
Musriroh, R., Irawan, W. and Alisah, E.
Application of Mamdani Method on Fuzzy Logic to Decision Support of Traffic Lights Control System at a Crossing of Malang City.
DOI: 10.5220/0008520002360241
In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 236-241
ISBN: 978-989-758-407-7
Copyright
c
2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
green lamp. Determination of input variables used in
this study based on data from the Department of
Transportation of Malang City is the input variable
vehicle volume (smp/hour) and input variables road
capacity (smp/hour) as a benchmark to determine the
universe of speech. While the output variable Green
Length Duration obtained from the maximum
duration of the green light at the intersection of 120
seconds and then divided as many as the intersection
of legs attached red light posts as much as three feet
intersection at intersection ITN Malang. So, the
output variable Duration of Green Lights during
maximum 40 seconds on each legs of intersection.
Based on the domain, we determined the
membership function of each variable (Lin & Lee,
1996). Based on the data that exists by using the
theory of quartile on statistics (Md. Amjad Hossain
et al, 2011). Table 1 and table 2 contain the design
of fuzzy set in traffic control system in Malang City.
Table 1: Fuzzy Set Table (Input).
VARIABLE
THE SET
DOMAIN
Volume of
Vehicles
(smp/hour)
Smoothly
[702, 825]
Effective
[763, 887]
Dense
[825, 948]
Road Capacity
(smp/hour)
Less
[850, 969]
Enough
[909, 1029]
Surfeited
[696, 1088]
Table 2: Fuzzy Set Table (Output).
VARIABLE
THE SET
DOMAIN
Green Light
Duration
(seconds)
Fast
[0 20]
Medium
[10 30]
Slow
[20 40]
The fuzzy set and the membership function of the
Green Length Duration variable based on the
Vehicle Volume variables and the Road Capacity
variables are represented as figure 1, 2, and 3.
Figure 1: Set of Fuzzy Volume of Vehicle Variable.
Figure 2: Set of Fuzzy Road Capacity Variable.
Figure 3: Set of Fuzzy Green Light Duration Variable.
2.2 Application of Implication
Function
The rules are formed to express the relation between
input and output. Each rule is an implication. The
operator used to connect between two inputs is the
AND operator, and that maps between input-output
is IF-THEN. Propositions that follow the IF are
called antecedents, whereas the proposition that
follows the THEN is called consequent.
Table 3: Table of Implication Function.
Green Light
Duration
Road Capacity
Less
Enough
Surfeited
Volume
of
Vehicles
Smoothly
Fast
Fast
Fast
Effective
Fast
Medium
Medium
Dense
Medium
Slow
Slow
In the Mamdani Method, the implication function
used is MIN, which means the membership function
obtained as a consequence of this process is the
minimum value of the vehicle volume and road
capacity variables. So, we get fuzzy area on green
lamp duration variable for each rule.
2.3 Defuzzification
The composition between the implication functions
using the MAX function is by retrieving the
maximum value from the rule output then combining
the fuzzy regions of each rule with the OR operator
(Nguyen, 2003).
Application of Mamdani Method on Fuzzy Logic to Decision Support of Traffic Lights Control System at a Crossing of Malang City
237
,
where
is the value of the fuzzy solution
membership until the -rule and
is the
consequent membership value of each fuzzy rule
to-, with The crisp solution is
obtained by taking the center point (
) fuzzy area.
Generally formulated:
for the continuous domain, with is the value of the
defuzzification result and the membership function
of that point, whereas is the value of the -th
domain.
2.4 Determination of Green Light
Duration
The fuzzy set used in this study to determine the
duration of the green light in traffic control system
in Malang City based on the policy of
Transportation Department of Communication and
Information Malang. The fuzzy set includes the
variable volume of the vehicle and the capacity of
the road as input, and the duration of the green light
as output. ITN junction has 4 legs intersection as
follows:
West Leg : Bend. Sigura – gura Street
East Leg : Veteran Street
South Leg : Bend. Sutami Street
North Leg : Sumber Sari Street
Here's the proportion of traffic flow at the busiest
hour:
Table 4: Traffic Flow.
Time
Leg
Volume of
Vehicles
(smp/hour)
Road
Capacity
(smp/hour)
Busy
Time
WEST
702
850
EAST
914
1088
SOUTH
948
1102
NORTH
780
974
The current traffic system in Malang City based on
the survey result is traffic flow from the north leg
intersection Sumber Sari Street diverted directly to
the east leg intersection Veteran Street. So, the north
leg intersection Sumber Sari Street are not found in
red light posts. To set up a traffic control system
based on fuzzy logic, there are three cases of traffic
flow analysis from three legs namely Bend. Sigura-
gura Street, Veteran Street, and Bend. Sutami Street.
Figure 4: Cross of ITN in Malang.
2.4.1 Determination of Green Light from
West Cross Leg
The vehicle volume on the west cross leg is 702
smp/hour which included in the fuzzy set of
SMOOTHLY and EFFECTIVE. The membership
function for SMOOTHLY is
Therefore, the vehicle volume on the west cross leg
is 702 smp/hour in the fuzzy set of SMOOTHLY,
we obtain
The membership function for EFFECTIVE is
Therefore, the vehicle volume on the west cross leg
is 702 smp/hour in the fuzzy set of EFFECTIVE,
we obtain
Therefore, the volume of vehicles can be said
smoothly with 19.2% membership function. And the
ICMIs 2018 - International Conference on Mathematics and Islam
238
volume of vehicles can be said to be effective with
the membership function of 80.8%.
The road capacity is 850 smp/hour which included
in the fuzzy set of LESS and ENOUGH. The
membership function of LESS is
and
.
The membership function of ENOUGH is
and
.
Therefore, road capacity can be said less with 30%
membership function and the road capacity can be
said to be enough with 70% membership function.
Based on the rules according to the conditions, it is
obtained:
Table 5: Table of Implication Function.
Green Light
Duration
Road Capacity
Less
Enough
Surfeited
Volume
of
Vehicles
Smoothly
Fast
(0.192)
Fast
(0.192)
Fast
(0.00)
Effective
Fast
(0.30)
Medium
(0.70)
Medium
(0.00)
Dense
Medium
(0.00)
Slow
(0.00)
Slow
(0.00)
So that the rules of green light duration are as
follows:
[R1]. If the volume of vehicle is smoothly and the
road capacity is less than the duration of the green
light is fast.
.
[R2]. If the volume of vehicle is smoothly and the
road capacity is enough then the duration of the
green light is fast.
[R4]. If the volume of vehicle is effective and the
road capacity is less than the duration of the green
light is fast.
.
[R5]. If the volume of vehicle is effective and the
road capacity is enough then the duration of the
green light is medium.
The composition of rules with the maximum
function to find the fuzzy solution area is shown as
follows:
.
Based on figure 3 and same manner, the solution is
When
, then the value
of
as follows:
When
, then the value
of
as follows:
When
, then the value
of
as follows:
Application of Mamdani Method on Fuzzy Logic to Decision Support of Traffic Lights Control System at a Crossing of Malang City
239
Thus, the membership function for the results of this
composition is
Defuzzification in determining the duration of the
green light is by the centroid method. Moments for
each region as follows:
Then the area of each region as follows:
The center point (Castillo, 2008) obtained is
So, the duration of the green light at the west leg in
Sigura-gura Street is 16 seconds.
2.4.2 Determination of Green Light from
East Cross Leg
The determination of the green light duration in the
east leg using Mamdani method in fuzzy logic
consists of the above four stages with volume of
vehicles is 914 smp/hour and road capacity is 850
smp/hour. Formation of fuzzy set, application of
implication function with MIN function, rule
composition with MAX function, and
defuzzification with centroid method obtained by
output duration of green light from east leg Veteran
Street is 28.1≈28 seconds.
2.4.3 Determination of Green Light from
South Cross Leg
The determination of the green light duration in the
south leg using Mamdani method in fuzzy logic
consists of the above four stages with volume of
vehicles is 948 smp/hour and road capacity is 1102
smp/hour. Formation of fuzzy set, application of
implication function with MIN function, rule
composition with MAX function, and
defuzzification with centroid method obtained by
output duration of green light from south leg Bend.
Sutami Street is 29.7 ≈ 30 seconds.
3 CONCLUSIONS
The timing of the change of traffic light at the UB-
ITN intersection from the Data of the Transportation
Department of Malang City is still not effective to
break down the traffic jam. Plot of vehicle volume
data with duration of green light of the
Transportation Department of Malang City is
{(702, 24), (914, 22), (948, 31)}. So, for the leg
intersection that large volume of vehicles has a
shorter duration of green light, and vice versa.
Therefore, once the traffic light control system is
obtained, the duration of the green light is
proportional. Plot the vehicle volume data with the
duration of the green light of the traffic light control
system is {(702, 16), (914, 28), (948, 30)}.
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