by Abubakar usman atiku sps/17/mce/00030

2. INTRODUCTION
In daily language, there is a great deal of imprecision, or we can say
“fuzziness” such as the statements: “He is tall” or “He is young”. The
classifications, e.g., healthy, large, old, far, cold, are fuzzy terms in the
sense that they cannot be sharply defined. In other words, these are the
statements that are uncertain and imprecise.
When we speak of the subset of healthy people in a given set of people,
it may be impossible to decide whether a person is in this subset or not.
We can give a yes-or-no answer, but there may be loss of information
since the degree of healthiness is not taken into consideration.
Fuzzy Logic : is a logic that allows for imprecise or ambiguous
answers to questions, forming the basis of computer programming
designed to mimic human intelligence
Fuzzy Logic, in computer science, a form of logic used in some expert
systems and other artificial-intelligence applications in which variables
can have degrees of truthfulness or falsehood represented by a range
of values between 1 (true) and 0 (false). With fuzzy logic, the outcome
of an operation can be expressed as a probability rather than as a
certainty. For example, in addition to being either true or false, an
outcome might have such meanings as probably true, possibly true,
possibly false, and probably false. Microsoft ® Encarta ® 2009.

3. PURPOSE OF THE REVIVE
 To understand the use of fuzzy traffic model in
traffic engineering and its application in traffic
Engineering.
STATEMENT OF THE PROBLEM
 Currently fuzzy model is being used in traffic
modeling; this review is done in other to
understand the current research and the state of the
art in transportation engineering

4. Aim
 To proposes a fuzzy rule-based car-following
model that assumes that a decision made by a
driver is the result of a fuzzy reasoning process
and then predicts the possibilities of the reaction of
the follower vehicle
Objectives
 To Understand the driver car-following behavior
using a fuzzy logic car-following model
 To look at other related works that use the fuzzy
model in car moving theory.

5. Literature Review
 Fuzzy logic is a form of many-valued logic in which the truth values of variables may be
any real number between 0 and 1. It is employed to handle the concept of partial truth,
where the truth value may range between completely true and completely false. By
contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or
1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi
Zadeh L.A.(1965). Fuzzy logic had however been studied since the 1920s, as infinite-
valued logic notably by
 Łukasiewicz and Tarski (2000). A first attempt to give different degree of truth was
developed by Jan Lukasiewicz and A.
 Tarski formulating a logic on n truth values where n ≥ 2 in 1930s. This logic called n-
valued logic differs from the classical one in the sense that it employs more than two truth
values. To develop an n-valued logic, where 2 ≤ n ≤ ∞,
 Zadeh modified the Lukasiewicz logic and established an infinite-valued logic by
introducing the concept of membership function.
 Let X be a classical set of objects, called the universe, whose generic elements are denoted
by x. An ordinary subset A of X is determined by its characteristic function χA from X to
{0, 1} such that, χA(x) = 1 if 0 if x x / ∈ ∈ A, A.
 In the case that an element has only partial membership of the set, we need to generalize
this characteristic function to describe the membership grade of this element in the set.
 Note that larger values denote higher degrees of the membership. For a fuzzy subset A of
X, this function is defined from X to [0, 1] and called as the membership function (MF)
denoted by µA, and the value µA(x) is called the degree of membership of x in A. Thus we
can characterize A by the set of pairs as following: A = {(x, µA(x)), x ∈ X}.

6.  Fuzzy System Modeling
A fuzzy system is a system where inputs and outputs of the
system are modeled as fuzzy sets or their interactions are
represented by fuzzy relations. A fuzzy system can be
described either as a set of fuzzy logical rules or a set of fuzzy
equations. Several situations may be encountered from which
a fuzzy model can be derived: a set of fuzzy logical rules can
be built directly; there are known equations that can describe
the behavior of the process, but parameters cannot be precisely
identified; too complex equations are known to hold for the
process and are interpreted in a fuzzy way to build, for
instance a linguistic model; input-output data are used to
estimate fuzzy logical rules of behavior. The basic unit for
capturing knowledge in many fuzzy systems is a fuzzy IF-
THEN rule. A fuzzy rule has two components: an IF-part
(referred to as the antecedent) and a THEN-part (referred to as
the consequent). The antecedent and the consequent are both
fuzzy propositions. The antecedent describes a condition, and
the consequent describes a conclusion that can be drawn when
the condition holds.

7. CURRENT RESEARCH IN THE AREAS
 Fuzzy rule-based models for the car-following problem:
In the car-following situation, one follows a set of driving rules built
over time through experience. Examples of the rules that the FV
might apply are as follows:
 Accelerate if the lead vehicle (LV) accelerates,
 Decelerate and keep longer distance if the LV decelerates and the
distance between cars is short.
Understanding driver car-following behavior using a fuzzy logic
car -following model
The fuzzy logic car-following model was developed by the
Transportation Research Group (TRG) at the University of
Southampton (Wu et al., 2000). McDonald et al., 1999. collected
carfollowing behavior data on real roads and developed and
validated the proposed fuzzy logic car-following model based on the
real-world data. The fuzzy logic model uses relative velocity and
distance divergence (DSSD) (the ratio of headway distance to a
desired headway) as input variables. The output variable is the
acceleration-deceleration rate. The DSSD is the average of the
headway distance that is observed when the relative speeds between
vehicles are close to zero. This model adopts fuzzy functions (fuzzy
sets described by membership functions) as the formula for the input-
output relationship. Figure bellow depicts the structure of the fuzzy
logic car-following model.

8. Input variable validation
The following eight conditions were applied to the fuzzy inference system estimation
in order to obtain satisfactory performance of the fuzzy logic model. - Velocity of the
driver’s own vehicle (Vd)
 Headway distance to the lead vehicle (HD)
 Relative velocity between the lead vehicle and the driver’s vehicle (RV =
d(HD)/dt)
 Velocity of the lead vehicle (Vl = Vd+RV)
 Time headway (THW = HD /Vd)
 Inverse of time to collision (1/TTC, TTC = HD/RV, where the value is infinite
when RV = 0.)
 Angular velocity (This value is calculated using the following approximate
formula: (width*RV)/HD2, where the width of the lead vehicle is assumed to be
2.5m.)
 Distance divergence (DSSD, calculated from HD divided by the desired headway.
The desired headway was chosen to be the average of the headway observed when
the relative speeds between vehicles were close to zero.)
The performance of the fuzzy logic model was evaluated by the Root Mean Square
Error (RMSE) of the model prediction:
 where Ŷi is a predicted value using the fuzzy logic model at time increment i, Yi is
raw data at time increment i, and N is the number of data using a TRG
instrumented vehicle. Although a three-input model suggested better RMSE
performance than a one-input model or a two-input model, the two-input model
using relative speed and distance divergence was adopted because of the
complexity of the model structure and its applicability to a wide range of car-
following situations. For details of the input variable validation, refer to Zheng,
2003.

9. Model validation
The fuzzy logic car-following model describes driving operations
under car-following conditions using linguistic terms and
associated rules, instead of deterministic mathematical functions.
Car-following behavior can be described in a natural manner
that reflects the imprecise and incomplete sensory data
presented by human sensory modalities. The fuzzy logic car-
following model treats a driver as a decision-maker who decides
the controls based on sensory inputs using a fuzzy reasoning.
There are two types of fuzzy inference system that uses fuzzy
reasoning to map an input space to an output space, Mandani-
type and Sugeno-type. The main difference between the
Mamdani and Sugeno types is that the output membership
functions are only linear or constant for Sugeno-type fuzzy
inference. A typical rule in the Sugeno-type fuzzy inference
(Sugeno, 1985) is: If input x is A and input y is B then output z is
x*p+y*q+r;
 where A and B are fuzzy sets and p, q, and r are constants.
 The constant output membership function is obtained from a
singleton spike (p=q=0).

10. Modelling the heavy vehicle drivers’ lane changing decision under heavy
traffic conditions.
The fuzzy rule base of the lane changing decision model, describes the heavy
vehicle drivers’ decision to move into either the right or the left lane, based
on the above mentioned explanatory variables. Typical fuzzy rule for LCFL
model with two and three sets, in natural language are presented below.
If (Front Relative Speed is Low) and (Left Lag Relative Speed is Low) and (Average
speed in Current Lane is Low) and (Average speed in Left Lane is High) then (LCFL
is yes). If (Front Relative Speed is Low) and (Left Lag Relative Speed is Intermediate)
and (Average speed in Current Lane is Low) and (Average speed in Left Lane is
High) then (LCFL is yes).
The fuzzy sets and systems for the lane changing decision model :- The
explanatory variables in motivating the heavy vehicle drivers to move into
the slower lane include: the front space gap, the rear space gap, the lag space
gap in the right lane and the average speed of the surrounding vehicles in the
current lane. The average speed in the current lane is assumed to be the
average speeds of the heavy vehicle and the front and rear vehicles. The
explanatory variables in motivating heavy vehicle drivers to move into the
faster lane include: the front relative speed, the lag relative speed in the left
lane and the average speeds of the surrounding vehicles in the current lane
and the left lane. The average speed in the adjacent lanes is the average speed
of the first two lead and the first two lag vehicles in that lane. The number of
fuzzy sets which could be used for any of the explanatory variables in the
lane changing decision model is restricted to drivers’ perception capabilities.
Lane changing manoeuvre has a high level of interaction between the driver
who performs a lane changing manoeuvre and the surrounding traffic

11. Behavioral problems associated with the driver
When conducting Car-following test involving stranger driver(s) that are just part of the experiment
their behavior usually changes expecially when the equipment is exposed to them, change of speed is
usually noted and other strange behaviors that may change the values when conducting the
matematecal calculations on the fuzzy system. Example of such experiment are given bellow.
Behavioral problems
An AIST instrumented vehicle and a TRG instrumented vehicle are used for behavioral data collection
(Brackstone et al., 1999; Sato & Akamatsu, 2007). Both vehicles are equipped with various sensors and
driving recorder systems in order to detect the vehicle driving status and to measure the driver’s
operations. Velocity is measured using a speed pulse signal, and acceleration is detected by a G-sensor.
The relative distance and relative speed to the leading and following vehicles are recorded with laser
radar units (AIST instrumented vehicle) or microwave radar (TRG instrumented vehicle) that are fixed
within the front and rear bumpers. Figure bellow presents an overview of the AIST instrumented
vehicle. This vehicle collects the following data:
 Driving speed by speed pulse signal,
 Relative distance and speed to the leading and following vehicles by laser radar units,
 Vehicle acceleration by G-sensor,
 Angular velocity by gyro sensor,
 Geographical position by D-GPS sensor,
 Application of gas and brake pedals by potentiometers,
 Position of driver’s right foot by laser sensors,
 Steering wheel angle by encoder,
 Turn signal activation by encoder, and
 Visual images (forward and rear scenes, lane positions, and driver’s face) by five CCD cameras.

12. CONCLUTION
Future directions in the subject area
 The process of lane-changing is purely stochastic.
However, in literature there are some attempts in
microscopic models where the process of lane-
changing is described by using a fuzzy logic-based
system thus it would be interesting to
implemented a fuzzy logic-based system to refine
the lane-changing rules.
 A Stochastic Continuous Cellular Automata Traffic
Model with Fuzzy Decision Rules the experiments
should involving on- and off-ramps and loop-
detectors to analyze different and more realistic
situations such as city roads with many
interactions and traffic lights.

13.  fuzzy set theory by Lotfi Zadeh, proposal of fuzzy logic, 1965.
 Łukasiewicz and Tarski, infinite-valued Fuzzy logic, 1920s.
 Zadeh, Concept of membership function, 1967.
 Wu et al., McDonald et al Transportation Research Group
(TRG) University of Southampton, 2000.
 Sugeno, Sugeno-type fuzzy inference, 1985.
 A.J.R. Amaya, O. Lengerke, C.A. Cosenza, M.S. Dutra, and
M.J.M. Tavera. Comparison of defuzzification methods:
Automatic control of temperature and flow inheat
exchanger. Automation Control-Theory and Practice,
InTech, December 2009.
 A. Aw and M. Rascle. Resurrection of second order models
of traffic flow. SIAM Journal of Applied Mathematics,
60(3):916–938, 2000.