The document discusses fuzzy logic and its application in traffic modeling. It provides background on fuzzy set theory and fuzzy logic. It then summarizes research using fuzzy logic models for car-following behavior. One study developed a fuzzy logic car-following model using relative speed and distance as inputs and acceleration as the output. The model was validated using real-world driving data. Other research applied fuzzy rule-based models and inference systems to lane changing decisions under heavy traffic conditions.
In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic Fuzzy Vogel’s Approximation Method is proposed to find an initial basic feasible solution. Intuitionistic Fuzzy Modified Distribution Method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. The solution procedure is illustrated with suitable numerical example.
In this paper fuzzy VRPTW with an uncertain travel time is considered. Credibility theory is used to model
the problem and specifies a preference index at which it is desired that the travel times to reach the
customers fall into their time windows. We propose the integration of fuzzy and ant colony system based
evolutionary algorithm to solve the problem while preserving the constraints. Computational results for
certain benchmark problems having short and long time horizons are presented to show the effectiveness of
the algorithm. Comparison between different preferences indexes have been obtained to help the user in
making suitable decisions
In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic Fuzzy Vogel’s Approximation Method is proposed to find an initial basic feasible solution. Intuitionistic Fuzzy Modified Distribution Method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. The solution procedure is illustrated with suitable numerical example.
In this paper fuzzy VRPTW with an uncertain travel time is considered. Credibility theory is used to model
the problem and specifies a preference index at which it is desired that the travel times to reach the
customers fall into their time windows. We propose the integration of fuzzy and ant colony system based
evolutionary algorithm to solve the problem while preserving the constraints. Computational results for
certain benchmark problems having short and long time horizons are presented to show the effectiveness of
the algorithm. Comparison between different preferences indexes have been obtained to help the user in
making suitable decisions
Fuzzy logic is often heralded as a technique for handling problems with large amounts of vagueness or uncertainty. Since its inception in 1965 it has grown from an obscure mathematical idea to a technique used in a wide variety of applications from cooking rice to controlling diesel engines on an ocean liner.
This talk will give a layman's introduction to the topic and explore some of the real world applications in control and human decision making. Examples might include household appliances, control of large industrial plant, and health monitoring systems for the elderly. We will look at where the field might be going over the next ten years, highlighting areas where DMU's specialist expertise drives the way.
I Planned to give a specific training on Fuzzy Logic Controller using MATLAB simulation. This type of intelligent controller is very useful for the research work in all discipline.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
Artificial Intelligence lecture notes. AI summarized notes on uncertainty and handling it through fuzzy logic, tipping problem scenarios are seen in it, for reading and may be for self-learning, I think.
Fuzzy Logic and Neuro-fuzzy Systems: A Systematic IntroductionWaqas Tariq
Fuzzy logic is a rigorous mathematical field, and it provides an effective vehicle for modeling the uncertainty in human reasoning. In fuzzy logic, the knowledge of experts is modeled by linguistic rules represented in the form of IF-THEN logic. Like neural network models such as the multilayer perceptron (MLP) and the radial basis function network (RBFN), some fuzzy inference systems (FISs) have the capability of universal approximation. Fuzzy logic can be used in most areas where neural networks are applicable. In this paper, we first give an introduction to fuzzy sets and logic. We then make a comparison between FISs and some neural network models. Rule extraction from trained neural networks or numerical data is then described. We finally introduce the synergy of neural and fuzzy systems, and describe some neuro-fuzzy models as well. Some circuits implementations of neuro-fuzzy systems are also introduced. Examples are given to illustrate the cocepts of neuro-fuzzy systems.
This presentation includes what is fuzzy logic, characteristics, membership function with example, fuzzy set theory, De-Morgans Law, Fuzzy logic V/S probability, advantages and disadvantages and application areas of fuzzy logic. This is a presentation is useful for IT students.
Fuzzy Logic
Where did it begin?
What is Fuzzy Logic?
Fuzzy Logic in Control Systems
Fuzzy Logic in Other Fields
Fuzzy Logic vs. Neural Networks
Fuzzy Logic Benefits
Fuzzy logic is often heralded as a technique for handling problems with large amounts of vagueness or uncertainty. Since its inception in 1965 it has grown from an obscure mathematical idea to a technique used in a wide variety of applications from cooking rice to controlling diesel engines on an ocean liner.
This talk will give a layman's introduction to the topic and explore some of the real world applications in control and human decision making. Examples might include household appliances, control of large industrial plant, and health monitoring systems for the elderly. We will look at where the field might be going over the next ten years, highlighting areas where DMU's specialist expertise drives the way.
I Planned to give a specific training on Fuzzy Logic Controller using MATLAB simulation. This type of intelligent controller is very useful for the research work in all discipline.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
Artificial Intelligence lecture notes. AI summarized notes on uncertainty and handling it through fuzzy logic, tipping problem scenarios are seen in it, for reading and may be for self-learning, I think.
Fuzzy Logic and Neuro-fuzzy Systems: A Systematic IntroductionWaqas Tariq
Fuzzy logic is a rigorous mathematical field, and it provides an effective vehicle for modeling the uncertainty in human reasoning. In fuzzy logic, the knowledge of experts is modeled by linguistic rules represented in the form of IF-THEN logic. Like neural network models such as the multilayer perceptron (MLP) and the radial basis function network (RBFN), some fuzzy inference systems (FISs) have the capability of universal approximation. Fuzzy logic can be used in most areas where neural networks are applicable. In this paper, we first give an introduction to fuzzy sets and logic. We then make a comparison between FISs and some neural network models. Rule extraction from trained neural networks or numerical data is then described. We finally introduce the synergy of neural and fuzzy systems, and describe some neuro-fuzzy models as well. Some circuits implementations of neuro-fuzzy systems are also introduced. Examples are given to illustrate the cocepts of neuro-fuzzy systems.
This presentation includes what is fuzzy logic, characteristics, membership function with example, fuzzy set theory, De-Morgans Law, Fuzzy logic V/S probability, advantages and disadvantages and application areas of fuzzy logic. This is a presentation is useful for IT students.
Fuzzy Logic
Where did it begin?
What is Fuzzy Logic?
Fuzzy Logic in Control Systems
Fuzzy Logic in Other Fields
Fuzzy Logic vs. Neural Networks
Fuzzy Logic Benefits
Design of Mobile Robot Navigation system using SLAM and Adaptive Tracking Con...iosrjce
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A NEW APPROACH IN DYNAMIC TRAVELING SALESMAN PROBLEM: A HYBRID OF ANT COLONY ...ijmpict
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.
A Presentation of fuzzy input. To model and analyze traffic flow, different approaches have been proposed, such as mathematical, statistical, simulation, and artificial intelligence methods. One of the artificial intelligence methods that has been applied to traffic flow is fuzzy logic, which is a form of multi-valued logic that deals with uncertainty, vagueness, and imprecision.
ABSTRACT
Automobiles have become an integrated part of our daily life. The development of technology has improved the automobile industry in both cost & efficiency. Still, accidents prove as challenge to technology. Highway accident news are frequently found in the newspapers. The automobile speed has increased with development in technology through years and the complexity of the accidents has also increased. Higher speeds the accidents prove to be more fatal. Man is intelligent with reasoning power and can respond to any critical situation. But under stress and tension he falls as a prey to accidents. The manual control of speed & braking of a car fails during anxiety. Thus automated speed control & braking system is required to prevent accidents. This automation is possible only with the help of Artificial Intelligence (Fuzzy Logic).
In this paper, Fuzzy Logic control system is used to control the speed of the car based on the obstacle sensed. The obstacle sensor unit senses the presence of the obstacle. The sensing distance depends upon the speed of the car. Within this distance, the angle of the obstacle is sensed and the speed is controlled according to the angle subtended by the obstacle. If the obstacle cannot be crossed by the car, then the brakes are applied and the car comes to rest before colliding with the obstacle. Thus, this automated fuzzy control unit can provide an accident free journey.
Constructing a classification model is important in machine learning for a particular task. A
classification process involves assigning objects into predefined groups or classes based on a
number of observed attributes related to those objects. Artificial neural network is one of the
classification algorithms which, can be used in many application areas. This paper investigates
the potential of applying the feed forward neural network architecture for the classification of
medical datasets. Migration based differential evolution algorithm (MBDE) is chosen and
applied to feed forward neural network to enhance the learning process and the network
learning is validated in terms of convergence rate and classification accuracy. In this paper,
MBDE algorithm with various migration policies is proposed for classification problems using
medical diagnosis.
MEDICAL DIAGNOSIS CLASSIFICATION USING MIGRATION BASED DIFFERENTIAL EVOLUTION...cscpconf
Constructing a classification model is important in machine learning for a particular task. A
classification process involves assigning objects into predefined groups or classes based on a
number of observed attributes related to those objects. Artificial neural network is one of the
classification algorithms which, can be used in many application areas. This paper investigates
the potential of applying the feed forward neural network architecture for the classification of
medical datasets. Migration based differential evolution algorithm (MBDE) is chosen and
applied to feed forward neural network to enhance the learning process and the network
learning is validated in terms of convergence rate and classification accuracy. In this paper,
MBDE algorithm with various migration policies is proposed for classification problems using
medical diagnosis.
Sampling based positioning of unmanned aerial vehicles as communication relay...Inkonova AB
In the last years, the use of Unmanned Aerial Vehicles (UAVs, also known as “drones”) have found application in different environments that are dangerous or inaccessible by humans like inspection or mapping of underground mining stopes or shafts. During a drone mission it is often required to maintain connectivity with the ground station (referred hereinafter as GS). Even in autonomous flights, real-time communication provides several advantages like active operator supervision and eventual mission correction, in-flight mapping data transfer in case of drone crash inside an inaccessible area and others. In this context, we are interested in using a drone “leader” to explore unknown, dangerous and/or inaccessible underground areas, while keeping constant communication with the GS.
In this paper, we address the problem of using a swarm of autonomous drones, “repeaters”, as a relay chain to maintain communication between a GS and the drone leader responsible for exploration and data acquisition. We propose a sampling-based solution for dynamical positioning of the relay chain. Our method is fully decentralized, scalable and can deal with the case when the trajectory of the main drone is unknown. Simulation results are provided to show the performance of the proposed algorithm.
To simulate the behavior of the relay chain, we use a 2D simulation environment where the trajectory of the leader is predefined but not provided to the repeaters. The model used for the drone’s motion is based on a control signal that is provided as an acceleration and velocity that are bounded, and the drone is modeled as a point in space without orientation (also known as “headless” or “head-free”). In trivial situations, our algorithm can position the relay chain from the current and past mapping data from the leader. Further exploration and analysis of the utility functions to evaluate the sampled positions could drastically improve the performance. A higher level coordination for the whole drone repeaters’ chain could be achieved by using Behavior Trees, which would also increase the robustness and reliability of the whole system.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Student information management system project report ii.pdf
Review of fuzzy microscopic traffic flow models
1.
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.