Fuzzy Perspectives in Traffic Engineering

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					                 Fuzzy Perspectives in Traffic Engineering
                                        Serge Hoogendoorn
                                 Delft University of Technology
  Faculty of Civil Engineering and Geosciences, Transportation and Traffic Engineering section
              Stevinweg 1 – P.O. Box 5048, NL-2600 GA Delft, The Netherlands
    Telephone: +31.15.2785475; Fax: +31.15.2783179; E-mail: s.hoogendoorn@ct.tudelft.nl
                                   Sascha Hoogendoorn-Lanser
                                 Delft University of Technology
  Faculty of Civil Engineering and Geosciences, Transportation and Traffic Engineering section
              Stevinweg 1 – P.O. Box 5048, NL-2600 GA Delft, The Netherlands
        Telephone: +31.15.2785061; Fax: +31.15.2783179; E-mail: s.lanser@ct.tudelft.nl
                                         Henk Schuurman
                                   Ministry of Transport
                  Transport Research Center, Highway Engineering division
          Boompjes 200 – P.O. Box 1031, NL-3000 BA Rotterdam, The Netherlands
 Telephone: +31.10.2825889; Fax: +31.10.2825842; E-mail: h.schuurman@avv.rws.minvenw.nl


                                           ABSTRACT
This paper presents an outlook on the perspectives of applying fuzzy logic techniques in traffic
and transportation systems analysis and control. To this end, the theoretical and methodological
principles of the fuzzy logic approach are outlined. An overview is given of the fuzzy logic
applications in the transportation and traffic-engineering field, especially in the areas of
estimation and prediction of traffic engineering parameters, modeling the behavior of road users
and traffic control. The results of a critical analysis and assessment are presented, yielding a list
of strong and weak points of the fuzzy logic approach. Finally, research proposals are given.

AKNOWLEGDEMENTS
This paper conveys the results of an investigation into the perspectives of fuzzy logic in the field
of traffic engineering research, carried out by the TRAIL Research School for Transport,
Infrastructure and Logistics on behalf of the Transport Research Center of the Dutch Ministry of
Transport (AVV). The research team consisted of both experts in the field of traffic engineering
(traffic engineering section of the faculty of civil engineering and geosciences of the Delft
University of Technology) and fuzzy logic (control engineering section of the faculty of
information technology and systems of the Delft University of Technology).

BACKGROUND
Human decision making and reasoning in general and in traffic and transportation in particular,
are characterized by a generally good performance. Even if the decision-makers have incomplete
information, and key decision attributes are imprecisely or ambiguously specified, or not
specified at all, and the decision-making objectives are unclear, the efficiency of human decision
making is unprecedented. For instance, a police officer controlling the traffic at an intersection
may outperform advanced intersection controllers, even though he does not exactly know how
many vehicles have been waiting for how long, or what the exact magnitude of the capacity of the
intersection is. As another example, the most advanced central management systems rarely
outperform the traffic operators: although the operators control network traffic mainly based on
their expert knowledge and experience, they seem to be able to efficiently control traffic, using
qualitative and vague information about the traffic conditions. Although a driver can only very
roughly estimate the gap to the preceding vehicle, he is still able to maintain a sufficient distance
in most circumstances. Crucial in all these cases is the ability of humans to reason using vague
variables and their ability to reconcile different conflicting objectives, although they may be slow,
sub-optimal, and inconsistent in their decision-making.
In these problems, fuzzy set theory and fuzzy logic are approaches that are much closer to real
human observation, reasoning and decision making than other (traditional) approaches, such as
probability theory. These fuzzy approaches have been applied successfully in a wide range of
industrial processes (cement kilns, incineration processes, wastewater treatment) and products
              s,
(e.g. camera’ washing machines). Applications in the field of traffic engineering have only
recently emerged in larger numbers, and in many cases seem very promising. Most of these
applications have an experimental and preliminary nature, whereas real-life applications of fuzzy
sets and fuzzy logic in the field of traffic engineering are rare. However, from a number of
applications the potential of the fuzzy approach becomes already apparent.
In illustration, Middelham (1) developed a fuzzy ramp-metering controller that was evaluated in a
simulated environment. Based on the results of this study, the Dutch Ministry of Transport carried
out a pilot study on a metered on-ramp near the Dutch city of Zoetermeer. To this end, the
operational ramp-metering algorithm was modified to suit the implementation of fuzzy-based
ramp-metering algorithms, besides the two existing, conventional metering algorithms. It was
found that the fuzzy controller performed better than the other two (higher capacity and higher
speeds, and resulting shorter queues, lower densities; see (2)). These results revealed the potential
of fuzzy sets and fuzzy logic, and justified for a broader exploration of the possibilities of fuzzy
logic techniques in traffic and transport systems.

Research objectives
The aim of this paper is to present a concise outlook on perspectives of fuzzy logic techniques in
traffic and transportation systems. To this end, the paper will deal with the following subjects:
• Present the theoretical and methodological principles of the fuzzy logic approach.
• Present an overview of fuzzy logic applications in the transportation and traffic field.
• Briefly discuss analogue applications of fuzzy logic in other fields.
• Give a critical analysis of the strong and weak points of fuzzy logic.
• Show the perspectives of fuzzy logic for further and wider application in transportation and
  traffic and discuss further research proposals and application of fuzzy logic in transportation
  and traffic.

A PARKING SPACE FORECASTING SYSTEM USING FUZZY LOGIC
Before presenting the basics of a fuzzy system, an example of a fuzzy model system to predict
available parking space is presented (see (3)). The objective of such a prediction system is to
achieve a more efficient use of the available parking space capacity and to reduce the total
distance traveled by drivers searching for a parking spot. The predicted available parking space is
shown to drivers entering the downtown area. Of course, drivers will only react to the system if
the information is reliable. Therefore, a system is needed which predicts the available free
parking space at the time the driver arrives at the chosen parking garage.
The main motivation for using fuzzy logic for this specific problem is the complexity of the
modeling task: a large number of parameters can be identified, while their influence is not
precisely known. However, experts are available having some (vague) ideas concerning the
dynamics of the system. Fuzzy logic is ideally suited for model development when the exact
dynamics of the system are only partly known and understood, but some vague ideas and expert
knowledge are available.


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                                                                           (
                  Figure 1: Fuzzy parking space prediction system [source: 3)]
To design a fuzzy system, the following general steps have been taken:
• Definition of system boundaries (expected parking duration, location of parking garages).
• Definition of relevant variables, both input and output (see Figure 1).
• Fuzzification of the variables.
• Definition of relations between the defined variables (the rule bases; see Figure 1).
• Defuzzification of variables.
• Calibration of the model.
• Evaluation of the model.
The developed parking space forecasting system was tested with data of six parking garages in
                                        s
the same city. After tuning the system’ parameters using expert knowledge, a very good
prediction performance was achieved (92% prediction quality). Figure 1 depicts the prediction
system.
THE FUZZY SET APPROACH
In recent years, fuzzy set theory has found a large number of applications and it has become one
of the methods for dealing with complexity, uncertainty and imprecision in various systems. The
fuzzy set theory has found its place between other theories, such as probability theory, but also
neural networks and interpolate systems (see (4) and (20)).
Fuzzy sets arise from an extension of the classical sets for representing concepts that exhibit a
gradual transition from membership to non-membership. Mathematically, a set is a collection of
elements that share a common property. Whether an element has a particular property, however,
can not always be determined in an exact way. There are a large number of concepts in which an
element can have partial membership to a set.
Consider, as an example of a fuzzy set, the concept of “congestion”. A driver can experience
congestion, depending on the speed of the traffic. One can speak of congestion if the speed of the
traffic, as the individual driver experiences it, is relatively low. On a highway, at a speed of
80km/hr, one might speak of a beginning congestion. Below a speed of 40km/hr, there is
definitely congestion. For the speed in between, however, one speaks of congestion in an
increasing degree as the speed decreases from 80 km/hr to 40 km/hr. Therefore, congestion is a
gradual concept that is not defined precisely, but one whose boundary is vague and extends over a
particular speed range (see Figure 2).


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                                Figure 2: Fuzzy set of ‘congestion’
Fuzzy set theory has presented itself as a new tool representing uncertainty after the probability
theory, which was for a long time the sole tool for describing (another kind of) uncertainty.
However, the randomness assumed by probability theory describes only a restricted class of
uncertainty in system, while the majority of complex systems and real-life problems are non-
random in nature

Why use a fuzzy set approach?
A key motivation for the use of fuzzy sets is the improved handling of uncertainty. Traditionally,
uncertainty is considered undesirable, and one tries to reduce it as much as possible in order to
come to “precise” conclusions. However, the real world is imprecise and uncertain. Man’          s
perception of the real world is also ambiguous and imprecise as reflected by our natural language.
Despite the vagueness in linguistic descriptions, however, a lot of information can be conveyed
linguistically, provided one can deal with the imprecision.
Computers are especially incompetent in dealing with the vagueness and imprecision that is part
of everyday life. People, however, can handle most of these problems, dealing with the
imprecision, to the extent that is sufficient in most cases. Humans can reason in an appropriate
way, and make use of the imprecision in a manner that leads to solving complex problems.
According to one of the major principles in fuzzy set theory, the ability of humans to deal with
uncertainty is ultimately connected to their ability to solve complex problems within a reasonable
amount of time. That is, allowing more uncertainty tends to reduce complexity and will increase
credibility in the resulting model and allows, moreover, a computationally feasible solution. The
main area of application of fuzzy systems is herewith coined by the vast majority of complex
systems where relatively few data exist, where only imprecise, uncertain or ambiguous
information is available, or where expert knowledge is expressed vaguely in natural language. In
addition to this, fuzzy systems can also cope with the non-linearity found in most real-life
problems. A fuzzy controller can therefore, in principal, mimic any other (conventional)
controller and achieve the same performance; it can be seen as a universal function approximator.

Fuzzy logic and approximate reasoning
The theory of fuzzy sets has been proposed as an extension of the conventional set theory to cases
where the boundaries of a set cannot be defined in a crisp manner. The consequences of the
theory, however, have not been limited to the set theory only. Almost immediately, the
connection between the fuzzy set theory and a form of logic has been recognized, leading to the
introduction of fuzzy logic: a logic based on fuzzy set theory. This relation is similar to the
relation between the conventional set theory and binary logic. The ultimate goal of fuzzy logic is
to provide foundations for approximate reasoning with imprecise propositions using fuzzy set
theory as the principal tool. The following is an example of approximate reasoning with linguistic
terms that cannot be dealt with by the classical predicate logic:
                         Old automobiles are usually rare collectibles.
                         Rare collectibles are expensive… … … … … …
                         Old automobiles are usually expensive.

Basic elements of a fuzzy system
The heart of a typical fuzzy system is formed by a knowledge base in which the approximate
working of the fuzzy system is described as collection of fuzzy IF-THEN rules. An inference
mechanism compares the inputs of the system against the knowledge stored in the knowledge
                                s
base and determines the system’ output by using the given inputs and the available knowledge in
the knowledge base. Usually, the input signals are crisp, i.e. the inputs to the system are specified
in a precise manner. In many cases the outputs are also crisp since a precise action is required
from the fuzzy system. In fuzzy control systems, for instance, which has been one of the first
fields in which fuzzy systems have been applied, the control signal to the process must be crisp,
while the measurements concerning the system variables (e.g. the outputs of the system) are also
crisp. For that reason, the inputs to the fuzzy system are presented through a fuzzifier to the
inference mechanism, and the fuzzy outputs of the inference system are often defuzzified before
outputting them to the outside world.

Application areas of the fuzzy set approach
Since fuzzy set theory is primarily concerned with uncertainty, its management, and the reduction
of complexity, the application of fuzzy sets and fuzzy logic is successful in the following
situations:
• Processes where human reasoning and decision-making are involved, such as in supervisory
  tasks, planning and scheduling.
• Processes where one needs to blend various types of information such as quantitative
  information (equations describing parts of a system), (imprecise) measurements and human
  experience expressed in linguistic terms.
• Very complex systems, the understanding of which is limited and where general conclusions
  or tendencies should be derived and for which a computational solution including all (partly)
  known variables is impossible.
• Relatively simple systems for which analytic or numeric solutions exist, but which can be
  simplified to a large extend using fuzzy techniques and hardware. Fuzzy systems are,
  however, mainly considered when the system is highly non-linear, partly unknown or when
  additional heuristic knowledge is available which cannot be translated to formal analytical
  descriptions.
• Problems characterized by meanings of sentences expressed in natural language (‘computing
             ;
  with words’ see (5)).
• Systems requiring the capability to capture human common-sense reasoning and recognition
  resulting in a more human friendly interface.

FUZZY LOGIC APPLICATIONS IN TRAFFIC ENGINEERING
Many phenomena in traffic systems, such as route choice behavior, traffic management, or
driving behavior, typically result from subjective decisions. Depending on the context of the
problem, the basic input data needed to make these decisions include travel time, travel cost,
congestion duration, distance and velocity difference to a preceding vehicle, scenery rating, etc.
Some of these quantities are typically crisp, while others are inherently vague and can best be
described using linguistic variables.
In some situations, very precise input data are available to the decision-maker. Assuming that an
adequate model assisting the decision-maker exists, satisfactory solutions can be expected from
the resulting decisions that are made. However, in most situations, precise input data are not
available: that is, uncertainty, imprecision and ambiguity surrounds the input data. Moreover,
frequently, a decision is not based on objective reasoning, but rather on the decision maker’      s
experience, intuition and subjective appraisal of the situation, that is personal preferences,
personal assessment of routes, etc. This subjective evaluation will vary across the different actors
relevant for the considered phenomena, due to the limited information processing capabilities of
the actors (information vagueness), and the inherent vagueness in the perception of different
attributes (intrinsic vagueness). For instance, another driver may perceive what one driver may
perceive as a ‘ short’travel time, as a ‘rather long’travel time.
Hence, a large range of problems in the field of traffic engineering is characterized by variables
that are uncertain, subjective, imprecise and ambiguous. Traditionally, the research field of traffic
engineering has suffered from the lack of suitable analytical tools that can deal with vagueness in
the human perception and the decision making process. Even if traditional modeling approaches
are principally able to capture most process characteristics adequately, in a number of cases the
costs of development of such complex models, incorporating the complicated mechanics of the
process at hand, are tremendous.

Overview of fuzzy logic applications in traffic engineering
In the survey both ‘ practical’applications, that is real-life traffic engineering applications, as well
as ‘ research’ applications of fuzzy logic have been considered. Both application types are
reported in the literature, although the number of research applications is much larger.
It is of dominant importance to delimit the relevant fields of applications, and consequently
provide a clear impression of the research results with respect to fuzzy theory applications in
traffic engineering achieved so far. The studied publications have been classified according to the
relevant fuzzy operation types. This study has mainly focused on monitoring, modeling behavior,
estimation and prediction and control. Other identified fuzzy operation types are database
handling, optimization, Decision-Support Systems, and expert systems. Perpendicular to this
classification, the publications were classified according to the application area (e.g. parking
management, project planning, and route- and travel choice problems). Table 1 shows the results
of the literature survey, where publications have been classified according to this two-
dimensional classification scheme. It clearly shows the various research areas where fuzzy logic
has been applied.
As Table 1 indicates, the literature survey revealed that fuzzy logic has already been applied to a
large number of traffic engineering problems: several publications exists on the application of
fuzzy logic to congestion- and incident-detection, modeling freeway driving-behavior, modeling
route-choice behavior, parking management and traffic control. From the survey, we conclude
that although improved performance using fuzzy logic has only been convincingly proven for a
small number of real-life traffic engineering applications, such as congestion and incident
detection, intersection control and ramp-metering control, these few applications are generally
very promising. Additionally, application of fuzzy logic in simulation studies usually yield very
satisfactory results, increasing the belief in the potential of applying fuzzy logic to real-life traffic
engineering problems. In this respect, the following general conclusions can be drawn:
• Most of the applications of fuzzy logic to traffic engineering problems are still in the
  development phase. That is, only a small number of results of application of fuzzy in real-life
  applications have been found. Instead, most of the approaches are applied in a simulated
  environment using oversimplified networks, unrealistically small number of decision
  attributes, etc.
• Usually, the results from application of the fuzzy approach in either a real-life or simulated
  environment are satisfactory. Very promising real-life results are reported with respect to
  ramp metering and intersection control (see (1) , (2) and (15)).
• The main results achieved by application of fuzzy set theory is the ability to model
  vagueness, uncertainty, and ambiguity, inherent to a number of phenomena and decision
  processes in traffic engineering, such as route-choice (14), and car-following behavior (see
  (10), (12), and (13)). Fuzzy also enables the representation of qualitative expert knowledge
  (4). Moreover, a number of important traffic engineering variables is inherently vague, and
  can best be represented as such (11).
• From the survey it is concluded that fuzzy logic enables the fusion of data from different
  sources, thereby increasing the accuracy of the estimations and predictions and compensating
  for missing data (8). Moreover, fuzzy approaches provide the means to quickly and
  inexpensively develop models to describe complex traffic processes, even if only some basic
  vague ideas on the characteristics of the phenomena are available (4). Also, fuzzy control
  enables the trade-off of various, potentially conflicting objectives (increase throughput,
  decrease fuel consumption and environmental impacts, and increase safety; see (15)).
• Generally, the fuzzy approaches found in the literature are not very state-of-the-art from a
  fuzzy-theory point of view. That is, in a large number of publications, the employed
  modeling, calibration and elicitation techniques do not efficiently use the available fuzzy
  methodologies.
                                                                                              estimation +
                                                          monitoring

                                                                       databases




                                                                                               prediction
                                                                                   modeling
                                                                                   behavior




                                                                                                                                 decision


                                                                                                                                            systems
                                                                                                                                 support
                                                                                                             optimi-


                                                                                                                       control



                                                                                                                                             expert
                                                                                                              zation
                                  Fuzzy operation type:

Application area
FREEWAY TRAFFIC
   Non-interrupted flow
        Freeway
            Flow surveillance / analysis
            Simulation
            Safety
            Facility control
            Traffic control system
                       ramp metering
                       influencing speed
                       lane control
                       not specific
        Non-freeway
            Flow surveillance / analysis
            Simulation
            Safety
            Facility control
            Traffic control system
   Interrupted flow
            Flow surveillance / analysis
            Driving behavior analysis
            Signal control
                       local
                       coordinated
                       not specific
            Incident detection
TRANSPORT NETWORKS
            Route / travel choice
            Public transport management
            Safety
            Prediction
PARKING MANAGEMENT
PROJECT PLANNING/EVALUATION
Table 1: Overview of literature survey results. The shaded areas reflect the number of
publications found in the literature.
More specifically, the literature survey revealed that the following application areas in traffic and
transportation benefit from the application of fuzzy logic.

Traffic monitoring and state estimation
In general, the literature papers very good results. For instance, Busch et al. (6) paper a three-
minute decrease in the time needed to detect an incident in comparison to the existing system.
Moreover, increases in monitoring and estimation performance are expected, due the combination
of different information sources (see (7)). Moreover, using an appropriate rule base, also
incomplete data can be handled (see (8)). Kirschfink et al. (9) have used fuzzy logic to develop a
traffic network data analysis system, enabling improved communication with network operators
due to the use of linguistic variables.
Several variables relevant in traffic engineering are uncertain, imprecise and ambiguous. For
example, the level-of-service perceived by the road-users is an imprecise variable. Hence, we
need mathematical tools able to handle such vague variables appropriately. Chakroborty and
Kikuchi (10) and Ndow and Ashford (11) show that fuzzy logic can provide such tools.

Modelling driving behaviour
Fuzzy driving models and car following models discussed in the literature, yield realistic results
while remaining rather simple (relatively little decision variables) and transparent (decision
process is describes in linguistic terms and qualitative rules), while having a reasonably short
development time (for example see (12), and (13)).
Since decisions of the drivers are based on vague perceptions of attributes such as velocity,
distance and velocity difference to preceding vehicle, etc., and vague rules determining the
       s
driver’ actions learned from experience, fuzzy logic can be used to adequately model the
vagueness in the different decision attributes and the decision process.

Route choice behaviour
Regarding the operational performance of route choice behavior models, only simulation results
are reported. However, since Henn (14) has shown that the traditional discrete choice models are
a special case of the fuzzy route choice models, the performance of fuzzy route choice models
should be at least on par with the traditional models, given that the calibration of the fuzzy model
is feasible.
Moreover, by using fuzzy ranking schemes, groups of travelers having different attitudes towards
risk can be identified. More fundamentally, fuzzy logic is suitable to model the vague way in
which travelers perceive information. Additionally, inherently vague attributes (scenery, safety)
can be incorporated.

Traffic state prediction
The most interesting application of fuzzy logic is the use of expert knowledge in a fuzzy rule
base, to predict the available space in a parking garage. Hellendoorn and Baudrexl (1) quickly
develop such a forecasting system, which shows very good prediction performance.

Traffic control
In (3) the results of a field test of a fuzzy logic based ramp metering system are reported: it is
found that the fuzzy ramp metering controller outperforms the other metering algorithms (higher
capacities and less travel time delays on the main freeway). Other applications of fuzzy control
that yield improved performance are intersection control, speed regulation control, and dynamic
route guidance.
Generally, the proposed control schemes are transparent and therefore understandable by the
traffic operator, since the rules are expressed in linguistic terms. For instance, Chen et al. (15)
develop a fuzzy ramp-metering control algorithm from procedural knowledge of traffic operators.
Moreover, expert knowledge regarding the behavior of the highly complex and non-linear traffic
systems can be incorporated (see (1)). The final practical point here, is the reasonably short
development time, reported in the literature.

ANALOGIES WITH OTHER FIELDS OF RESEARCH
Rather than only considering applications of fuzzy logic in the field of transportation and traffic
engineering, our research also aimed to identify analogies with other, related application areas.
We observed that further applications of fuzzy logic in traffic engineering may benefit from
investigation of the analogies in other fields of science.
In (4) some specific examples of fuzzy logic applications from other application areas than traffic
engineering are given, to get a better insight into the possibilities of fuzzy logic in traffic
engineering. The examples were chosen in such a way, that they related to familiar problems in
the four categories of monitoring and state estimation (fuzzy logic systems for steady-state
security analysis of power networks, and the recognition of live stock from sound sequences; see
respectively (16), and (17)), modeling behavior (modeling control actions of an experienced
process operator; see (17)), prediction and control (prediction in cold-rolling control, see (18)).
We can conclude that a lot can be learned from analogue problems in other application areas.
Therefore, we recommend further investigation of the analogies with other application areas.

MERITS AND DRAWBACKS OF A FUZZY LOGIC APPROACH
In combining the results from the literature survey and studying the application of fuzzy logic in
other research areas, the merits and drawbacks were recognized. Let us briefly elaborate on both.

Merits of a fuzzy logic approach
The benefits of the approach stem from the following aspects:
• Fuzzy systems are able to capture and deal with meanings of words and sentences expressed
  in natural language, resulting in a transparent model formulation. Moreover, communication
  of the system with users (man-machine-interface) is improved.
• Fuzzy systems are able to blend different types of quantitative and qualitative information,
  e.g. imprecise measurements and human experience in linguistic terms.
• Because of the ability of fuzzy logic to incorporate qualitative information, fuzzy systems are
  able to adequately model processes where human reasoning and decision making are
  involved, such as supervisory tasks, planning and scheduling.
• Since the decision making process is described in linguistic expressions, expert knowledge
  can be used. This enables the control of complex traffic processes where several, conflicting
  objectives are pursued for which a compromise is to be found.
• Fuzzy control is successful in providing a transparent and flexible control structure (fuzzy
  production rules), potentially enabling short development time and easily adaptable
  controllers.
• Fuzzy logic techniques enable modeling processes which are possibly only partly understood,
  or not understood at all, using measurement data from the process (fuzzy identification).
  Fuzzy logic can either be used when a model is present, but the model parameters are not
  known precisely, or when no prior knowledge about the system is present (or used) at all, and
  the fuzzy model is constructed using measurements only.

Drawbacks of a fuzzy logic approach
The following is a summary of the general weak points observed in fuzzy logic techniques:
• The calibration of the parameters describing the membership functions, i.e. their form and
  their support and location, remains a problem. In this respect we should note that the
  influence of the different parameters is usually local, which facilitates manual tuning to some
  extent.
• The ‘curse of dimensionality’ when many variables play a role and a fine subdivision of the
  range of the fuzzy variables should be made.
• Although currently under development, a complete methodology or theory with respect to the
  stability analysis of fuzzy controller systems does not yet exist, although this is also not the
  case for many traditional non-linear system theories.
Although some of the research findings show improved performance, for example, several
publications paper a significant increase in incident detection performance, much of the cases
discussed:
• are merely based on pure simulation results. That is, the performance of the fuzzy system is
  assessed using a simulated approach only;
• do not rely on realistic assumptions;
• use a clear sub-optimal reference case. That is, the performance of the fuzzy system is
  compared to the performance of an oversimplified system. For example, a fuzzy ramp-
  metering system is only compared to a state-feedback controller, and not to an ‘ideal optimal
  controller’(although the latter may not be practically feasible);
• or do not compare the results with (classic) methods at all.
Overall, we may conclude that better performance using fuzzy logic has not been convincingly
proven: although fuzzy logic has been applied successfully to some traffic engineering
applications the potential of the fuzzy methodology has yet to be proven in the traffic engineering
practice.

PROPOSALS OF APPLICATION OF FUZZY LOGIC AND RESEARCH DIRECTIONS

Summary of potentials
From experiences with the application of fuzzy logic in traffic engineering and other related
research areas, the use of fuzzy logic seems beneficial to a number of applications in traffic
engineering. These consist of among others:
• Traffic state and vehicle identification.
• Human choice and decision processes (route-choice, modal-chain choice, etc.), Of which the
  input attributes and inference mechanism can be modeled using fuzzy logic.
• Driver behavior (car-following, lane-choice and lane function choice behavior).
• Control of complex traffic processes.
In (4) the used methods have been described and their performances have been discussed both
objectively and critically. Combining these viewpoints result in recommendations on interesting
application development and research directions for fuzzy logic in transportation and traffic for
applications addressed in the literature.
Moreover, from analogies with other applications of fuzzy logic, either in the field of
transportation and traffic, or in related fields, applications areas for which the use of fuzzy logic
techniques is recommended can be determined.

Recommendations for additional research for application of fuzzy method in practice
Application of fuzzy logic in practice is deemed especially fruitful for a number of traffic
engineering applications. However, additional research is necessary and invaluable in order to
establish operational demonstrators. In this respect, the following applications are relevant
(see (4)):
• Pilot study for supervisory control of an isolated ramp-metering installation.
• Investigation of the potential of fuzzy dynamic lane assignment controllers.
• Preparation of a co-ordinated ramp metering controller.
• Transportation network state surveillance.
• Research regarding the automated recognition and classification of vehicles and vehicle types
  from audio-video surveillance data.

Recommendations for model improvement using fuzzy modelling techniques
Additionally, in (4) a number of models to which a fuzzy modeling approach can be beneficial
are proposed. With respect to extending currently used models or the development of new
models, research regarding the following subject matters is deemed valuable:
• Modeling multi-modal trip chain choice behavior.
• Network state prediction using expert knowledge.
• Modeling lane configuration choice behavior and within lane configuration lane choice
  behavior (dynamic lane assignment control).
• Extension of currently employed microscopic simulation models.

Methodological improvements
Finally, several methodological improvements of fuzzy logic applications in traffic engineering
have been proposed. These are among others:
• Reduction of complexity by rule-chaining/de-coupling (multi-modal trip chain behavior, co-
  ordinate ramp metering, Dynamic Lane Allocation control).
• Calibration of models and controllers, e.g. using genetic algorithms.

Readily applicable fuzzy techniques
Finally, several readily applicable fuzzy methods have been proposed. Of these, the following
seem especially suited for application in a real-life environment:
• Incident and congestion detection using fuzzy logic.
• Isolated and co-ordinated ramp metering control.
• Local and centralized intersection control.

Example application: Modeling multi-modal trip chain choice behavior.
In the past, researchers have attempted to model the multi-modal travel choice process using,
among others, multi-nominal logit and nested logit approaches. However, it has been observed
that these traditional random utility models are not able to predict travel choice behavior
sufficiently accurate. It is envisaged that the model performance can be improved by careful
consideration of the rationale behind the human decision process. Based on the successful
application of fuzzy logic in route choice modeling, we envisage that fuzzy logic can be applied
to model multi-modal travel choice behavior.
We propose an alternative multi-modal travel choice model that considers mode-specific and non-
mode-specific trip chain attributes influencing travel choice behavior during the different stages
of the choice process, based on the fuzzy modeling paradigm (for details we refer to (19)). The
fuzzy model comprises a hypothesized hierarchy that resembles the actual choice process and
accounts for the relevant trip chain attributes at each stage of the choice process.
Since fuzzy rule chaining can model such hierarchical processes satisfactory, the decision process
is described using fuzzy set theory. Using this fuzzy mechanism, improved handling of mode-
specific and non-mode-specific attributes is possible, by more refined description of the way
humans perceive, appraise and reason with trip chain attributes. That is, the developed models
explicitly account for differences in image, perceived level of comfort, and safety of separate
transport modes.
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 Figure 3: Determining the fuzzy utility of a chain alternative by establishing mode-specific
                            and mode-unspecific sub-utilities.


The distinction of mode-specific trip chain attributes enlarges the insight into travel choice
behavior in general and more specifically, into the role of among others comfort, information and
safety. The structure of the presented models is transparent, enabling the synthesis and analysis of
the travel choice process. Knowledge can be extracted from the calibrated rules and the calibrated
membership functions.
Figure 3 shows the hypothesized fuzzy multi-modal travel choice model for a public transport
route choice problem, assuming that travelers base their decision on the appraisal of a transport
mode. Mode-specific trip chain attributes are combined into mode fuzzy sub-utilities. Typically, a
fuzzy bus sub-utility is derived from bus in-vehicle time, time spend waiting for a bus at the first
stop and time spend waiting for a bus at transfer points (rule base 1). In a similar fashion a fuzzy
walking time is derived (rule base 5). Subsequently, the various mode fuzzy sub-utilities serve as
input for rule base 6 establishing the fuzzy utility of the alternative.


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                  Figure 4: Fuzzy system to establish the ‘preferred’ alternative.
To establish the ‘ preferred’ or chosen travel alternative we infer the fuzzy trip chain attributes
into a fuzzy utility for each travel alternative by means of fuzzy inference using a rule base. The
fuzzy utilities can be defuzzified and subsequently the resulting crisp utilities can be ordered to
establish the ‘ preferred’ travel alternative. Alternatively, the fuzzy utilities are ranked directly
using a fuzzy ranking mechanism. Figure 4 shows the different steps in the fuzzy modeling
approach.

CONCLUSIONS
Many parameters and variables in traffic engineering are characterized by uncertainty,
subjectivity, imprecision and ambiguity. Consequently, in the mathematical analysis phase of
traffic processes of which parameters and variables are uncertain, ambiguous or subjectively
estimated, adequate mathematical methods must be employed that are able to satisfactory deal
with uncertainty, ambiguity and subjectivity.
In this paper we have discussed the potential application of fuzzy set theory and fuzzy logic to
solve complex traffic engineering problems. To this end, we have classified and analyzed of up-
to-date results in applying fuzzy set theory in monitoring, modeling and controlling complex
traffic engineering processes. Moreover, we have discussed the adequacy of the fuzzy approach
for treating uncertainty, subjectivity, ambiguity and indetermination present in traffic
engineering, by presenting an overview of applications of fuzzy logic in traffic and transportation.
From these reviews, and from analogies with applications of fuzzy logic in other engineering
fields, critical reviews of current fuzzy logic applications in traffic engineering have been
presented. Also, potential research directions were proposed.

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