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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. Title: Creator: CorelDRAW 7 Preview: This EPS picture was not saved with a preview included in it. Comment: This EPS picture will print to a PostScript printer, but not to other types of printers. ( 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). Titel: FCONGES3.EPS from CorelDRAW! Gemaakt door: CorelDRAW! Voorbeeld: Deze EPS-figuur is niet opgeslagen met een ingesloten voorbeeld. Commentaar: Dit EPS-bestand kan worden afgedrukt op een PostScript-printer, maar niet op een ander type printer. 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. Title: Creator: CorelDRAW 7 Preview: This EPS picture was not saved with a preview included in it. Comment: This EPS picture will print to a PostScript printer, but not to other types of printers. 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. Title: Creator: CorelDRAW 7 Preview: This EPS picture was not saved with a preview included in it. Comment: This EPS picture will print to a PostScript printer, but not to other types of printers. 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. REFERENCES 1. Middelham, F., Fuzzy Logic Demo (in Dutch). Rijkswaterstaat, AVV, Rotterdam, 1993; 2. HEIDEMIJ, Evaluation Toeritdosering met Fuzzy Logic (in Dutch). Research Report 672/CE96/1275/12047, March, 1996. 3. Hellendoorn, H., and R. Baudrexl, Fuzzy Neural Traffic Control and Forecasting. In: Inter- national Joint Conference Of The 4th IEEE International Conference On Fuzzy Systems and The 2nd International Fuzzy Engineering Symposium IEEE International Conference On Fuzzy Systems. V 4 1995. IEEE, Piscataway, pp. 2187-2194. 4. Hoogendoorn S.P., G. Copinga and U. Kaymak (1998), Perspectives of Fuzzy Logic in Traffic Engineering – main document. Research Report, TRAIL Research School, Delft, report on behalf of Dutch Ministry of Transport. 5. Zadeh, L.A., The Concept of a Linguistic Variable and Its Applications to Approximate Reasoning. In: Information Sciences Part I, vol.m 8, nr. 3, 1973, pp. 199-249. 6. Busch, F., M. Cremer, A. Ghio, and T. Henninger, A Multi-Model Approach For Traffic State Estimation And Incident Detection On Motorways. In: Proceedings Of The First World Congress On Applications Of Transport Telematics And Intelligent Vehicle-Highway Systems, Paris, Volume 3. 1994, pp. 1245-1252. 7. Palacharla P., and P. Nelson, Understanding Relations Between Fuzzy Logic And Evidential Reasoning Methods. In: Proceedings of the 1994 IEEE International Conference on Fuzzy Systems, IEEE Piscataway, 1994. pp. 19-24. 8. Choi, K. and S.H. Lee, Data Fusion for Generating the Link Travel Times with Insufficient Datasources. In: proceedings of the 1997 ITS World Conference, Berlin, 1997. 9. Kirschfink, H., R. Lange, and B. Jansen, Monitoring, Control and Management on the Motorway Network in Hessen using Intelligent Traffic Modeling. In: proceedings of the ’97 ITS Word Conference, Berlin, 1997. 10. Chakroborty. P. and S. Kikuchi, Car-Following Model Based on Fuzzy Inference System. In: Transportation Research Record 1365, 1992, pp. 82-91. 11. Ndoh, N.N., and N.J. Ashford, Evaluation of Transportation Level of Service. In: Transportation Research Record 1461, 1994, pp. 31-37 12. Jürgensohn, T. and C. Raupach, Über den Einsatz von Fuzzy-logic in der Modellierung menschlichen Regelverhaltens. In: VDI-berichte (948), 1992, pp. 235-250 (in German) 13. Rekersbrink, A., Mikroscopische Verkehrssimulation mit Hilfe der Fuzzy Logic. In: Straßenverkehrstechnik 2, 1995 (in German) 14. Henn, V., Fuzzy Route Choice Model For Traffic Assignment. In: Proceedings of the 9th mini EURO conference “Fuzzy sets in Traffic and Transportation Systems”, Budva, 1997. 15. Chen, L.C., A.D. May and D.M. Auslander, Freeway Ramp Control Using Fuzzy Set Theory For Inexact Reasoning. In: Transportation Research 24A, nr. 1., 1990, pp. 15-25. 16. Kaymak, U., R. Babuska, H.R. van Nauta Lemke, G. Honderd. A Fuzzy Logic System for Steady-State Security Analysis of Power Networks. To appear in: Journal of Intelligent and Fuzzy Systems, 1998. 17. Setnes, M., R. Babuska, Fuzzy Relational Models for Classification. In: Proceedings of 97, IFSA’ Prague, Czech Republic, 1997 18. Terano, T., K. Asai, and M. Sugeno, Applied Fuzzy Systems, AP Professional, 1994 19. Hoogendoorn-Lanser, S., Structured Modelling of Multi-Modal Urban Travel Choice Behaviour, 4th TRAIL PhD Congress, 1998. 20. Babuska, R., Fuzzy Modelling and Identification. PhD. Thesis, Delft University of Technology, Faculty of Electrical Engineering

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