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Since 1965 when the fuzzy logic and fuzzy algebra were introduced by Lotfi Zadeh, the fuzzy theory successfully found its applications in the wide range of subject fields. This is mainly due to its ability to process various data, including vague or uncertain data, and provide results that are suitable for the decision making. This paper aims to provide comprehensive overview of literature on fuzzy control systems used for the management of the road traffic flow at road junctions. Several theoretical approaches from basic fuzzy models from the late 1970s to most recent combinations of real-time data with fuzzy inference system and genetic algorithms are mentioned and discussed throughout the paper. In most cases, fuzzy logic controllers provide considerable improvements in the efficiency of traffic junctions’ management.

The condensed traffic together with the increasing number of cars requires constantly evolving and more complex solution of traffic situation including the traffic signal control. The monitoring and controlling of traffic within the city became a crucial task because of the ability to take control of roads and thus directly impact on the quality of life. Nowadays, the traffic signal controllers use almost real-time data and combine them with sophisticated algorithms. These algorithms used at first simple mathematic rules that were suitable for the purpose of lower load of intersections but started to be outdated with the development of dense road network and increasing number of vehicles. Current algorithms have to be more adaptive and intelligent in order to handle ever-changing traffic situations. It means that the decision support systems should be able to implement and handle almost real-life rules which are very similar to the human thinking.

These conditions are fulfilled by the implementation of fuzzy logic processes and fuzzy logic algebra into the controlling scheme. For example, humans would think in the following way to control traffic situation at a certain junction: “if the traffic is heavier on the north or south lanes and the traffic on the west or east lanes is less, then the traffic lights should stay green longer for the north and south lanes.” Such rules can now be easily accommodated in the fuzzy logic controller. The main strength of the fuzzy logic is that it allows fuzzy terms and conditions such as “heavy,” “less,” and “longer” to be quantized and understood by the computer [

Fuzzy numbers are special cases of fuzzy sets that represent vague, imprecise, or ill-known values. Like the fuzzy set a fuzzy number is defined by a membership function, which specifies membership degree for each element

Since 1965 when the fuzzy logic and fuzzy algebra were introduced by Lotfi Zadeh, the fuzzy theory successfully found its applications in the wide range of subject fields. The traffic signal control and the management of roads and junctions within the city are no exceptions. The first attempt of applying fuzzy logic in the light signalling equipment using fuzzy logic controller was realized in the late 1970s by Pappis and Mamdani. However, since then, the evolution of fuzzy logic controlling systems came to the more complex, more adaptive, and more intelligent frameworks that allow not only the use of fuzzy logic but also combination with real time data and optimization using, for example, genetic algorithms and neural networks.

There have been several standard studies [

For the purpose of this paper, we selected and reviewed a solid series of papers reported in the literature. In order to provide a comprehensive overview of the topic, we employed the most popular and recognized databases of scientific paper (e.g. ScienceDirect, Web of Science, or Scopus). Nevertheless the main scope of this paper is not only to present possible ways of evolution and implementation of fuzzy logic in the traffic management but also to refer to the chronology of the evolution and to common relations among presented models. Individual models presented in this contribution are significantly described and usually depicted in the form of simple scheme, so the reader can easily compare them. In most cases, fuzzy logic controllers (and their adjustments and variations) provide considerable improvements in the efficiency of traffic junctions’ management compared to the traditional adaptive and nonfuzzy systems.

The organization of this paper is quite simple and straightforward and is given as follows. After the introduction of the topic in Section

Fuzzy logic in the LSE (light signalling equipment) was presented for the first time in 1977 by Pappis and Mamdani [

The goal was to determine the offset parameter, that is, to determine the time difference between the start of the green phase on the first and the second intersection.

The publication by Bisset and Kelsey [

The 1993 publication [

Block diagram of the fuzzy traffic control system [

The control system was applied on a real independent multilane intersection in the city of São Paulo. The inputs into the control system did not change, and still there were the number of passing vehicles and the column length, whereas the output was again the extension of the green light (

Hoyer and Jumar [

Kim’s thesis [

Sayers et al. [

The 1995 paper by Kagolanu et al. [

Neural network diagram [

Tan et al. [

Diagram of detectors’ placement [

Figure

In his article Kim [

An attempt to innovate the issue of LSE fuzzy control came from Beauchamp-Baez et al. [

Block diagram of the isolated intersection control system “

And subsequently they included a module for phase “sequencer” (PS), which also used the fuzzy logic (block diagram Figure

Block diagram of the isolated intersection control system “

The quality of the two above mentioned control systems (

The Finn Niittymaki came with a new idea of using the fuzzy logic for the SLE control, when he, in his article [

The authors Heung and Ho [

Control block diagram [

Sayers et al. [

Trabia et al. [

The issue of a multiphase control was also elaborated by the Finn Niittymäki in the publication [

Block diagram of the FUSICO three-stage algorithm [

The proposed control system showed, upon comparison with conventional methods of LSE control and fuzzy control system

Block diagram of the application of fuzzy control in the traffic area [

Niittymäki verified the results of the FUSICO scientific project in practice by implementation of the fuzzy control system ((

Block diagram of the fuzzy control system [

The results showed that the fuzzy control systems exceeded the conventional control systems in all parameters determining the quality of control, time of travel, number of stops, and the length of column.

Niittymäki and Könönen [

Multistage fuzzy control system with a fuzzy “block” public transport preference control [

In the article [

Niittymäki summarized all his discoveries in the thesis “

Niittymäki and his colleagues summarized their further research in an article [

The simulations in the HUTSIM application were also used in the publication [

The method of fuzzy decision making for intelligent traffic control and warning system was patented in the North America in 2001. This should warn the drivers of the congestions [

The author Ella Bingham [

Block diagram of the neurofuzzy traffic control system [

In relation to the articles [

The authors Wei et al. proposed in their work [

Three levels of traffic signal control [

The basic idea of the article [

Four-level fuzzy-Neural network diagram [

The first level of the Neural network processed sharp values of the input variable whose output was also a sharp value. The second layer of the Neural network calculated parameters of the fitness functions (positions in the universum). The authors of the article called the third level “the rules’ level.” Each of the nodes of the third level represented one of the fuzzy rules. The last (fourth) level was the defuzzification level with a sharp value of a selected output variable.

The authors Wei and Wang further presented on the idea of a three-level LSE control system in the publication [

Three levels of LSE traffic control system [

The main change consisted of the expansion of the lowest level by a module, which predicted a value of the input variable using the fuzzy Neural network. The authors moved the fuzzy inference system from the highest level to the second (middle) level. According to the authors a system assembled in this way solves the issues of stochastic traffic systems, such as an intersection with LSE, much better.

Kuo and Lin proposed in their publication [

Block diagram of the control process (graphic representation of system process) [

Based on the vehicle detection in the intersection area first the secondary input variables were assessed (“width” of the intersection and longitudinal slope of the intersection lanes), which served to trigger the selected cases 1 to 4. The combination of main input variables detected during the cycle (average speed, congestion factor, and vehicle position) further triggered the defined rules. The defuzzification process resulted in the appropriate setting of the LSE signal plan. From the system design it is obvious that the authors expanded the number of input variables by input variables reflecting the geometry of the intersection and the vehicle position determined based on the distance from the intersection stop line.

Murat and Gedizlioglu [

Block diagram of the LSE fuzzy control system [

Jacques et al. [

Expert publications dedicated to the application of fuzzy algorithms in the LSE control system after the year 2002 do not bring entirely new ideas; they mostly focus either on improvement of algorithms of other authors or on certain expansion of the control systems.

One of the other articles dealing with the application of the fuzzy algorithm in the LSE control system in combination with the genetic algorithm is the thesis by Chiou and Lan [

Illustration of the fuzzy rule and fitness function selection using the genetic algorithm [

In the 2009 article [

The authors Zhang et al. [

The authors Hu et al. also presented an interesting LSE control system in their 2007 article [

The block diagram of the genetic fuzzy generator database [

Hu et al. further elaborated on the idea of application of an advanced LSE control system in the following article [

Diagram of the hierarchic fuzzy control system [

Yang et al. [

HFLC architecture (hierarchical fuzzy logic controller) [

Authors Cheng and Yang proposed in their thesis [

In their article [

Block diagram of the transportation system [

Li and Zhang proposed in their article [

Block diagram of the fuzzy control system [

Zarandi and Rezapour [

Block diagram of the multilevel LSE fuzzy control system [

The publication of Rhung et al. [

Block diagram of the control system [

Wen et al. in their publication [

Block diagram of the “FRL” system of intersection control [

Chen et al. [

Niittymaki and Kikuchi [

In the article [

Relationship between learning automata and their environment [

In the recent study [

FUZZY-TIM: fuzzy logic setting the duration of the green of individual phases;

FUZZY-SEQ: fuzzy logic modifying the phase sequence;

FUZZY-MIX: combination of the two previous control systems (two-level fuzzy control system).

Lu et al. improved in their paper [

Another score of articles combining fuzzy logic and genetic algorithm is the 2011 publication by [

The article [

Illustration of the feedback within the control system [

Another series of articles combining the genetic algorithm and fuzzy logic for four-arm intersection control with LSE is the publication [

Block diagram of the multiphase fuzzy control system [

Yang et al. proposed in their article [

Block diagram of two-level fuzzy control system containing hybrid GA [

In this paper, we have conducted a comprehensive review of the literature dealing with the use of fuzzy sets and fuzzy logic theory in the field of traffic control systems. The review focused on various approaches which describe and predict the driver’s behaviour and optimize the flow of the traffic. The first works published in the late 1970s of the 20th century showed the possibility of using the vague description of the traffic state and using it for precise decision and control of light signalling. In the course of development there was a rise in works taking into account more complex systems and also more theories. The review covers all the above-mentioned approaches and discusses, to some extent, the advantages and drawbacks of the proposed models. Many studies involved comparison with the real datasets and proved the advantages of the exploitation of fuzzy sets and fuzzy logic.

Based on the literature survey, there are still open questions and issues that can be addressed in the near future studies. The challenges involve (i) the control of large number of crossroads simultaneously to ensure the continuous flow of the traffic especially in cases of traffic jams, (ii) the use of modern UAV based data collection and rapid mapping methods to avoid the traffic jams, (iii) the introduction of parameters describing situations of emergency when traffic accident occurs, (iv) the introduction of large sensors networks involving also the nonstandard parameters (driver mood, drastically changing weather, etc.), (v) the optimization of neural networks for description of traffic and their combination with fuzzy logic, and (vi) the use of robotic vehicles without drivers.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The study has been supported by the Education for Competitiveness Operational Program, European Social Fund (Project CZ.1.07/2.3.00/20.170 of the Ministry of Education, Youth and Sports of the Czech Republic), and by the Project 14-26831S of the Czech Science Foundation.