Intelligent Fuzzy Traffic Signal Control System for Complex Intersections Using Fuzzy Rule Base Reduction

Abstract

In this study, the concept of symmetry is employed to implement an intelligent fuzzy traffic signal control system for complex intersections. This approach suggests that the implementation of reduced fuzzy rules through the reduction method, without compromising the performance of the original fuzzy rule base, constitutes a symmetrical approach. In recent decades, urban and city traffic congestion has become a significant issue because of the time lost as a result of heavy traffic, which negatively affects economic productivity and efficiency and leads to energy loss, and also because of the heavy environmental pollution effect. In addition, traffic congestion prevents an immediate response by the ambulance, police, and fire brigades to urgent events. To mitigate these problems, a three-stage intelligent and flexible fuzzy traffic control system for complex intersections, using a novel hybrid reduction approach was proposed. The three-stage fuzzy traffic control system performs four primary functions. The first stage prioritizes emergency car(s) and identifies the degree of urgency of the traffic conditions in the red-light phase. The second stage guarantees a fair distribution of green-light durations even for periods of extremely unbalanced traffic with long vehicle queues in certain directions and, especially, when heavy traffic is loaded for an extended period in one direction and the short vehicle queues in the conflicting directions require passing in a reasonable time. The third stage adjusts the green-light time to the traffic conditions, to the appearance of one or more emergency car(s), and to the overall waiting times of the other vehicles by using a fuzzy inference engine. The original complete fuzzy rule base set up by listing all possible input combinations was reduced using a novel hybrid reduction algorithm for fuzzy rule bases, which resulted in a significant reduction of the original base, namely, by 72.1%. The proposed novel approach, including the model and the hybrid reduction algorithm, were implemented and simulated using Python 3.9 and SUMO (version 1.14.1). Subsequently, the obtained fuzzy rule system was compared in terms of running time and efficiency with a traffic control system using the original fuzzy rules. The results showed that the reduced fuzzy rule base had better results in terms of the average waiting time, calculated fuel consumption, and CO₂ emission. Furthermore, the fuzzy traffic control system with reduced fuzzy rules performed better as it required less execution time and thus lower computational costs. Summarizing the above results, it may be stated that this new approach to intersection traffic light control is a practical solution for managing complex traffic conditions at lower computational costs.

1. Introduction

Traffic congestion in large cities and urban and suburban areas is an ever more challenging problem because of the constantly increasing population growth and vehicular usage [1]. Intelligent control mechanisms for traffic flow systems are required to improve the efficiency of the available resources (road capacities, fuel, time, etc.). In addition, the time lost due to heavy traffic indirectly affects economic productivity and leads to energy loss. Traffic congestion has a significant negative impact on the countries’ economies and health conditions [2,3]. Heavy traffic jams and congestion can be caused by accidents or unpreventable emergencies. Additionally, structured traffic jams occur due to the overload of the roads at specific times of the day, and of the week, etc., particularly during rush hours [4]. Road intersections are generally categorized into two types: isolated and intricate. To tackle the issue of traffic congestion, concentrating solely on isolated intersections is insufficient if the goal is mitigating extensive traffic congestion in urban areas and large cities. Thus, addressing intricate intersections (complex network intersections) is crucial for alleviating traffic bottlenecks and solving related problems [5].

To address these problems, it is crucial to develop more and more advanced intelligent traffic light control systems for complex intersections. Researchers, along with other stakeholders, have attempted to (as much as possible) optimize traffic control systems to solve the problems caused by the saturation of traffic flow. Currently, research is focused on intelligent and efficacious traffic signal control systems in order to provide the possibility of better decisions under fluctuating conditions in the traffic situations. The most promising approaches so far use computational intelligence (CI) and artificial intelligence (AI) techniques, such as reinforcement learning, evolutionary algorithms, neural networks, fuzzy systems, and their respective combinations [1,6]. In this study, a novel intelligent fuzzy control method and implemented system are proposed that have been so far tested on simulated traffic in various topologies of intersections.

Over the past decades, there has been a continuous increase in the successful utilization of fuzzy control systems across diverse applied sectors, such as in traffic control systems, industrial processes, robotics, or flight motion control. The main reason for this growing trend is that traditional control theory is only suitable for handling a limited class of systems efficiently, primarily well-defined linear or quasi-linear ones without any uncertainty elements. Consequently, fuzzy rule bases, which are suitable for implementing non-linear control systems and can handle vague information and vagueness and imprecision, are a better choice than other approaches for controlling such complex systems with uncertainty. Obviously, as traffic flow conditions are fluctuating, unpredictable, inconsistent, and inaccurate, the fuzzy control approach may be better than the other control models.

Fuzzy models have two advantages that have led to the wide spread of this technology. The first is the ability to reduce algorithmic complexity by proper granularization of the state space, while the second is transparency and thus easy applicability and tenability of the model. Complexity reduction is a result of the appropriate granulation of the input state universe, in our case, of the traffic intensity range. Obviously, the more refined this granulation is, the higher the complexity is. However, the more refined the granulation is, the more adequate (“good”) the approximated model is. These two contradictory requirements may be brought into optimal balance, as was shown in [7].

The primary concept of fuzzy control is a combination of fuzzy set theory initially proposed by Zadeh and of symbolic expert control used in traditional AI [8]. The concept of control by a fuzzy rule system with linguistic values was implemented soon by Mamdani and turned out to be sufficiently efficient for the control of a highly nonlinear process [9]. Later, Takagi and Sugeno proposed an alternative type of rules, where they assumed that nonlinear phenomena can be sectioned and treated as linear in each [10]. However, a subsequent analysis revealed that the transient areas between these sections are not smooth and cause some difficulties when those sections differ strongly in the parameters [11]. Because of this, in this research, this potential alternative model has been ignored, even though it has been shown that the two types of fuzzy rule bases are mathematically equivalent in limit [12]. (For this choice, cf. also [13].)

Mamdani-type fuzzy systems are defined by IF–THEN type production rules using linguistic variables, as follows:

Rule R_i: IF x₁ is A₁, x₂ is A₂, …, x_m is A_n, THEN y is B,

where A_i and B are linguistic values (terms) represented by fuzzy sets for the input variables x and output variable y, respectively. This type of fuzzy system uses linguistic terms for both the premises and consequents [14] (in contrary to the Takagi–Sugeno controller, which has crisp functions in the output). The knowledge base of a fuzzy controller system comprises the design parameters of the fuzzy controller defining the way of discretization (granulation) and of normalization of the universe of discourse, the fuzzy partition of the input and output variables, and accordingly, the concrete membership functions of the primary sets. As shown above, the rule base is characterized by a set of linguistic statements that are represented in the form of IF…THEN rules. The number of rules to be generated for making optimal decisions depends on the number of inputs and linguistic terms considered for each input [15,16]. A traditional fuzzy rule-based system consists of a complete rule base with all possible combinations of input terms, although some of these rules may be insignificant from the perspective of the actual application [17]. Thus, when implementing a classic Mamdani-type fuzzy control rule base, all the antecedent fuzzy sets of theoretically possible combinations and rules must be considered.

For example, consider a scenario with five antecedents (premises) and one consequent. Assume that each antecedent has been partitioned into seven linguistic values, {zero, small, medium, large, very large, extreme, and extremely large}. Thus, the total number of the rules to be generated from these input variables is 7⁵ = 16,807, which is the so-called dense inference rule base, and which requires rather high computational time and large storage space. Obviously, in the Mamdani-type traditional fuzzy control system, when the number of linguistic values increases, the number of rules increases exponentially, which slows down the control system and may even essentially influence its performance. Furthermore, from a hardware perspective, dense rule bases in fuzzy systems require expensive hardware (cf. [15]). In this paper, the authors repeatedly suggest that it is very important to keep the number of fuzzy rules as low as possible while ensuring the efficiency of the output produced by the system.

To overcome this challenge, researchers have proposed various fuzzy rule reduction techniques to avoid or reduce the effect of the problem of combinatorial explosion. Various approaches to complexity reduction have been introduced in the literature (see details of the reduction techniques in Section 2.3). Given this fact and the unpredictable nature of traffic conditions, including inaccuracies and difficulties in computational time, this study proposes the use of Mamdani-type fuzzy control approaches, integrated with a novel hybrid reduction method applied on the fuzzy rule base, to solve complex intersections using an efficient fuzzy inference system. The proposed approach was designed to reduce the number of significant fuzzy rules in the original rule base without largely compromising its performance.

In the past decades, numerous researchers have endeavored to address obstacles associated with traffic signal control by employing fuzzy control and other CI techniques. Next, an overview of the related literature is reviewed.

H. Mu et al. proposed a traffic signal control system for urban traffic intersection groups based on a fuzzy control approach. The researchers designed a distributed control system comprising local fuzzy controllers and a specialized case controller. Each local fuzzy controller regulates the traffic flow at its designated intersection. When traffic conditions exceed the capacity of the local fuzzy controller, a specialized case controller is activated. Based on the simulation results, the authors concluded that the fuzzy control approach could accommodate variations in traffic flow with significantly enhanced efficiency [18]. S. Jafari et al. presented an improvement of the road traffic control prediction based on a fuzzy system approach in a net of multiple intersections. In that study, a Takagi–Sugeno (TS, see [10])-type fuzzy model approach was applied and simulated, and the behavior of adjacent intersections was investigated. The simulation results showed that the TS fuzzy model performed better than fixed-time scheduling in terms of decreasing the length of queuing times for vehicles at intersections [19]. J. Jin et al. proposed an optimization framework for two-intersection road traffic control based on evolutionary algorithms. They simulated and evaluated the performance of their proposed approach using SUMO, and finally, the authors recommended that the developed framework could optimize traffic control for large-scale networks [20]. Further studies combining our novel method with evolutionary techniques may be rather interesting.

A. Peter et al. conducted research on efficient traffic control systems using a rule-based fuzzy system with priority. The authors simulated the proposed approach using MATLAB and SUMO for a single intersection and classified the simulation case into three types: four-way, two-way, and one-way high-density traffic flows. The results demonstrated that, under all traffic conditions, their proposed approach performed better than the fixed-time traffic light control system [21]. S. Komsiyah et al. presented a traffic light analysis study and simulation using a Mamdani-type fuzzy inference system for isolated intersections. Again, the Mamdani-type fuzzy method performed better than the conventional traffic flow control system [22].

R. Jimenez-Moreno et al. presented an ambulance car detection method for smart traffic light applications with a fuzzy controller. They presented a two-stage artificial intelligence (AI) algorithm. In the first stage, emergency vehicles were detected using a deep neural network with a ResNet-50 architecture. In the second stage, the duration of the green-light time was controlled, while emergency vehicles were detected using a fuzzy inference system. Finally, the authors concluded that the integration of deep learning techniques and fuzzy systems enables intelligent traffic light applications to prioritize emergency vehicles without the direct intervention of human control [23]. N. Iksan et al. proposed an intelligent traffic system with a focus on ambulance cars, again using a fuzzy control system. They designed a four-legged intersection using radio frequency identification (RFID) to detect the appearance of ambulance cars and applied infrared sensors to detect road traffic conditions based on the number of vehicles in the intersection. The values detected by the RFID and infrared sensors were used as the input values for the fuzzy control system to determine the priority degree for each lane. This priority value was then transmitted to the server to switch the green light to the lane where the ambulance car intended to pass. Finally, the authors proved that the fuzzy control system is an appropriate control method for prioritizing emergency cars, particularly when collisions occur [24].

A. Jovanovic et al. conducted research on restricted crossing U-turn (RCUT) traffic control using interval type-2 fuzzy logic. The researchers designed the RCUT so that it had significantly lower demand from the minor streets than from the arterial streets. To investigate the effectiveness of the proposed approach, the authors simulated numerous experimental scenarios using the VISSIM software, focusing on the vehicle queue length and number of stops per vehicle. The results showed again that the proposed approach outperformed conventional traffic signal control [25]. F. Maheen et al. proposed a fuzzy control approach for traffic light control systems at four-way intersections and T-crossings. The authors designed and implemented their fuzzy traffic light control system in MATLAB to reduce waiting times and vehicle queue sizes at intersections. As expected, their system outperformed traditional traffic control systems [26].

The reviewed literature results revealed that, unequivocally, fuzzy control systems are a rather promising approach to solve the problem of traffic congestion and are definitely better than other control methods for resolving complex traffic issues. However, the majority of the reviewed studies failed to consider abnormal traffic situations, such as extremely unbalanced vehicle queues in conflicting directions and, at the same time, prioritizing emergency vehicles without significantly affecting non-emergency vehicles. The greatest problem of all these results is, however, that they do not avoid the problem of computational complexity and tractability of the respective approach in the case of larger intersection networks.

In this study, the concept of the hierarchical three-stage intelligent fuzzy traffic signal control system presented in [27] for isolated intersections was extended to more complex intersections, and integrated with a novel hybrid fuzzy rule base reduction approach (see Figure 1). The antecedent research investigated the inadequacy of conventional traffic control methods and also of existing traffic signal control systems. For an easy overview, a simple case study was carried out, in which only two and three adjacent intersections were considered. It is, however, easy to further expand the proposed approach to multiple intersections (e.g., for topologies of larger cities or for modeling connections to neighboring cities), which may be implemented in the same fashion, although, as a matter of course, it requires more resources, faster computers, and more time.

Thus, to create a smart fuzzy traffic control system that can effectively handle complex intersections, the concept of a new fuzzy traffic signal control system was proposed. This innovative system integrates a novel hybrid size reduction method for fuzzy rule bases that utilizes the idea of fuzzy rule interpolation and of the classic state reduction technique applied in digital design in a novel combination. This new system improves the overall quality of the fuzzy inference process and can solve traffic congestion problems rather efficiently, even for complex and multiple intersections. The details of the fuzzy rule reduction technique will be described in Section 2.3.

2. Basic Model, Methods, and Tools

Most traffic signal control systems currently in use worldwide do not offer optimal and efficient solutions to unpredictable traffic conditions. So, they do not match the contradiction of the available transportation infrastructure and the growing traffic intensity—which will also remain in the future due to budget and resource constraints in most cities and countries.

2.1. Existing Traffic Signal Control Systems and New Proposed Model

Traffic signal control systems (TSCS) play a crucial role in ensuring a smooth traffic flow, particularly when the control of a certain intersection is synchronized with that of other nearby intersections. The primary goal of traffic signal control is to ensure that travelers can navigate intersections safely and efficiently [28]. Many signal timing parameters can affect the intersection efficiency, such as cycle length, movement green time, and clearance intervals. Traffic signal control systems commonly use three light signals, namely red, yellow, and green. They indicate stop, transition, and go ahead, respectively [28,29].

Existing traffic signal controllers can be classified into three types: fixed time, actuated, and adaptive operation types. Fixed-time traffic signals follow a predetermined schedule, with the cycle length, phase duration, and interval duration as fixed values. The main drawback of this system is that it is not responsive to traffic demands, thus it does not provide optimal signals which would minimize congestion and enhance safety, owing to the dynamic nature of the traffic. Unlike fixed-time signals, actuated signals respond to the presence of vehicles or pedestrians in order to start the corresponding specific phases of traffic at intersections. However, they only consider the actual traffic conditions monitored by inductive loop detectors buried under the road surface and they fail to consider broader traffic conditions, such as the actual size of the vehicle queues and the presence of urgent traffic situations. Consequently, neither the fixed-time nor the actuated traffic signal control systems can effectively respond to the dynamic nature of natural traffic conditions [30].

To address these issues, researchers have proposed the implementation of heuristic adaptive traffic signal control systems since the 1970s [31]. Adaptive traffic signal control systems adjust signal timing based on real-time traffic data collected using magnetic (loop) detectors. Many types of such control systems are currently in use, including SCOOT, SCATS, UTOPIA, and PRODYN. These systems are designed to respond quickly to changes in traffic flow and to provide green-signal times. However, they also have several drawbacks such as being centralized and relying on large communication networks that are prone to failure. Additionally, these systems can be limited in their ability to accurately assess traffic conditions because they only consider the presence of vehicles in the lanes immediately before the intersection, and do not consider the longer queues that may be caused by heavy traffic [30,32]. A further drawback of these existing traffic signal control systems is that they cannot be expanded to large-scale regional networks because they are centralized and the sensors are situated beneath the lane pavement (e.g., see [33,34]).

The proposed new model is a more sophisticated fuzzy traffic signal control system consisting of three stages, as discussed above. The proposed model was implemented and simulated in two case studies, which are explained in Section 2.5 using SUMO (sumo-GUI 1.14.1) [35]. The proposed and implemented software has three components: a graphical user interface (GUI) designed using SUMO that acts as a server; a fuzzy inference module that determines the green-light duration depending on the collected traffic data; and a main function (program) that acts as a client to gather real traffic data during simulation, provide traffic data for the fuzzy inference engine, and to enable the fuzzy inference system to connect with the GUI using the Traffic Control Interface (TraCi 1.19.0), which is a package of SUMO (see Figure 2). The main program component of the algorithm (the “middle program” of the proposed system) performs at least four functions. First, it collects real traffic data from SUMO by connecting via TraCi during the simulation and provides the necessary information for the fuzzy engine. Second, it prioritizes emergency vehicles if any are detected, without significantly affecting non-emergency vehicles. For instance, if an (some) emergency car(s) appears in the current red-light phase direction, the system checks the time left in the current green-light phase to switch to the red light. If it takes more than 5 s to turn to the red light, the algorithm adjusts the duration of the current green light to a maximum of 3 s and switches to the red light to prioritize the emergency car(s) detected from the direction of the current red phase.

Next, the algorithm compares the queue size in the direction where there is no emergency vehicle and the waiting times for the current green- and red-light phases. Finally, it adjusts the green-light duration that is received from fuzzy inference and provides for the appropriate phase depending on the real traffic data collected using a lane area detector (e2) while considering the short vehicle queue size based on the threshold waiting time of a short vehicle queue. The algorithm of the main function was implemented in the same fashion as the fuzzy rules to dynamically handle traffic flow at intersections, using TraCi in Python to realize the objective of the proposed fuzzy traffic control system. The system can effectively handle uncommon traffic conditions. These include the simultaneous arrival (potential occurrence of collisions) of emergency vehicles in one or multiple directions and also unexpectedly long vehicle queues for an extended period in the directions where no emergency vehicles appear, where short (or even very short) “non-emergency vehicle” queues require passing in the red-phase direction. Thus, the new approach is significantly more effective and is scalable for complex intersection strategies compared to all so far existing intelligent fuzzy traffic approaches. The reason why it is scalable is that it integrates a novel hybrid reduction method that will be explained in the next section. So, it also offers a more advanced set of intelligent features.

In the simulation, real traffic data were collected by using the lane area detector in the SUMO package. Theoretically, in the proposed model, real traffic data are assumed to be supplied by a smart camera connected to an intelligent fuzzy traffic controller with additional functions, such as image processing and sound recognition. The smart camera is supposed to detect approaching vehicles that are in unusual traffic conditions, identify the size of vehicle queues, and provide all the necessary information to the fuzzy inference system. This system is capable of taking action based on the information provided by a smart camera. However, for the purpose of the simulation, a hypothetical lane area detector was used to retrieve real traffic data.

The proposed model was structured and implemented in modular software using Python. The main characteristics of the modular software provided an improvement of the implemented system owing to its better reusability, robustness, and flexibility. Because the model is modular, it ensures that the system is flexible, robust, and easily extendable to large-scale traffic networks, and is easier to maintain than the existing traffic control systems. Moreover, the primary objective of the proposed model is to address intricate traffic intersections effectively. The secondary objective was to design a computationally efficient system, and so it was developed by using an innovative fuzzy control mechanism based on a sparse “Mamdani-type” fuzzy rule base obtained by the new reduction algorithm. This enabled the new model to improve the extension of fuzzy traffic control systems to extensive traffic networks with lower computational time and storage-space requirements.

An example for the possible structure of the complex intersection to be handled by the new method is shown in Figure 3. It has various types of intersections, including T-junctions. However, so far, only two simple case studies were simulated: one consisting of two adjacent intersections and the other of three connected intersections. For these two case studies, five scenarios were identified to evaluate the proposed system and were compared with the original dense Mamdani-type fuzzy rule-based controller and also with the traditional fixed-time controller.

In the simulation experiments, the following scenarios were investigated. Scenario 1: Increase the number of incoming vehicles from east to west and west to east while maintaining a low number of vehicle arrivals from conflicting directions (north to south and vice versa). In this scenario, the vehicles do not turn to the right or left; they only move forward. Scenario 2 is the opposite of Scenario 1, which increases the number of incoming vehicles from north to south and south to north, whereas a small number of vehicles from conflicting directions (turning left or right) are not allowed. Scenario 3 increases the number of incoming vehicles from east to west, east to north, east to south, west to east, west to north, and west to south while keeping a low number of cars arriving from the conflicting directions. In this scenario, vehicles can turn to the left, turn to the right, and move straight forward from all directions. Scenario 4 is the opposite of Scenario 3, which increases the number of incoming vehicles from the north going to the other three directions and from the south also going to the other three directions, while a low number of vehicles from contradictory directions is maintained. Scenario 5 has an equal distribution of vehicle numbers from all directions, while cars from all directions may go straight forward, turn to the left, and turn to the right.

The simulation was performed using SUMO, employed in conjunction with the fuzzy traffic controller developed using Python and the SciKit-Fuzzy library (version 0.4.2) [35]. The graphical user interface was created using SUMO netedit 1.14.1, a component of SUMO that offers an intuitive graphical user interface for designing and modifying traffic road networks ranging from simple road layouts to complex urban infrastructure. Netedit accommodates a wide range of inputs and outputs, making it possible to design, adjust, and implement various traffic scenarios, including the detailed management of vehicles, routes, and additional simulation elements. The SUMO simulation software also offers a comprehensive array of output files that facilitate the quantitative assessment of the simulation scenarios. These output files encompass traffic data sourced from modeled detectors, vehicle trajectories, emissions, and energy consumption. To assess the efficacy of the proposed system, CO₂ emission and fuel consumption were also evaluated using an emission model integrated with the SUMO software. This model calculates emissions at every discrete time step during the simulation [35].

The TraCi tool was used to integrate the fuzzy inference system developed in Python with the SUMO graphical user interface. TraCi is the tool in the SUMO simulator that enables the real-time control and monitoring of simulation variables from external applications, particularly from Python [36]. A lane area detector was used to collect real traffic data during the simulation in an area along the lanes. This gives similar information to a real-world vehicle tracking camera. In contrary to induction loops, a lane area detector provides the length of the queue specified by the length attribute (pos and endPos) [35]. This way, in the simulation, the lengths of the vehicle queues, the waiting times, the emergency vehicles, and some other traffic data were collected using the lane area detector of SUMO.

2.2. Advantages of the Fuzzy Control Method

As it has been stressed above, the fuzzy control approach is more intelligent and more suitable for traffic signal control systems compared with traditional signal control theory-based approaches since it is able to imitate human experts by using mappings for inputs and outputs that are granulated in a way that is suitable for overview and the granules are described in natural linguistic terms (“extremely short”, “very short”, ”long”, ”very long”, etc.). These are easy to understand and to be included in the design and setup of a real-world scenario, since the whole approach operates in a similar manner to human experts. To design and implement the fuzzy controller, the control engineer (expert) gathers information (necessary data) on how the intelligent decision of the fuzzy controller should act in the case of a given situation. The collected information on how to make an intelligent decision may have come from a human expert with experience in the control task. Sometimes, the control engineer can observe, investigate, and understand the plant dynamics (the area of the problem) and create a set of rules for how to control the system without external help [37,38]. Thus, the fuzzy control method was chosen to further develop and extend existing fuzzy traffic signal control approaches towards a more intelligent, adaptive, and flexible solution that is simultaneously computationally more feasible.

2.3. The Proposed Novel Fuzzy Rule Base Reduction Method

The traditional Mamdani-type fuzzy rule system is commonly employed to facilitate more effective decision-making by comprehensively encompassing all potential rules, as previously mentioned. Despite its effectiveness, this approach may not be practical for tackling intricate tasks involving numerous variables, owing to its high computational complexity. Thus, this approach has limitations because of its significant computational time burden and large memory requirements [39,40]. Due to the exponential cardinality of the rule base, the practical usability of the Mamdani fuzzy-type system has rarely exceeded five or six input variables in real-life applications. If our proposed system is to be refined further, the number of rules will further increase, and it may become very difficult to manage, especially in real-life systems with the 100 s of intersection. In the next section, a novel approach will be proposed, which is based on the combination of the idea of manipulating the Mamdani-type dense rule base by an interpolation-type reduction and a technique extending the algorithm of state reduction in digital design.

To overcome the disadvantages of the traditional fuzzy rule-based control method, researchers have proposed various approaches to minimize fuzzy rules without essentially affecting the performance of the original system. Originally, the idea of fuzzy rule interpolation in sparse rule bases was proposed by Kóczy and Hirota (referred to in the literature as the KH method) and presented a size reduction by interpolation in fuzzy rule bases. The KH method proposes that, by reducing the size of the fuzzy rules, the information of the original base should be essentially preserved to ensure that the remaining rule base of the model is suitable for practical applications. So, if the original model is a linguistic qualitative model, it is expected that the reasoning in the reduced model will also include linguistic qualitative statements concerning the output. The criterion for accuracy in this case is that the retransformation of the conclusion to linguistic terms by finding the best approximating term for every omitted antecedent in the original rule base should be identical to the corresponding omitted consequent [41].

Other researchers have also attempted to develop a method for minimizing the size of the fuzzy rule base. For instance, R. Hampel et al. also presented a minimization of the number of variable parameters to optimize the fuzzy controller [42]. H. Bezine et al. proposed a reduction in large-scale fuzzy rule bases for the fuzzy control of robot manipulators [43]. M. K. Ciliz proposed a novel tuning and rule reduction approach that was applied for the development of knowledge-based fuzzy controllers with applications to vacuum cleaners [44]. J. Dombi et al. developed a modified Mamdani-like model to decrease the computational requirements in Mamdani-type fuzzy control systems [45]. C. W. Tao presented fuzzy rule combination as one of the fuzzy rule reduction techniques in a research paper on the reduction approach for fuzzy rule bases of fuzzy controllers. In his paper, the rule combination approach for the dominant consequent matrix containing redundant (dependent) vectors was described. After the redundant vectors were identified, he combined identical consequent vectors to produce a new reduced fuzzy rule [39].

In this study, two fuzzy rule size reduction techniques (partly introduced earlier) were combined by observing the behavior of our system. These two fuzzy rule reduction techniques are the fuzzy rule interpolation and the rule combination by merger techniques. To test the efficiency of this new combination approach, the fuzzy rule base obtained from the original by applying fuzzy reduction techniques was simulated using the two simple case studies described in the next section, and the results were compared with the results obtained by applying the original fuzzy rule base. The main reason for selecting these two reduction techniques is that the interpolation method cannot be directly applied to fuzzy rules with linguistic values that do not exhibit a full ordering. To apply the interpolation algorithm, it is essential to meet certain prerequisites, one of which is that the state variables, including the input universe X and the output universe Y, must be bounded and gradual. This requirement ensures that full ordering exists in each based on the concept of gradual rules [46]. Gradual reasoning based on these rules can namely be applied only whenever the input and output variables are gradual themselves. In most industrial applications, variables such as the spatial position, velocity, acceleration, pressure, and temperature are used, and therefore, a natural full ordering exists [47].

Thus, sparsening the rule base combined with the rule interpolation technique were applied to reduce some fuzzy rules of the proposed system where they fulfill the conditions for gradual reasoning and full ordering, as is shown in

Table 1. Sample of fuzzy rules that fulfill gradual reasoning conditions, before reduction.

	Qg	Zero	Small	Medium	Large	Very Large
Dht
zero		medium	medium	medium	long	very long
small		short	medium	medium	long	very long
medium		short	short	medium	long	very long
large		short	medium	medium	long	very long
very large		short	medium	medium	long	very long

and

Table 2. Fuzzy rules that are obtained by reduction from those in Table 1.

	Qg	Zero	Medium	Very Large
Dht
zero		medium	medium	very long
medium		short	medium	very long
very large		short	medium	very long

. However, applying the interpolation technique to reduce the size of the remaining fuzzy rules was impossible, because the terms there failed to satisfy the full (linear) ordering condition.

According to [47], gradual reasoning does not fulfill all the requirements of real-life variables. They described in their paper an example of traffic light colors: red, yellow, and green, which are used in the traffic control systems. However, there is no internal structure in the set {red, yellow, green} in the sense that yellow is not “between” red and green in the sense of an ordering, so the gradual reasoning approach is not applicable because each of the light colors requires another independent behavior from the side of the driver. To minimize the number of fuzzy rules in the subsystems that do not satisfy ordering, a combination approach that was motivated by the state merger algorithm used in the Boolean state minimization was implemented. (This is essentially a technique where for partial rule sets, where the input combinations could be merged, simplified—fewer input variables—rules could be obtained, like in the block identification in a Karnaugh table).

This was proposed in a form by R. Rovatti et al., who introduced a combination approach similar to Boolean synthesis methodologies for fuzzy rule minimization. In their study, a fuzzy-to-Boolean mapping was devised, which takes advantage of this relationship to enable the minimization of a given set of fuzzy rules through existing Boolean synthesis algorithms. For example, consider a fuzzy controller system containing two input variables x₁ and x₂ with three and two linguistic values, {small, medium, large} and {large, very large}, respectively. If the fuzzy output variable is y, it has two linguistic values {yes and no} [48]. The fuzzy rule base of the fuzzy controller is as follows:

R1: If (x₁ is small) and (x₂ is large), then y is yes.

R2: If (x₁ is medium) and (x₂ is large), then y is yes.

R3: If (x₁ is large) and (x₂ is large), then y is yes.

R4: If (x₁ is small) and (x₂ is very large), then y is no.

R5: If (x₁ is medium) and (x₂ is very large), then y is no.

R6: If (x₁ is large) and (x₂ is very large), then y is yes.

From R1 to R3, the fuzzy rules of the inference system are reduced to a single rule of R’, as follows:

R’: If [(x₁ is small) or (x₁ is medium) or (x₁ is large)] and (x₂ is large), then y is yes [48].

Here, the proposed fuzzy rules are reduced using the combination approach applied for Boolean synthesis algorithms. These variables do not fulfill the interpolation criteria described above (see

Table 3. Sample of fuzzy rules that do not fulfill the gradual reasoning conditions, before reduction.

	Wtg	z	sh	m	l	vl
Wtr
z		g	g	g	g	g
sh		r	g	g	g	g
m		r	r	g	g	g
l		r	r	r	g	g
vl		r	r	r	r	g

where z = zero, sh = short, m = medium, l = long, and vl = very long, for both Table 3 and Table 4.

and

Table 4. The fuzzy rules obtained by reduction from those in Table 3.

	Wtg	z	z/sh/m/l/vl	sh	sh/m/l/vl	m	m/l/vl	l	l/vl	Vl
Wtr
z			g
sh					g
sh/m/l/vl		r
m							g
m/l/vl				r
l									g
l/vl						r
vl								r		g

); so, another method must be applied. The proposed novel reduction approach algorithm is summarized in the verbal pseudo-code description shown in Figure 4. This algorithm was proposed for application to the fuzzy rule base of a traffic signal light control system, as described in the next section.

2.4. The New Intelligent Fuzzy Traffic Signal Control System

The hierarchical three-level fuzzy traffic control system proposed in this study builds upon and expands on the model introduced in [27] by including innovative components such as the middle program component depicted in Figure 2. This component enables the system to remotely manipulate a GUI, which has been simulated using SUMO, to dynamically adjust the traffic light duration based on the real-time traffic conditions obtained through a lane area detector. For simplification, it has been implemented and evaluated in several case studies of two and three adjacent intersections (see Figure 5 and Figure 6). The system was developed in a way that uses a minimal number of fuzzy rules, as discussed previously. In this section, the new method will be described.

The proposed fuzzy traffic control system is a three-level hierarchical architecture that operates in a cascaded manner (as illustrated in Figure 1). The architecture comprises four modules, each one to address one of the issues discussed above and to resolve the limitations of the existing traffic signal timing controllers. The first stage in the cascaded system includes two algorithmic modules: Prioritized Emergency Car Module (PECM) and Heavy Traffic Evaluation Module (HTEM). The second-stage module is the Calculating Waiting Time Module (CWTM), and the third one is the Extension Time Decision Module (ETDM).

The PECM module is implemented for the detection of emergency car(s) approaching from all directions (current green-light and red-light phases) and granting priority if there is need for that. This module operates continuously to guarantee optimal traffic control in the absence of emergency vehicles.

The philosophy of the decision here is the following. In an ordinary situation, there are no emergency cars coming at all. However, if it happens that emergency cars are approaching, and an equal number of emergency vehicles are simultaneously detected in the current red- and green-light directions, priority is always given to the emergency vehicles in the current green-light phase, which is the realistic approach. However, if the number of emergency vehicles present in the red-phase incoming road is (considerably) greater than that in the present green-phase direction(s), the green light changes in 3 s to red and prioritizes the emergency cars detected in the red-light phase. This module contains two inputs and one output. The inputs are the number of emergency cars detected in the current red-phase direction (E_r) and the green-light phase (E_g). The output of this module is an indicator of the possible priority of emergency vehicles (P_em). Three linguistic values can be assumed for both antecedent and consequent variables. As the input terms, the linguistic values {none, few, many} were chosen. The output values are “no emergency car” (none), “at least one emergency car detected in the red-light phase” (E_r), and “at least one emergency car is detected in the green-light phase” (E_g). Therefore, for this module, nine fuzzy inference rules were used to establish the fuzzy rule base (3 × 3 = 9).

The HTEM module assesses the degree of the heaviness of the traffic in the current red-light phases and identifies the urgency of the traffic flow in these red phases. The antecedent variables of this module vehicle are the queue length of the red-light phases (Q_r) and the waiting time of the vehicles in the red-light phases (W_tr). The consequent variable of HTEM is the identified degree of heavy traffic (D_ht). For all variables, there are five linguistic values, {zero, small, medium, large, very large}, that can be assumed by Q_r and D_ht. The linguistic values for W_tr are labeled as {zero, short, medium, long, very long}. Hence, based on the linguistic values of the input variables, it is possible to create fuzzy rules for the HTEM using a 5 × 5 = 25 size inference rule base.

The aim of the second stage module (CWTM) is to ensure a fair distribution of green-light durations, particularly during prolonged heavy traffic flow in one direction(s), even when only short (or very short) vehicle queues exist in the conflicting directions waiting for passing. In response to these circumstances, the module switches the green light to red, as required, when this waiting time is too long. CWTM has four antecedent variables and one consequent. The antecedent variables are the waiting time of the cars in the red-light phase (W_tr), the waiting time of the cars in the green-light phase (W_tg), the degree of heavy traffic in the red phase (D_ht), and the current traffic conditions of the green-light phase (Q_g). The consequent (non-fuzzy) variable is the decision to switch off or keep on the green-light phase (S_wr). Two input variables, namely W_tr and W_tg, have five linguistic values to which five membership functions are given, {zero, short, medium, long, very long}, while D_ht has only two linguistic values, with two membership functions labeled {zero, small}, and Q_g has also two linguistic values, namely {large, very large}. The output variable also has two linguistic (in reality, symbolic) values: “keep the green light” {keepg} and “switch the green light to red”, if necessary {switchr}. Thus, 5 × 5 × 2 × 2 = 100 fuzzy rules are used to create an inference engine for this module.

Here, an exceptional fuzzy rule set was used as the submodule of the CWTM. Although basically only 100 fuzzy rules are required for this module, while the simulation is performed, some vehicle data in the range of the linguistic values {medium, large, very large} of D_ht and {zero, small, medium} of Q_g can be generated in order to refine the decision. Therefore, when defuzzification is impossible for the linguistic values of D_ht and Q_g because of the number of vehicle intervals as mentioned, as the rule base is too sparse, the output calculation will become zero. Therefore, to handle this error, a further 3 × 3 × 5 × 5 = 225 fuzzy rules had to be added as a submodule of CWTM.

The fourth module in the proposed system is ETDM, which calculates the extension time for the green-light phase based on the results of the first and second stage modules, as well as the current traffic conditions of the current green-light phase. Therefore, ETDM has four input variables and one output variable. The two input variables D_ht (the output of HTEM) and Q_g (the current vehicle queue of green-light phase) have five linguistic values, where the following five membership functions are assigned: {zero, small, medium, large, very large}. S_wr (the output of CWTM) has two values, namely {keepg, switchr}, and the last input variable is the output variable of PECM, P_em, which has three linguistic values, namely {none, E_r, E_g }. Here, the set of 5 × 5 × 2 × 3 = 150 fuzzy rules was the size of the original Mamdani-type fuzzy rule base. The output of this module is an extension of the green-light time (G_e) and has five linguistic values (see Figure 7).

To optimize the above—rather large—fuzzy traffic control system in terms of computational time and storage space, our novel hybrid fuzzy reduction technique was applied (see the algorithm presented in Figure 4). This includes interpolation and applying the Boolean state reduction approach to all modules (PECM, HTEM, CWTM, and the exceptional submodule of CWTM, ETDM [27]). The size of the fuzzy rule base could be reduced essentially in the examples presented in Table 1, Table 2, Table 3 and Table 4. Finally, the number of original fuzzy rules was reduced from {9, 25, 100, 225, 150} to {6, 16, 36, 27, 57} for the modules. Thus, the proposed approach reduced the size of the fuzzy rule base from 509 to 142, that is, by 72.1% compared with the original inference rule sets. The remaining fuzzy rules (27.9%) were applied for the control, and after the simulation, they were evaluated for case studies with systems consisting of two and three adjacent intersections. Then, the results were compared to the results obtained with the original fuzzy rules. The novel hybrid reduced fuzzy rule base approach was applied for all other modules, similarly, and results were obtained as illustrated Table 2 and Table 4.

2.5. Case Studies for the Proposed Three-Stage Fuzzy Traffic Control System

To demonstrate the effectiveness of the proposed approach, two simple case studies with simulation experiments were conducted for two and three adjacent traffic intersections using the SUMO graphical user interface. This simulation was characterized by four incoming directions, with three lanes for each intersection. This provides 12 different lanes for each intersection, and allows cars to go straight, turn left, or turn right at each intersection (see Figure 5 and Figure 6 here, blue indicates lane area detectors, whereas yellow and red indicate the vehicles). For simplicity, in the case studies, isosceles triangular membership functions were used for all the input and output variables (see Figure 7 and Figure 8). Triangular membership functions are rather commonly deployed in fuzzy control systems because of their simplicity of use and interpretation. They are simple to understand, and their mathematical formulas are computationally efficient. These characteristics make them suitable for real-world applications, such as traffic control systems. Numerous studies suggest that applying more complex membership function shapes, such as Gaussian, does not lead to significant differences in the results when defuzzification or discrete values are obtained at the output, and triangular membership functions remain a widely used form of membership functions.

3. Simulation and Discussion of the Proposed Approach

An appropriate measure of effectiveness should be determined in order to evaluate the performance of the traffic signal control systems. Most studies have measured the effectiveness (MoE) of traffic signal control systems at intersections using the waiting time of a vehicle, average queue length, number of vehicle stops, and vehicle throughput [49]. Two experimental simulation modes were used in this study. The first one was based on a graphical user interface (GUI) using SUMO on two and three connected intersections (See Figure 5 and Figure 6). For the GUI simulation, the average waiting time, fuel consumption, and CO₂ emission metrics were used to compare the effectiveness of the proposed reduced intelligent fuzzy traffic control system (IFTCS) with that of the original IFTCS and fixed-time traffic control system (traditional traffic control system) using TraCi and SUMO. The SUMO software emission model package was used to calculate the fuel consumption and CO₂ emissions.

The second experimental simulation mode was implemented without a GUI to compare the reduced and original IFTCS in terms of the average extension green time using the SciKit-Fuzzy library in Python. Because the proposed system assesses the size of vehicle queues, identifies the degree of heavy traffic, detects emergency cars, and adjusts the duration of traffic lights according to traffic conditions and waiting times of vehicles using fuzzy inference rules, the output of the last stage (ETDM) is used to compare the performance of the reduced and original IFTCS. Moreover, to evaluate the computational efficiency of the proposed fuzzy traffic signal control system in terms of execution time, the time taken was assessed by the fuzzy traffic signal control system with reduced fuzzy rules and was compared with that of the system controlled by the original fuzzy rule base in both GUI and non-GUI experimental simulation modes.

The GUI experimental simulation was employed to evaluate the effectiveness of the proposed intelligent fuzzy traffic control system using the identified metrics. A comparison was made between the proposed IFTCS, the original IFTCS, and the traditional (non-fuzzy) fixed-time traffic control systems. To achieve this, five traffic condition scenarios were created and applied. Scenario 1 involves an increased number of vehicles moving from east to west and west to east while maintaining a low number of vehicle arrivals from conflicting directions, such as north to south, and vice versa. In this scenario, the vehicles do not turn right or left; they move forward only. Scenario 2 is the opposite of Scenario 1. In Scenario 3, the number of incoming vehicles from the east increased in all possible directions, including east to west, east to north, east to south, west to east, west to north, and west to south. However, the number of cars arriving in the conflicting directions remains low. In this scenario, vehicles can turn to the left, turn to the right, or move forward in all directions. Scenario 4 is the opposite of scenario 3. Scenario 5 had an equal distribution of vehicle numbers from all directions, allowing cars from all directions to move straight forward, turn to the left, and turn to the right (see Section 2.1 for details).

Likewise, an experimental simulation was conducted for a non-graphical user interface mode to evaluate the effectiveness of the proposed reduced IFTCS and was compared with the IFTCS using the original fuzzy rules. Simulations and comparisons were performed by classifying traffic flow conditions into three categories: low, medium, and high traffic flow. The range of the traffic flow intervals was determined using the fuzzy linguistic values of the input variables, including the vehicle queues (Q_r and Q_g) and waiting times of the vehicles (W_tr and W_tg). The low traffic flow condition was assigned to the linguistic values {zero, small} and {zero, short}, whereas the medium traffic flow rate was assigned to the linguistic value {medium}. The high traffic flow rate was assigned to the range of linguistic values {large, very large} and {long, very long}. Subsequently, a comparison was made in terms of the average extension time of the green light for all types of classified traffic flow conditions with the same data for both the IFTCS with and without reduced fuzzy rules.

Results and Discussion

Experimental simulations were conducted for the GUI experimental mode based on the identified scenarios for road systems with both two and three adjacent intersections for each type of controller, namely, the proposed reduced IFTCS, the original IFTCS (this fuzzy controller used original fuzzy rules), and the fixed-time traffic control system. The obtained results are shown in

Table 5. Results of the experimental simulation of the two adjacent intersection system using the GUI of SUMO.

Scenario	Type of Controller	Average Waiting Time	Fuel Consumption	CO2 Emission
1	Fixed-time controller	1,790,282.4	2,298,613,738.7	7,247,415,117.2
	Original fuzzy Controller	13,396.4	173,311,481.4	546,688,625.1
	Reduced fuzzy controller	10,184.5	170,411,598.2	537,543,315.9
2	Fixed-time controller	1,206,463.6	1,714,681,836	5,404,387,945
	Original fuzzy Controller	8261.2	146,179,509.1	461,042,514.3
	Reduced fuzzy controller	7952.9	145,707,088.7	459,552,321.0
3	Fixed-time controller	3,712,683.06	2,039,936,937.4	6,425,517,819.5
	Original fuzzy Controller	377,650.8	219,393,449.2	691,123,702.1
	Reduced fuzzy controller	377,519.6	219,656,878.2	691,956,218.5
4	Fixed-time controller	3,034,792.3	1,703,982,614.3	5,352,386,144.7
	Original fuzzy Controller	421,154.8	164,981,866.6	518,530,186.6
	Reduced fuzzy controller	420,190.0	164,912,364.1	518,318,464.2
5	Fixed-time controller	8,226,686.9	3,090,390,684.1	9,727,539,903.6
	Original fuzzy Controller	1,516,203.0	412,007,886.4	1,297,162,656.2
	Reduced fuzzy controller	1,516,203.0	412,007,886.4	1,297,162,656.2

and

Table 6. Results of the experimental simulations conducted on the three adjacent intersection system using SUMO.

Scenario	Type of Controller	Average Waiting Time	Fuel Consumption	CO2 Emission
1	Fixed-time controller	4,141,440.3	2,671,363,621.2	8,732,837,723.9
	Original fuzzy Controller	116,432.5	161,975,090.8	509,638,957.1
	Reduced fuzzy controller	44,480.2	155,551,391.7	489,283,128.5
2	Fixed-time controller	216,0982.5	2,268,354,046.5	7,176,264,829.3
	Original fuzzy Controller	489,705.5	198,997,541.6	627,161,552.7
	Reduced fuzzy controller	486,736.5	179,480,145.1	565,073,006.7
3	Fixed-time controller	8,016,445.8	3,614,394,444.3	11,931,153,691.5
	Original fuzzy Controller	707,736.6	285,066,606.4	895,313,592.2
	Reduced fuzzy controller	698,793.7	285,093,048.2	895,372,353.6
4	Fixed-time controller	5,172,492.0	2,799,442,074.0	8,849,963,764.8
	Original fuzzy Controller	1,099,891.2	252,423,086.8	794,314,688.9
	Reduced fuzzy controller	694,595.9	233,404,237.8	733,778,810
5	Fixed-time controller	9,612,733.0	4,230,330,676.5	14,623,172,779.3
	Original fuzzy Controller	1,295,266.6	437,689,355.8	1,378,238,892.9
	Reduced fuzzy controller	1,260,168.5	430,754,107.4	1,356,294,701.4

, and it may be seen that both the reduced and original IFTCS clearly outperformed the traditional traffic control systems in all scenarios and indicators (average waiting time, fuel consumption, and CO₂ emission). The improvement in the reduced and original IFTCS over a fixed-time traffic signal control system in terms of the average waiting time increased from 77.34% to 98.93%, and from the smallest to the largest, at both two and three adjacent intersections in all scenarios. Therefore, it may be stated that the proposed fuzzy traffic controller performs much better than the traditional traffic signal control in all scenarios and in terms of all proposed indicators (see Table 5 and Table 6). In addition, the proposed IFTCS using the reduced fuzzy rules performed slightly better than the original IFTCS, as shown in Figure 9 and Figure 10. The proposed approach performed better on three intersections than on two intersections, compared with the IFTCS utilizing the original fuzzy rules (see Figure 9 and Figure 10). Thus, the efficiency of the reduced fuzzy rule bases increased when the number of intersections increased, proving the applicability of the proposed system for multiple or complex intersections.

Similarly, for the non-GUI experiment, a simulation was conducted with the identified qualitative traffic conditions to prove the effectiveness of the proposed approach. The results prove that almost all of the newly proposed intelligent fuzzy traffic control systems were competitive with the original IFTCS, as shown in

Table 7. Average green-light time extension under low traffic flow conditions.

Simulation Number	Input Fuzzy Variables						Output Fuzzy Variables
	Qr	Qg	Emg	Emr	Wtg	Wtr	Ge (Original IFTCS)	Running Time per Sec (Original IFTCS)	Ge (Proposed IFTCS)	Running Time per Sec (Proposed IFTCS)
1	5	10	0	0	5	10	21.3	2.7	21.3	1.9
2	14	6	0	0	15	5	21.6	4.6	21.6	0.9
3	20	25	1	0	45	50	37.5	7.1	30.0	2.0
4	15	20	0	1	75	65	18.9	4.7	29.4	1.0
5	25	30	1	1	70	90	43.6	5.6	36.0	1.2
Average							28.6	4.94	27.7	1.4

and Figure 11, in terms of the average extension green-light duration. However, the original intelligent fuzzy traffic control system (IFTCS) performed slightly better at prioritizing emergency car(s) than the reduced fuzzy rules of the intelligent fuzzy traffic control system under the low and medium traffic flow conditions, and especially when a single emergency car was detected only in the red-light phase and no emergency car(s) were detected in the green-light phase. For example, as listed in

Table 8. Average green-light time extension for medium traffic flow condition.

Simulation Number	Input Fuzzy Variables						Output Fuzzy Variables
	Qr	Qg	Emg	Emr	Wtg	Wtr	Ge (Original IFTCS)	Running Time per Sec (Original IFTCS)	Ge (Proposed IFTCS)	Running Time per Sec (Proposed IFTCS)
1	20	35	0	1	65	60	9.0	4.5	31.8	1.1
2	30	40	1	0	70	65	58.9	6.4	36.3	2.6
3	45	35	0	0	85	80	40.1	4.3	41.3	2.0
4	25	65	0	0	55	125	47.5	3.9	50.4	1.2
5	60	45	0	1	40	50	8.3	4.3	59.2	0.6
Average							32.8	4.68	43.8	1.5

, the original IFTCS extended the green signal time by 9 s, which implies it switched from the green light to the red phase in order to prioritize the detected emergency car. However, in the case of the reduced IFTCS, the green light was extended by 31.8 s. Thus, the original IFTCS performed slightly better than the proposed IFTCS in prioritizing emergency vehicles, particularly when the emergency car(s) was detected only in the current red-light phase and no emergency car(s) was detected in the current green-light phase under medium traffic conditions. This is the rationale behind the fuzzy controller utilizing the original fuzzy rules, where the latter base has the full list of possible rules with originally defined linguistic values, whereas the reduced fuzzy rules are reduced by 72.1%. However, when the traffic flow conditions increased to high traffic flow, both were comparable (see

Table 9. Average green-light time extension for high traffic flow condition.

Simulation Number	Input Fuzzy Variables						Output Fuzzy Variables
	Qr	Qg	Emg	Emr	Wtg	Wtr	Ge (Original IFTCS)	Running Time per Sec (Original IFTCS)	Ge (Proposed IFTCS)	Running Time per Sec (Proposed IFTCS)
1	45	50	0	0	130	135	55.8	1.7	59.7	1.1
2	50	55	1	1	150	145	74.4	2.4	64.5	1.1
3	65	60	2	0	160	155	84.9	1.7	84.9	0.3
4	80	75	1	2	220	250	8.3	2.3	8.3	0.5
5	90	100	2	2	250	300	85.0	3.7	85.0	0.8
Average							61.8	2.36	60.5	0.76

and Figure 11). To compare the effectiveness of the proposed approach, the same data in the scenario of medium traffic conditions (Table 8) in the absence of an emergency car(s) were simulated. The results showed that the original and the proposed IFTCS were comparable in terms of the average extension duration when there were no emergency cars, as shown in

Table 10. Average green-light time extension for medium traffic flow condition (no emergency car(s)).

Simulation Number	Input Fuzzy Variables						Output Variables
	Qr	Qg	Emg	Emr	Wtg	Wtr	Ge (Original IFTCS)	Ge (Reduced IFTCS)
1	20	35	0	0	65	60	42.5	31.8
2	30	40	0	0	70	65	46.1	31.8
3	45	35	0	0	85	80	40.1	41.3
4	25	65	0	0	55	125	47.5	50.4
5	60	45	0	0	40	50	50.0	59.2
Average							45.2	43.0

.

To facilitate a comparison of the running times of the proposed IFTCS using the reduced and original fuzzy rules, an experiment was conducted using the Python time package at two intersections using a graphical user interface (SUMO). Three scenarios were created to conduct experimental simulations. The first scenario involved a 2000-step simulation, while the second scenario consisted of 16,000 steps, and the third scenario of 32,000 steps in the SUMO simulation. In all scenarios, the number of vehicles was equally distributed for all routes, and going straight forward, turning left, or turning right was possible. The obtained results clearly demonstrate that the proposed new reduced IFTCS performs better than the IFTCS using the original fuzzy rules in all scenarios, as shown in Figure 12.

Moreover, the running (execution) times of the proposed IFTCS and the original IFTCS were evaluated without a graphical user interface using the Python time package, as shown in Table 7, Table 8 and Table 9. The proposed IFTCS outperformed the original IFTCS under all the classified traffic conditions. For low traffic flows, the execution of the proposed IFTCS improved by 71.7%, whereas for medium and high traffic flows, the average execution time of the IFTCS with reduced fuzzy rules improved by 67.9% and 67.8%, respectively, compared with the original IFTCS (see Figure 13). Thus, the results demonstrate that the proposed approach requires significantly less computational time than the original system in both the GUI and non-GUI experimental simulations. In addition to the better performance of the proposed system compared to the original fuzzy rules in terms of execution time, the original fuzzy rules require a longer preparation time to start the simulation than the reduced fuzzy rules.

In general, the experimental simulation results demonstrate that the proposed intelligent fuzzy traffic signal control system enhances both the safety and transportation efficiency. This was achieved by considerably decreasing the waiting time, reducing fuel consumption and CO₂ emissions, and properly addressing unusual traffic issues. Furthermore, the results indicate that the system is a promising solution for complex intersection systems with fewer resources because it successfully reduces the extensive fuzzy rule base with finer performance than the controller using the original fuzzy rules.

4. Conclusions and Future Work

Traffic congestion has emerged as one of the most challenging issues globally owing to the growing usage of vehicles on the road, as well as the limited budget and resources available for upgrading existing transportation infrastructure (such as roads). The aim of this study was to overcome these challenges by proposing an innovative fuzzy traffic signal control system integrated with a reduced fuzzy rule base for complex control strategies. In this study, a set of simple case studies was investigated.

The main drawback of the traditional rule-based fuzzy controller is that when the number of rules increases exponentially with the linguistic terms, it requires high computational time, large storage, and overall, its running time is too slow. This is because traditional fuzzy control models fail to achieve their full potential at complex intersections in the real world. To address this issue, it is recommended to modify the inference engine to a more efficient one by reducing the number of fuzzy rules, which results in lower computation time and less storage capacity. In this study, the problem was addressed by employing a novel hybrid combination of fuzzy rule reduction techniques, namely interpolation and extended Boolean state table reduction approaches, thereby reducing the number of significant fuzzy rules. Using the combined novel hybrid approach, the total number of fuzzy rules was reduced from 509 to 142, which means that only 27.9% of the original remained in the results.

Two types of experimental simulations were conducted to evaluate the effectiveness of the proposed approach based on a GUI using SUMO and Python, and a non-graphical user interface using the SciKit-Fuzzy package in Python. A comparison was made in terms of the average waiting time of vehicles, fuel consumption, and CO₂ emissions for the GUI at two adjacent intersections and three adjacent intersections under five scenarios. In all scenarios, the proposed fuzzy controller performed better than the fuzzy controller using the original fuzzy rules and the traditional traffic control system. In the case of the non-GUI type experimental simulation, the average extension time of the green-light duration and running time of the system were used under three qualitatively classified traffic conditions: low, medium, and high traffic flow. The simulation experimental results clearly showed that the computation time of the reduced fuzzy rule system was much better than that of the non-reduced fuzzy rule base of fuzzy traffic control systems, and in terms of the extension of the green time, both were almost comparable under all conditions of traffic flow.

Future research may focus on expanding the experiments with two-intersection or three-intersection models to a more complex, arbitrary intersection structure, and possibly integrating it with deep neural networks or evolutionary learning to create an intelligent system capable of predicting traffic conditions. Simulations with multiple intersection systems can be used to investigate whether emerging features may be observed in the overall traffic flow under the control system.