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.

Complex systems can be effectively modelled by fuzzy cognitive maps. Fuzzy cognitive maps (FCMs) are network-based models, where the connections in the network represent causal relations. The conclusion about the system is based on the limit of the iteratively applied updating process. This iteration may or may not reach an equilibrium state (fixed point). Moreover, if the model is globally asymptotically stable, then this fixed point is unique and the iteration converges to this point from every initial state. There are some FCM models, where global stability is the required property, but in many FCM applications, the preferred scenario is not global stability, but multiple fixed points. Global stability bounds are useful in both cases: they may give a hint about which parameter set should be preferred or avoided. In this article, we present novel conditions for the global asymptotical stability of FCMs, i.e. conditions under which the iteration leads to the same point from every initial vector. Furthermore, we show that the results presented here outperform the results known from the current literature.

This study proposes a new model and approach for solving a realistic extension of the Time-Dependent Traveling Salesman Problem, by using the concept of distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interval-valued fuzzy degree repository based on the relations between rush hour periods and traffic regions in the “city center areas”, and then we utilized the interval-valued intuitionistic fuzzy weighted arithmetic average to aggregate fuzzy information to be able to quantify the delay in any given trip between two nodes (cities). The proposed method is illustrated by a simple numerical example.