# Efficient Intersection Management Based on an Adaptive Fuzzy-Logic Traffic Signal
## 2 Related Work
### Adaptive Controllers
[29] developed a sophisticated system architecture based on a Wireless Sensor Network (WSN) and multiple FL controllers. With the aim to find a low complex computational solution, they proposed the use of commercial off-the-shelf hardware to implement magnetometer sensors for the detection of queued vehicles, exchanging data through the IEEE 802.15.4 protocol. The system incorporated a phase-sorting module to compute the phase's execution order based on the queue lengths retrieved from an arrangement of magnetometers. Finally, a set of independent FL controllers (one controller for each phase) computed the appropriate green time duration. Using simulations, the authors showed that their proposal outperformed other FL solutions. Some authors also have proposed two-stage fuzzy systems to determine changing the phases' order, with the aim of deciding whether to extend or terminate a current phase [32]. [PERSON] [12] proposed a method based on an urgency degree computed in the first stage. The urgency was inferred from the number of vehicles queued during the red intervals and the duration of such intervals since the last green interval. Hence, the red interval with the greatest urgency is selected as the next phase. Then, in the second stage, the green interval delay was computed according to the number of vehicles on the current phase and the next phase. [PERSON] et al. [33] proposed a fuzzy system for the phases' order selection and green interval delay computation, which was optimized through a traffic flow prediction based on a wavelet NN. [PERSON] and [PERSON] [26] argued that in most of the FL-based controllers, the methods for formulating the rule base and the fuzzy sets are subjectively preset and therefore not optimally solved. Hence, they proposed a stepwise genetic fuzzy logic controller that considers traffic flows and queue lengths as state variables and the green extension as a control variable. [PERSON] et al. [34] proposed an adaptive method based on FL and the modified Webster formula [62; 63]. Using a fuzzy system, the method dynamically adjusted the green interval during its execution. When the green reaches the interval of the remaining 15 s, proper extensions or reductions were computed. This process was repeated at each remaining second until the green interval finishes or the extension overpasses 130% of an estimated maximum green time. At the end of each cycle, the next cycle length, as well as the effective green times, are computed through the modified [PERSON]'s formula. The method was tested using a microsimulation model in SUMO [64] with outstanding results. Most FL controllers are based on the also called type-1 fuzzy sets, where an expert should determine the degree of achieving the characteristics of the object. Many researchers argue these models are susceptible to producing inaccurate results by incorrect handling of the environmental uncertainties and disturbances. In response, some solutions, based on the called type-2 fuzzy sets, have been proposed [24; 28; 31]. In type-2 FL, an expert cannot determine exactly the degree of achieving the characteristics, requiring incorporating uncertainty to represent a fuzzy set. Nevertheless, since type-2 fuzzy sets are three-dimensional, they are computationally complex. To tackle this problem and improve the performance of signal controllers, [PERSON] et al. [28] and [PERSON] et al. [31] proposed two type-2 FL approaches. [PERSON] et al. proposed a system which is optimized by differential evolution. [PERSON] et al. proposed a general type-2 FL system whose parameters are optimized by a heuristic algorithm called _modified backtracking search algorithm_. Although the theoretical improvements of type-2 FL systems are encouraging, the number of parameters required for tuning is bigger than that of type-1 FL, which can lead to an increase in the time and computational complexity during the optimization process.