# Investigation of Critical Gap for Pedestrian Crossing Using Fuzzy Logic System
###### Abstract  
This paper assesses pedestrian crossing behavior and critical gaps at a two-way midblock crossing location. A critical gap is the shortest gap that a pedestrian accepts when crossing a road. A dataset was collected in 2017 in Edinburgh (UK). The analysis was performed using the fuzzy logic system. The adopted membership function of the fuzzy logic system is of a triangular form since it has a simple and convenient structure. The input variables that are used in the analysis are the number and length of rejected gaps and length of accepted gaps at the crossing location. The output variables are the critical gaps. The results show that assessing critical gap estimation of pedestrians crossing using fuzzy logic is achievable and produces reasonable values that are comparable to values that are reported in the literature. This outcome improves the understanding of pedestrian crossing behavior and could therefore have implications for transport infrastructure design. Further analysis using additional parameters including waiting time and demographic characteristics and alternative forms for membership functions are strongly encouraged. p edestrian crossing behavior; fuzzy logic systems; critical gap +
Footnote †: journal: Medical  
Many researchers have conducted research studies on pedestrian behavior and interactions of experimental, field and simulation approaches [18; 19; 20; 21; 22]. Most other studies have employed discrete choice techniques including binary logistic regression, logit and probit models to assess gap acceptance behavior and to predict values for the critical gaps [23; 24; 25; 26; 27]. These techniques, while robust and very widely applied in many fields, might not always produce efficient estimates in cases where there are repeated measurements. A known problem associated with pedestrians' crossing decisions is the multiple rejected gaps and non-independence of observations because of prior strong assumptions associated with such models. A single pedestrian often rejects more than one gap, and analyzing each rejected gap as a separate observation does not account for the fact that it is rejected by the same person. This introduces a source of vagueness when using conventional discrete choice models, in particular logit-based models. Further prediction techniques could offer possible potential enhancements and flexibility to investigations of pedestrians' crossing behavior. These alternative prediction techniques include genetic algorithms (GA), fuzzy logic (FL) and other artificial intelligence (AI) methods, and are increasingly used in many engineering applications [28; 29; 30; 31]. Fuzzy logic systems are powerful prediction tools in dealing with complex problems. These models or groups are mathematical means of representing that vagueness and rough information. They have the ability of distinguishing, expressing, explaining and operating this information, which is vague and lacks preciseness. They can be designed to calculate a distinction between data sets by simulating processes to match those of human reasoning [32]. The usefulness of fuzzy logic in this kind of investigation is evident since there is not a \"standard\" mathematical model available or one that can be derived from physical laws for adequately modelling pedestrians' crossing behavior. Furthermore, fuzzy systems were originally proposed as a solution to imitate the decision-making processes of the human beings by weighing rules; therefore, it seems logical to use them for modeling human behavior. There are many applications of fuzzy logic in many fields, including transportation (see, for example, [33; 34; 35; 4]. However, there is a significant lack of applications of fuzzy logic systems in transportation in comparison with other fields. An important feature of fuzzy logic analysis is the membership functions. There are different possible shapes for the membership functions, including triangular, trapezoidal, Gaussian, etc. (see [36; 37; 33] for an investigation of the efficiency of estimation of different forms).