# Investigation of Critical Gap for Pedestrian Crossing Using Fuzzy Logic System
## 7 Conclusions  
Most previous research on pedestrian behavior has adopted interaction field experimentation and simulation approaches. This current study adopts a fuzzy logic analysis approach. The critical gap, which is defined as the shortest gap that the pedestrian would accept, affects pedestrians' decisions about when to cross a road, and has been assessed using fuzzy logic analysis. This has been achieved by assessing the number and length of rejected gaps and accepted gaps for each individual pedestrian.  
Fuzzy logic analysis was then carried out to estimate the critical gap, which involved three steps. The fuzzification process was attained by translating the input data into fuzzy sets through fuzzy linguistic variables and membership functions. The inputs to the system included lengths and the number of rejected gaps for each individual at the crossing location and the length of the accepted gap. Three parameters were used for each input and output variable to identify the membership function (low, medium and high). Then, based on IF-THEN rules, the inference process was carried out. Lastly, a defuzzification step was functioned. In this case, the membership functions were used to calculate and produce fuzzy outputs. The output, the temporal critical gap, was found to be 6.0 s. This value is comparable with other values obtained using different statistical methods.  
The experiment shows that the critical gap for pedestrian crossing is possible to predict using fuzzy logic analysis. These results could complement other conventional methods that have been reported in the literature, including the graphical method and discrete choice models. This is a valuable outcome that might have useful implications for transport planners and highway engineers. Further research in this area is definitely required, with larger numbers of locations as well as consideration of further attributes of pedestrians, including additional variables such as pedestrian waiting time as well as other demographic characteristics in the analysis. The current investigation adopted a triangular membership function in the fuzzification process. Other types of functions, such as trapezoidal or Gaussian, can be attempted and the results can be compared in future research.  
Conceptualization, W.S.S. and M.M.A.L.; methodology, W.S.S. and M.M.A.L.; software, W.S.S. and M.M.A.L.; validation, W.S.S. and M.M.A.L. formal analysis, W.S.S. and M.M.A.L.; investigation, W.S.S. and M.M.A.L.; writing--original draft preparation, W.S.S.; writing--review and editing, W.S.S.; visualization, W.S.S. and M.M.A.L.; supervision, W.S.S.; project administration, W.S.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program. The work reported in this article has been conducted while the researcher is affiliated with Princess Nourah bint Abdulrahman University.  
We thank to the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program. The work reported in this article has been conducted while the researcher is affiliated with Princess Nourah bint Abdulrahman University.  
The authors declare no conflict of interest.