Defining shape of membership function for Mamdani's Fuzzy Inference System within park & ride share modelling

Abstract

The conducted survey were aimed on estimation of the number of potential Park and Ride users. The system is not popular in Poland and it is difficult to estimate (and calibrate) modal split function based on Stated Preferences survey. Because fuzzy approach can be justified in the case of rough data and significant impact of human factors, it is difficult to estimate necessary functions using traditional mathematical approach. It seems, that fuzzy methodology can be treated as a proper way to describe choice of mode of transport, especially in case of Park and Ride trips. The proposed approach is based on the Mamdani Fuzzy Inference System, where, as the part of the model, the membership functions were estimated according to the experts' survey. The survey had two level verification using Delphic approach and final results were obtained as an approximation of shapes of the functions proposed by experts. The methodology were tested on the real system implemented in Warsaw. The paper will present procedure for membership function estimation, application of the model. For calculation there was used Matlab software, with Fuzzy Logic Toolbox. Main goal of the paper is to present complexity and uncertainty of the modal split modeling process.