SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS

Abstract

Numerous algorithms have been proposed to solve the shortest-path<br />problem; many of them consider a single-mode network and crisp<br />costs. Other attempts have addressed the problem of fuzzy costs in<br />a single-mode network, the so-called fuzzy shortest-path problem<br />(FSPP). The main contribution of the present work is to solve the<br />optimum path problem in a multimodal transportation network, in<br />which the costs of the arcs are fuzzy values. Metropolitan<br />transportation systems are multimodal in that they usually contain<br />multiple modes, such as bus, metro, and monorail. The proposed<br />algorithm is based on the path algebra and dioid of $k$-shortest<br />fuzzy paths. The approach considers the number of mode changes,<br />the correct order of the modes used, and the modeling of two-way<br />paths. An advantage of the method is that there is no restriction<br />on the number and variety of the services to be considered. To<br />track the algorithm step by step, it is applied to a<br />pseudo-multimodal network.