solving best path problem on multimodal transportation networks with fuzzy costs

numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(fspp). the main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the costs of the arcs are fuzzy values. metropolitantransportation systems are multimodal in that they usually containmultiple modes, such as bus, metro, and monorail. the proposedalgorithm is based on the path algebra and dioid of $k$-shortestfuzzy paths. the approach considers the number of mode changes,the correct order of the modes used, and the modeling of two-waypaths. an advantage of the method is that there is no restrictionon the number and variety of the services to be considered. totrack the algorithm step by step, it is applied to apseudo-multimodal network.