Using the fuzzy sets theory in the multimodal transport network problem

In this work, an approach to solve multimodal transport network problems with uncertain costs in the edges is proposed. This kind of problem has been studied for several researchers who search solutions to the large numbers of problems relating on the transport systems like: traffic jam, pollution, delays, among others. In this work, the modelling of this problems is based on graph theory are presented, where each transport mode is represented by a subgraph and the whole graph is the union of all subgraphs. Besides, its mathematical formulation describes nonlinear conditions and the goal is to develop an algorithm that reaches a set of Pareto solutions, which find the best routes between origin and destination. A numerical example is used to illustrate the efficiency of the proposed approach.