Bi-objective shortest path problem with one fuzzy cost function applied to dangerous goods transportation on a road network

The shortest path problem is a very well-known network problem, whose complexity sensibly increases from polynomial complexity to become a NP-hard problem when a multi-objective function is taken into account. In this work, an algorithmic approach to a bi-objective problem is described, where one objective has a fuzzy value, which makes even harder to get a solution. This kind of approach finds an applicative use in the case of dangerous goods transport by road, where a tradeoff between the minimum cost and the minimum (or minmax) risk has to be solved in the delivery from a depot to petrol stations.