Fuzzy shortest path problem with finite fuzzy quantities

We discuss the problem of finding the shortest paths from a fixed origin to all nodes on a network not necessarily acyclic, with each arc length represented as positive fuzzy quantity with finite support. At first, we show that the only existing paper on this problem, Klein´s algorithm, in some cases lead to a dominated path in the sense of extension principle and then we introduce a new algorithm for the problem. The proposed algorithm is on the basis of the multiple labeling methods of Hansen and Dijkstra´s shortest path algorithm.