Fuzzy shortest path problem with finite fuzzy quantities

We discuss the shortest path problem from a specified node to every other nodes on a network in which a positive fuzzy quantity with finite support is assigned to each arc as its arc length. We define an order relation between fuzzy quantities with finite supports. Then by applying Hansen’s multiple labeling method and Dijkstra’s shortest path algorithm, we propose a new algorithm for finding the set of non-dominated paths with respect to the extension principle. Moreover, we show that the only existing approach for this problem, Klein’s algorithm, may lead to a dominated path in the sense of extension principle.