Interactions among paths in fuzzy shortest path problems

We concentrate on a shortest path problem on a network in which a fuzzy number, instead of a real number, is assigned to each arc length. As this type of problem is so called an "ill-posed problem", each arc merely being identified as on the shortest path or not. Therefore, based on possibility theory, we introduce the concept of the "degree of possibility" as to whether an arc is on the shortest path. A pair of paths from a source node to a destination node is considered to be "interactive" (corresponding to "dependence" in probability theory) because there may exist common arcs in both paths. An new algorithm for these problems is proposed by taking interaction among paths into consideration. The degree of possibility for each arc on a network is obtained by this algorithm. Finally, an illustrative numerical example is shown