Fuzzy shortest path problems incorporating interactivity among paths

This paper deals with a shortest path problem on a network in which a fuzzy number, instead of a real number, is assigned to each arc length. Such a problem is "ill-posed" because each arc cannot be identified as being either on the shortest path or not. Therefore, based on the possibility theory, we introduce the concept of "degree of possibility" that an arc is on the shortest path. Every pair of distinct paths from the source node to any other node is implicitly assumed to be noninteractive in the conventional approaches. This assumption is unrealistic and involve inconsistencies. To overcome this drawback, we define a new comparison index between the sum of fuzzy numbers by considering interactivity among fuzzy numbers. An algorithm is presented to determine the degree of possibility for each arc on a network. Finally, this algorithm is evaluated by means of largescale numerical examples. Consequently, we can find this approach is efficient even for real world practical networks.