The shortest path problem is to find the shortest distance between two specified modes in a network. An arc is called a single most vital arc in the network, if its removal from the network results in the greatest increase in the shortest distance. The availability of arcs plays a key role in network problems. The most vital arcs problems provide a means by which the importance of arc’s availability can be measured. In the traditional shortest path problem, the arc lengths are assumed to be crisp numbers. In this paper, the authors consider the case that the arc lengths are fuzzy numbers. In particular, the authors derive the membership function of the shortest distance by using a fuzzy linear programming approach. Based on this result, the authors then propose an algorithm for finding the single most vital arc in a network.
