Shortest Path Problems in Fuzzy Network

Abstract

We extend traditional shortest path models to fuzzy versions with the existence possibility of arcs and fuzzy arc length. First we consider the model where existence of each arc is fuzzy but its length is ordinary number. That is, we maximize the possibility of the existence of the path and minimize the length of the path, and seek nondominated paths since usually there does not exist a path optimizing both criteria at a time. In order to solve this problem, we first find an optimal path on an ordinary network with arcs whose existence possibility is maximum by Floyd-Warshall method. Next repeatedly arcs with lower existence possibilities are added to the network and nondominated paths are found. Further we extend this solution procedure to the shortest path problem whose arc lengths are fuzzy numbers.