Shortest Path Problems in Fuzzy Network

Abstract

We extend traditional shortest path models to fuzzy versionswith the existence possibility of arcs and fuzzy arc length. First,we consider the model where existence of each arc is fuzzy but its lengthis ordinary number. That is, we maximize the possibility of the existenceof the path and minimize the length of the path, and seek nondominatedpaths since usually there does not exist a path that optimizes both criteriaat a time. In order to solve this problem, we first find an optimal pathon an ordinary network with arcs whose existence possibility is maximumby the Floyd-Warshall method. Next, repeatedly arcs with lower existencepossibilities are added to the network and nondominated paths are found.Further, we extend this solution procedure to the shortest path problemwhose arc lengths are fuzzy numbers.