Network Flow with Fuzzy Arc Lengths Using Haar Ranking

Shortest path problem is a classical and the most widely studied phenomenon in combinatorial optimization. In a classical shortest path problem, the distance of the arcs between different nodes of a network are assumed to be certain. In some uncertain situations, the distance will be calculated as a fuzzy number depending on the number of parameters considered. This article proposes a new approach based on Haar ranking of fuzzy numbers to find the shortest path between nodes of a given network. The combination of Haar ranking and the well-known Dijkstra’s algorithm for finding the shortest path have been used to identify the shortest path between given nodes of a network. The numerical examples ensure the feasibility and validity of the proposed method.