Finding the Shortest Path With Neutrosophic Theory

In this chapter, the authors study a kind of network where the edge weights are characterized by single-valued triangular neutrosophic numbers. First, rigorous definitions of nodes, edges, paths, and cycles of such a network were proposed, which are then defined in algebraic terms. Then, characterization on the length of paths in such a network were presented. This is followed by the presentation of an algorithm for finding the shortest path length between two given nodes on the network. The proposed algorithm gives the shortest path length from source node to destination node based on a ranking method that takes both the length of edges and the number of nodes into account. Finally, a numerical example based on a real-life scenario is also presented to illustrate the efficiency and usefulness of the proposed approach.