Intuitionistic fuzzy shortest path in a multigraph

Abstract

Mutigraphs are a generalized model of graphs. Multigraphs may have multiple edges between a pair of its vertices. The existing algorithms to find the fuzzy shortest path or intuitionistic fuzzy shortest paths in graphs is not applicable to multigraphs. Our work here is on the theory of multigraphs. In this paper we develop a method to search for an intuitionistic fuzzy shortest path in a directed multigraph and then develop, as a special case, a fuzzy shortest path in a multigraph. We re-construct classical Dijkstra’s rule that is applicable to graphs with crisp weights which can then be extendable to IFN multigraphs. It’s claimed that the tactic might play a significant role in several application areas of technology, specifically in those networks that may not be shaped into graphs but however into multigraphs.