Evaluation of Shortest path of a Network Using Fuzzy Floyd Warshall Algorithm based on the uncertain environment

Abstract Solving the shortest path problem (SPP) by the Floyd-Warshall algorithm (FWA) is often found in the literature. In this article, we propose a fuzzy Floyd-Warshall algorithm for resolving the SPP in fuzzy circumstances with fuzzy parameters. In reality, the problems encountered are inherently unknown, and one of the most important issues is evaluating the shortest paths in different networks. Here we apply the canonical operation procedure on the fuzzy trapezoidal number to improve the Floyd-Warshall method and name it the fuzzy (FWA). Furthermore, we compare our algorithm with the existing FWA and the rectangular algorithm, and also we take the node (vertices) as the crisp number and the edges (links) value as a trapezoidal fuzzy number to solve most of the shortest path issues on a given network. Finally, we cite one numerical example to demonstrate the validity of our algorithm.