Shortest Path Solution of an Intuitionistic Fuzzy Network

Abstract

This study focuses on solving the shortest path problem in networks where edge weights are represented as Intuitionistic Fuzzy Numbers (IFNs). Intuitionistic fuzzy sets allow the incorporation of both membership and non-membership degrees, providing a more com- prehensive representation of uncertainty compared to traditional fuzzy sets. The Floyd- Warshall algorithm, a well-established method for finding the shortest paths in weighted graphs, is adapted to work with IFNs. The algorithm operates iteratively, leveraging the properties of IFNs and appropriate fuzzy arithmetic to handle uncertainty in edge weights effectively. The proposed approach ensures that the shortest path calculations consider both the degree of certainty and uncertainty, providing a more robust solution for real- world problems involving imprecise or uncertain data. Numerical examples are presented to demonstrate the effectiveness and accuracy of the adapted algorithm, highlighting its po- tential applications in fields such as transportation, logistics, and communication networks.