Domination of Fuzzy Directed Graphs in Complex Networks

Fuzzy digraphs form a robust generalization of traditional digraphs because of their ability to handle asymmetric, hierarchical, and unidirectional influence relationships in complex systems in an efficient manner. To better handle levels of uncertainties in various applications, some recent developments in fuzzy digraphs that possess high modeling capacity include intuitionistic fuzzy digraphs and picture fuzzy digraphs. Picture fuzzy digraphs are capable of modeling relationships using positive, neutral, and negative membership values to offer a well-rounded view of relationships in uncertain settings.Graph product operations, such as strong and tensor products, play a crucial role in constructing new picture fuzzy digraphs from existing structures, thereby facilitating the systematic analysis of uncertainty propagation and multi-criteria interactions across interconnected networks. The framework applies to uncertain decision-making in networks, such as supplier selection and social analysis, and integrates domination with graph products to enable fault detection, reduce downtime, and improve efficiency.