Fault-Tolerant Fuzzy Resolving Domination Set

In this paper, we introduce a new idea in fuzzy graph theory called the Fault-Tolerant Fuzzy Resolving Domination Set (FT-FRDS). This concept combines three important features: fault tolerance (ability to handle errors), resolving power (identifying nodes), and domination (covering or monitoring all nodes). The main contribution of this paper is the introduction of the Fault-Tolerant Fuzzy Resolving Domination Set (FT-FRDS) in fuzzy graphs. It ensures node identification and monitoring even when some nodes fail. The paper defines FT-FRDS, explores its properties, and provides examples to support its practical use. We also provide examples to help understand how it works. This concept is helpful because it makes sure that even if some nodes in the graph fail or stop working, the system can still identify and monitor other nodes correctly. This is especially useful for real-world problems like sensor networks, communication systems, and areas where high reliability is needed despite possible faults or uncertainty.