Finding Hamiltonian Cycles in Circular Intuitionistic Fuzzy Graphs

Finding a Hamiltonian cycle in a graph is an essential challenge in an uncertain context, and there are several approaches available for this. By combining Atanassov’s circular intuitionistic fuzzy sets (C-IFSs) and index matrices (IMs), this work presents a novel methodology. In particular, we suggest using an index-matrix approach to find the Circular Intuitionistic Fuzzy Hamiltonian Cycle (C-IFHC), which is a Hamiltonian cycle in a Circular Intuitionistic Fuzzy graph (C-IFG). The C-IFHC algorithm builds upon existing approaches for finding an Intuitionistic Fuzzy Hamiltonian Cycle (IFHC) in an Intuitionistic Fuzzy Graph (IFG). To showcase its practical applicability, we employ the C-IFHC algorithm to discover a Hamiltonian cycle in a real-world context involving the Ryanair airline network. This paper also introduces the concept of a circular extended intuitionistic fuzzy index matrix (C-EIFIM) and elucidates various operations associated with C-EIFIMs.