Notion of Complex Spherical Dombi Fuzzy Graph and Its Application in Decision-Making Problems

The complex spherical fuzzy graph (CSFG), which extends the concept of a spherical fuzzy graph (SFG), proves to be a more effective means of depicting relationships among diverse objects when these relationships are subject to uncertainty. In addition, the Dombi operators, featuring an adjustable operational parameter, offer valuable utility by accommodating distinct values. In this research paper, we present the concept of a complex spherical dombi fuzzy graph (CSDFG), an extension of a spherical dombi fuzzy graph (SDFG). Dombi operators are utilized as averaging operators, playing a crucial role in aggregating data into a single value for efficient decision-making. We implement Dombi operators on CSFGs. The complement of a CSDFG is defined, and self-complementry in CSDFGs is discussed. We explore homomorphism, isomorphism, weak isomorphism (W-isomorphism), and co-weak isomorphism (CW-isomorphism) to establish relationships between CSDFGs. We define regular, arc regular, and totally arc regular CSDFGs, explain their key properties, and demonstrate an application of CSDFG in decision-making problems.