Spherical fuzzy hypergraph in decision making

This study presents the Spherical Fuzzy Hypergraph (SFHG), an advancement that integrates the principles of fuzzy theory with hypergraph models, and improving decision-making processes. The SFHG extends the existing frameworks of Pythagorean fuzzy sets and Picture fuzzy sets. Unlike spherical fuzzy graphs, SFHGs are capable of representing multi-arity relations, which prove beneficial for various applications including partitioning, clustering, and covering tasks, particularly in circuit design and the simulation of complex system architectures. This paper develops the theory of SFHGs, explaining their distinctive characteristics with illustrative examples. The practical applicability of SFHGs is demonstrated through a real-world application by optimizing decision-making in e-marketing companies. The results demonstrate improvements over existing fuzzy graph methodologies.