Fuzzy SuperHyperGraph Neural Network (F-SHGNN)

Graph theory investigates relationships among entities through mathematical structures composed of vertices (nodes) and edges (connections) [1]. A hypergraph generalizes the classical graph by introducing hyperedges, which can join any number of vertices rather than just two, thereby enabling the modeling of complex multi-way relationships [2]. Building on this, the concept of a SuperHyperGraph has been proposed as a further extension of hypergraphs and has recently become a subject of active research [3, 4]. Graph Neural Networks (GNNs) are among the most extensively studied frameworks in artificial intelligence [5, 6]. The HyperGraph Neural Network (HGNN) extends GNNs by leveraging the expressive power of hypergraphs to capture higher-order dependencies [7, 8]. More recently, SuperHyperGraph Neural Networks have begun to emerge as an additional generalization [9]. Furthermore, these models have been augmented with fuzzy logic, giving rise to Fuzzy Graph Neural Networks and Fuzzy HyperGraph Neural Networks(cf. [10]). In this paper, we introduce and investigate the Fuzzy SuperHyperGraph Neural Network (F-SHGNN), a novel framework that integrates and extends SuperHyperGraph Neural Networks, Fuzzy Graph Neural Networks, and Fuzzy HyperGraph Neural Networks.