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Classical graph theory models a system by representing entities as vertices and pairwise relationships as edges. Hypergraphs extend this paradigm by allowing a hyperedge to connect any nonempty subset of vertices, thereby capturing multiway interactions in a single combinatorial object. Superhypergraphs push this idea further by iterating the powerset construction, which enables one to encode nested, hierarchical, and even self-referential incidence patterns across multiple levels within a unified framework. Over the past decades, graph- and hypergraph-based models have been combined with many uncertainty formalisms (e.g., fuzzy, intuitionistic fuzzy, neutrosophic, hesitant, and plithogenic settings) to better represent vagueness, hesitation, and incomplete information. In this paper, we introduce two superhypergraph-based frameworks that incorporate complex-valued uncertainty information: Complex Intuitionistic Fuzzy Superhypergraphs and Complex q-Rung Orthopair Fuzzy Superhypergraphs. These models lift the existing complex intuitionistic fuzzy and complex q-rung orthopair fuzzy hypergraph constructions to the superhypergraph level, providing a coherent mechanism for modeling uncertainty simultaneously across multiple hierarchical layers. We also establish basic structural properties, clarify their reduction to standard (lower-order) models, and present constructive procedures that support algorithmic use in hierarchical decision and network modeling.
Classical graph theory models a system by representing entities as vertices and pairwise relationships as edges. Hypergraphs extend this paradigm by allowing a hyperedge to connect any nonempty subset of vertices, thereby capturing multiway interactions in a single combinatorial object. Superhype...
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