Anti-Fuzzy Hypergraphs and Superhypergraphs: Max-Oriented Uncertainty Models for Higher-Order and Hierarchical Networks

Hypergraphs extend classical graphs by allowing hyperedges to connect more than two vertices, while superhypergraphs further generalize this framework through iterated powerset constructions that capture hierarchical and nested incidence structures. Within fuzzy graph theory, anti-fuzzy graphs provide max-oriented uncertainty models in which each edge grade is at least the maximum grade of its incident vertices. However, corresponding max-oriented frameworks for hypergraphs and superhypergraphs have not been systematically developed. To address this gap, we introduce anti-fuzzy hypergraphs and anti-fuzzy superhypergraphs, formulate their mathematical definitions, and establish basic well-definedness and canonical representation results. These models provide a unified foundation for max-based uncertainty modeling in higher-order and hierarchical network structures.