Modeling Hierarchical and Higher-Order Uncertainty in IT Systems Management Using Strong Intuitionistic Fuzzy Hypergraphs and Superhypergraphs

Hypergraphs extend classical graphs by allowing hyperedges to connect more than two vertices, providing a natural framework for representing higher-order relationships in complex systems. SuperHyperGraphs further generalize this concept through iterated powerset constructions, enabling the modeling of hierarchical, set-valued, and multi-level interaction structures. At the same time, intuitionistic fuzzy theory offers an effective mechanism for handling uncertainty by simultaneously representing membership and non-membership information. A strong intuitionistic fuzzy graph constitutes a special class in which edge membership and non-membership degrees are directly induced by the corresponding extremal degrees of their incident vertices. In this paper, we extend the strong intuitionistic fuzzy paradigm from graphs to hypergraphs and SuperHyperGraphs. Specifically, we introduce the notions of strong intuitionistic fuzzy hypergraphs and strong intuitionistic fuzzy (n)-SuperHyperGraphs and investigate their fundamental properties. We establish generalization relationships with existing graph-based models and analyze several structural characteristics, including monotonicity, inheritance under sub-superhypergraph restrictions, and threshold-based crisp core representations. The proposed framework provides a unified approach for modeling hierarchical and higher-order uncertain relationships in complex systems. Illustrative applications in IT cost management and IT configuration management demonstrate its capability to support the representation and analysis of multi-level dependencies and uncertainty in engineering management environments.