About this ebook
Graph theory provides a fundamental framework for modeling relationships using vertices and edges. Hypergraphs extend this framework by permitting hyperedges that connect any number of vertices simultaneously, and Super-hypergraphs further generalize hypergraphs through iterated powerset constructions to represent hierarchical connections. Concurrently, a variety of uncertainty-modeling paradigms—such as fuzzy sets, soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy offsets, hyper-intuitionistic fuzzy sets, and intuitionistic fuzzy multidirected sets—have enriched classical graph concepts. In this paper, we introduce the Intuitionistic Fuzzy Soft n-Super-hypergraph, a unified n-th order structure that seamlessly integrates intuitionistic fuzzy Super-hypergraphs with soft Super-hypergraphs. We present rigorous definitions, explore key structural properties, and highlight potential applications in decision-making under uncertainty, demonstrating how this framework effectively captures both complex hierarchical organization and nuanced uncertainty in real-world networks.
Graph theory provides a fundamental framework for modeling relationships using vertices and edges. Hypergraphs extend this framework by permitting hyperedges that connect any number of vertices simultaneously, and Super-hypergraphs further generalize hypergraphs through iterated powerset construc...
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