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Hypergraphs are considered a useful tool for modeling system architectures and data structures and to represent a partition, covering and clustering in the area of circuit design. In this paper, we apply the concept of intuitionistic fuzzy set theory to generalize results concerning hypergraphs. For each intuitionistic fuzzy structure defined, we use cut-level sets to define an associated sequence of crisp structures. We determine what properties of the sequence of crisp structures characterize a given property of the intuitionistic fuzzy structure. We also present applications of intuitionistic fuzzy hypergraphs.