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 introduce the notion of N-hypergraphs and investigate some of their properties. For each N-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 N-structure. We also describe an example application of N-hypergraphs.
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