On ${\mathcal N}$ -hypergraphs

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 ${\mathcal N}$ -hypergraphs and investigate some of their properties. For each ${\mathcal N}$ -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 ${\mathcal N}$ -structure. We also describe an example application of ${\mathcal N}$ -hypergraphs.