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.
