Affiliations: Punjab University College of Information Technology, University of the Punjab, Lahore, Pakistan | School of Mathematical Sciences, University of Jinan, Jinan, Shandong, P.R. China | Department of Mathematics, Yazd University, Yazd, Iran
Note: [] Corresponding author. Bijan Davvaz, Department of Mathematics, Yazd University, Yazd, Iran. E-mail: [email protected]
Abstract: 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.
Keywords: [TeX:] ${\mathcal N}$-hypergraph, strength of edge (class), [TeX:] ${\mathcal N}$-partition, dual [TeX:] ${\mathcal N}$-hypergraph, clustering problem
