Some Operations on Fuzzy Hypergraphs

Zengtai Gong1, Qian Wang1,2
1College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, P.R.China
2Colleage of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, 730030, P.R.China

Abstract

A hypergraph is a useful tool to model complex systems and can be considered a natural generalization of graphs. In this paper, we define some operations of fuzzy hypergraphs and strong fuzzy \(r\)-uniform hypergraphs, such as Cartesian product, strong product, normal product, lexicographic product, union, and join. We prove that if a hypergraph \(H\) is formed by one of these operations, then this hypergraph is a fuzzy hypergraph or a strong fuzzy \(r\)-uniform hypergraph. Finally, we discuss an application of fuzzy hypergraphs.