Fuzzy Hypergraphs

Abstract

Graph theory has found many application area in science, engineering, and mathematics. In order to expand the application base, the notion of a graph was generalized to that of a hypergraph, that is, a set X of vertices together with a collection of subsets of X. In this chapter, we fuzzify the notation of a hypergraph and state some possible applications. In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some basic theorems and some properties of bipolar fuzzy hypergraphs. Some basic concepts of bipolar fuzzy set are defined. It is shown that any bipolar fuzzy graph can be expressed as the bipolar fuzzy intersection graphs of some bipolar fuzzy sets.