Abstract:
This work aims to study the notions of interval valued fuzzy sets (IVFSs) and fuzzy graph
structures (FGSs) to build the interval valued fuzzy graph structures (IVFGSs) and develop
some interesting results. An FGS G = (V, Ei, η, ξi), (1 ≤ i ≤ n), is an algebraic framework
of the collection of vertices and disjoint subsets of edges along with two fuzzy mappings,
η : V → [0, 1] and ξi : Ei → [0, 1]. Based on this definition of FGSs and IVF sets, the novel
IVFGS will be introduced. After that, we’ll develop the Cartesian product, composition,
union, and intersection of IVFGSs and some of their properties. The strong interval valued
fuzzy graph structures were discussed, and it has been proved that the weighted mean of
these two strong structures again yields a strong structure. As for the degrees of vertices,
the vertex degrees and the ξi vertex degrees of weighted mean fuzzy graph structures were
discussed and explained with examples.
