Generalized Neutrosophic Hypergraphs

Neutrosopic sets were introduced by Smarandache [2] which are the generalization of fuzzy sets and intuitionistic fuzzy sets. The Neutrosophic sets have many applications in medical, management sciences, life sciences and engineering, graph theory, robotics, automata theory and computer science. The single valued neutrosophic graphs were introduced by Broumi, Talea, Bakali and Smarandache [5]. Recently in [9, 10, 6] proposed some algorithms dealt with shortest path problem in a network (graph) where edge weights are characterized by a neutrosophic numbers including single valued neutrosophic numbers, bipolar neutrosophic numbers and interval valued neutrosophic numbers. Hypergraphs and various properties that we can prove about them are the basis of many techniques that are used in modern mathematics. While graph edges are pairs of nodes, hyperedges are arbitrary sets of nodes, and can therefore contain an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality. Hyperedges are absurdly general. Likewise, the notion of data. To make this useful, one needs to constrain the form the hyper edges take. There are many research papers on fuzzy hypergraph in [7, 8] based on vertex set as a crisp set. In fact, in the definition of fuzzy graph, both the concepts of vertices and edges are fuzzy and there is an interrelation between the fuzzy vertices and fuzzy edges. The generalized strong intuitionistic fuzzy hypergraphs were discussed by Samanta and Mohinta [1]. In this paper, we generalize the concept of SVNHG by considering SVN-Vertex instead of crisp vertex set and interrelation between SVN-Vertices and family of SVN-Edges. The GSVNHG, generalized strong SVNHG and a few operations on them are defined here. Also some of their properties are studied.