Implementation of single-valued neutrosophic soft hypergraphs on human nervous system

Abstract

Single-valued neutrosophic soft set simultaneously incorporates the attributes of both single-valued neutrosophic set as well as soft set. Corresponding to each parameter, it nominates a triplet $(\mathfrak {t},\mathfrak {i},\mathfrak {f})$ to a statement, where $\mathfrak {t}$, $\mathfrak {i}$ and $\mathfrak {f}$, respectively, describe the truthness, indeterminacy and falsity of that statement. In this article, we proceed in the framework of single-valued neutrosophic soft set by introducing single-valued neutrosophic soft hypergraphs which are effective to produce visual representation of connection among multiple objects of a system. Various fundamental operations such as union, join, Cartesian product and normal product of these graphical structures are suggested. We also discuss the construction of line graph and dual of single-valued neutrosophic soft hypergraphs with algorithms. The r-uniform single-valued neutrosophic soft hypergraphs with their operations like direct product, lexicographic product and costrong product is illustrated. In addition to this, we introduce the concept of regular, totally regular and perfectly regular single-valued neutrosophic soft hypergraphs and elaborate it with interesting results. Further, the single-valued neutrosophic soft directed hypergraphs together with some other interesting concepts have also been presented. At the end, it is explained that in what way, one can use the single-valued neutrosophic soft directed hypergraphs in the study of human nervous system. The proposed hypergraphs can be employed in artificial intelligence and decision-support systems effectively.