Neutrosophic Graph Rewriting as a Computational Model

Overview & Synopsis

Graphs, which are made up of points connected by lines, are used to represent relationships between objects. They are useful for solving problems in computer science, logistics, biology, and other fields, including social networks and the internet. Neutrosophic graphs are graphs whose points and lines are characterized by membership, indeterminacy, and non-membership degrees. In the simplest case, only lines are characterized by these degrees. The process by which we transform one graph to another is called graph rewriting. It has been shown that graph rewriting can be described mathematically by pushouts, which are category-theoretic structures. It has also been shown that fuzzy graphs have this property, and here we prove that neutrosophic graph rewriting can be described by pushouts in a certain category. By providing a fuzzy version of category theory, it is possible to define fuzzy categorical structures and thus to define neutrosophic graph rewriting in a more suitable manner. Since graph rewriting is actually a model of computation, neutrosophic graphs are a neutrosophic model of computation. A hypergraph is a generalization of a conventional graph. It allows a single "hyperline" to connect many points, which is different from regular graph lines that only connect two points. Neutrosophic hypergraphs can be used to reformulate Wolfram's models, which are supposed to be a mathematical model of reality.