International Journal of Neutrosophic Science

The aim of this paper is to introduce a new types  of neutrosophic crisp relations as a generalization to  intuitionistic relations due to Indira et al.[9], and study some of its properties. Finally, the concepts of the star and retract neutrosophic relations  are introduces and studied and some properties of these concepts will be investigated.

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of this paper: These authors are motivated to re-describe the self-referential paradox inherent in Godel incompleteness theorem. Contribution: This paper will show how Neutrosophic Logic offers a unique perspective and solution to Godel incompleteness theorem.

The concept of strong neutrosophic graph is developed with example and some of their properties are investigated in this paper. Some definitions, homomorphism, isomorphism theorems and propositions in strong neutrosophic graphs are established. Basic operations (like union, intersection etc.,) and complement of strong neutrosophic graphs are also derived here.

The objective of this paper is to study some of AH-substructures in n-refined neutrosophic group. Also, it deals with some elementary properties of AH-subgroups, AH-normality, AH-homomorphisms, and endomorphisms especially in a non abelian n-refined neutrosophic group. 

The aim of this paper is to define for the first time the concept of n-refined neutrosophic group. This work is devoted to study some elementary properties of n-refined neutrosophic groups and to establish the algebraic basis of this structure such as n-refined neutrosophic subgroups, n-refined neutrosophic homomorphisms, and n-refined neutrosophic isomorphisms.