Neutrosophic quadruple algebraic structures

In this thesis, it was studied on the neutrosophic quadruple set theory. It was considered on; what the neutrosophic quadruple number & the refined neutrosophic quadruple number are, how they are expressed, what they are meaning. The opetations among these neutrosophic quadruple numbers were mentioned. The algebraic structures that are constructed on neutrosophic quadruple sets were examined with its basic definitions and properties, examples were given. It was studied the reflections on the neutrosophic quadruple numbers set such as group, ring in classical algebra. In this situation, there were given examples for purpose of increasing functionality of the topic. After that, basic definitions and theorems on neutrosophic quadruple vector spaces what is form of vector spaces, that is another important algebraic structure, on neutrosophic quadruples are mentioned. In last section of this thesis, the basic definitions of neutrosophic quadruple hyperstructures which is established with helping hyperoperations that is defined between neutrosphic quadruple numbers were mentioned and examples were examined.