Journal of Neutrosophic and Fuzzy Systems

This paper is dedicated to study the group of units (Von Shtawzen's group) of some numerical n-cyclic refined neutrosophic rings such as integer, rational, and real case. Where we write the elements of these abelian groups by using equations derived from the values of some circulant numerical  determinants.

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

The objective of this paper is to present 40 open problems about the n-cyclic refined neutrosophic rings. These questions concern the n-cyclic refined neutrosophic rings, n-cyclic refined neutrosophic number theory, and n-cyclic refined neutrosophic analysis. They will represent the future of the study of neutrosophic n-cyclic refined rings and the related structures.

The objective of this paper is to suggest two new conjectures concerning the invertible elements in 3-cyclic, and 4-cyclic refined neutrosophic rings of integers, where the invertibility condition shows that the solution of some Diophantine equations may determine the classification of the group of units of these algebraic rings.

In this article, Bipolar neutrosophic nano topology is introduced and some of its properties are studied. We found that, it is difficult to find a nano topology for every bipolar neutrosophic set. So we introduced a bipolar neutrosophic nano  topology, which is a generalization of bipolar neutrosophic nano topology and its fundamental features are investigated with appropriate examples. This approach is used for real life multi criteria decision making situations. The practical problems may be solved by finding CORE values through the criterion reduction.One can apply the basis of the bipolar neutrosophic nano  topology as the key factors of  a particular decision making problem using topological reduction of attributes in complete or incomplete information system.

The concepts of Neutrosophic secure edge domination number and neutrosophic total secure edge domination number in single valued neutrosophic graphs (SVNG) with strong arcs are introduced and analysed in this paper, and some of their properties are studied. The relationship between the neutrosophic secure edge dominance number  and its inverse  is presented. The concepts inverse neutrosophic total edge domination set and inverse neutrosophic total edge domination number are also defined. Some of these concepts' properties are investigated.