International Journal of Neutrosophic Science

The objective of this paper is to define and study the concepts of strong AH-submodule, and AH-homomorphism in a refined neutrosophic module. Also, this work describes the algebraic structure of all AH-endomorphisms defined over a refined neutrosophic module.

Neutrosophy began as a branch of philosophy that considered neutrality in addition to the positive and negative. It consists of the addition consideration of a neutral state to complement the binary approach of true or false. Its creator quickly extended it to the field of mathematics and it was gradually applied to all fields of science. Here, we present a reverse approach that highlights the importance of neutrality in all fields of study and application, citing some revealing examples. Furthermore, we explain that this importance of neutrality is intrinsic to all sciences because it is based on natural foundations. Indeed, neutrality is a forming part first of all of the human conception of things, of our way of thinking, of cognition in general but also of living things, matter and even particles. In addition to these most real-world physical concrete aspects, neutrality is inherent to mathematics, to logic first of all, but also to probabilities and statistics where neutrality which simply results from a large number of objects, the universe. Thus neutrosophy is well adapted to the majority of applied problems because its modeling is inspired by reality and that it allows, in particular, to deal with the component of uncertainty and indeterminacy that the real world comprises intrinsically.

This paper presents the refinement of neutrosophic hypergroup and studies some of its properties. Several interesting results and examples are presented. The existence of a good homomorphism between a refined neutrosophic hypergroup H(I1; I2) and a neutrosophic hypergroup H(I) is established. Keywords: Neutrosophy, neutrosophic hypegroup, neutrosophic subhypergroup, refined neutrosophic hypergroup, refined neutrosophic subhypergroup.

The aim of this paper is to define and study for the first time AH-substructures in n-refined neutrosophic vector spaces such as weak/strong AH-subspaces, and weak/strong AH-linear transformations between two n-refined neutrosophic vector spaces. Also, this paper introduces some elementary properties of these concepts. 

A single valued neutrosophic set (SVNS) is a useful tool to portray uncertainty in multi attribute decisionmaking. In this article, we develop hybrid averaging and hybrid geometric aggregation operator using sine trigonometric function to handle uncertainty in single valued Neutrosophic information, which are, sine trigonometricsingle valued neutrosophic hybrid weighted averaging (ST-SVNHWA) operator and , sine trigonometric-single valued neutrosophic hybrid weighted geometric (ST-SVNHWG) operator. We investigate properties, namely, idempotancy, monotonicity and boundedness for the proposed operators. Moreover, we give an algorithm to solve multi criteria decision-making issues which involve SVN information with ST-SVNHWA and STSVNHWG operators. Finally, an illustrative example of agricultural land selection is provided to verify the effectiveness. Sensitivity and comparative analyses are also implemented to assess the stability and validity of our method.