International Journal of Neutrosophic Science

In this paper, we will define the exponential form of a neutrosophic complex number. We have proven some characteristics and theories, including the conjugate of the exponential form of a neutrosophic complex number, division of the exponential form of a neutrosophic complex numbers, multiplication of the exponential form of a neutrosophic complex numbers. In addition, we have given the method of changing from the exponential to the algebraic form of a complex number.

The concept of neutrosophic become really handy now a days and based on non-standard analysis to mention mathematical outcomes, uncertainty, non-completed situations, inconsistency, distinctness. The main concept of Neutrosophic set based on membership values of truth, indeterminacy and falsity, which are independent, and which play vital role in situations like uncertainty, incomplete and inconsistence. From triangular to octagonal Neutrosophic number. They play vital role in modeling problems, science, biology and many more. Hence it is clear that these are necessary and have real life applications, but some real-life problems have more edges and their triangular to octagonal fail to overcome this situation (mention in table 1). Hence, nonagonal neutrosophic numbers give a wide scope of utilizations while managing more variances in the decision-making condition with nine edges for membership values of truth, indeterminacy and falsity. In this current article we present compression between triangular to nonagonal neutrosophic number and their requirement, explore differential equations in Neutrosophic environment as Linear, symmetric and asymmetric types further, their ∂-cute and then we present a real-life problem and solved it with TOPSIS technique of MCDM.

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T, I, F (truth, indeterminacy, falsehood) which can take a range of values. A previous paper in IJNS, 2020 shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. In any case, matter creation process in nature stays a major puzzle for physicists, scientists and other science analysts. To this issue neutrosophic logic offers an answer: "unmatter." This paper examines an extended model of unmatter, to incorporate issue soul solidarity. So, neutrosophic logic may demonstrate helpful in offering goal to long standing clashes.

The purpose of this article is to study neutrosophic polynomials i.e. polynomials which are Neutrosophic in nature and study its properties with the help of  neutrosophic numbers. Apart from this we discuss different types of neutrosophic polynomials with concrete examples and establish some theorems and results which will be useful for the further study. We also give a solution method to find the approximate roots of a neutrosophic polynomial equation.

This paper is concerned with the introduction of neutrosophic hypernear-rings. The concept of Neutrosophic A-hypergroup of a hypernear-ring A; neutrosophic A(I)-hypergroup of a neutrosophic hypernear-ring A(I) and their respective neutrosophic substructures are defined. We investigate and present some interesting results arising from the study of hypernear-rings in neutrosophic environment. It is shown that a constant Neutrosophic hypernear-ring in general is not a constant hypernear-ring. In addition, we consider the neutrosophic ideals, neutrosophic homomorphism and neutrosophic quotient hypernear-rings of neutrosophic hypernear-rings.