International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Polynomial ideals of a ring based on neutrosophic sets

A. Priya , P. Maragatha Meenakshi , Aiyared Iampan , N. Rajesh

In this paper, we introduce the notion of the neutrosophic polynomial ideal Ax of a polynomial ring R[x] induced by a neutrosophic ideal A of a ring R and obtain an isomorphism theorem of a ring of neutrosophic cosets of Ax. It is shown that a neutrosophic ideal A of a ring is a neutrosophic prime if and only if Ax is a neutrosophic prime ideal of R[x].

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Doi: https://doi.org/10.54216/IJNS.220401

Vol. 22 Issue. 4 PP. 08-19, (2023)

Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings

Mamika Ujianita Romdhini , Ashraf Al-Quran , Faisal Al-Sharqi , Hazwani Hashim , Abdalwali Lutfi

In this paper, our aim is to investigate the algebraic structures within the Q-complex neutrosophic soft model. We introduce two fundamental concepts: the Q-complex neutrosophic soft ring (Q-CNSR) and the Q-complex neutrosophic soft ideal (Q-CNSI). Q-CNSRs combine the properties of Q-complex neutrosophic soft sets (Q-CNSSs) with ring theory, effectively capturing uncertainty and indeterminacy present in ring operations through the incorporation of Q-complex neutrosophic membership values. Additionally, we define Q-CNSIs as subsets of Q-CNSRs that possess distinctive properties and hold significant roles in ring theory. Furthermore, we discuss and verify the specific algebraic properties of Q-CNSR and Q-CNSI. By examining these properties, we gain a deeper understanding of the algebraic behavior of Q-CNSR and Q-CNSI. In particular, we shed light on the relationship between Q-CNSRs and soft rings. This provides insights into how Q-CNSR relates to the broader framework of soft ring, highlighting the unique features and contributions of Q-complex neutrosophic soft structures in the realm of algebraic analysis. We have also verified the relations between Q-CNSR and Q-neutrosophic soft ring (Q-NSR), as well as between Q-CNSI and Q-neutrosophic soft ideal (Q-NSI). Through this comprehensive exploration, our objective is to advance the understanding of Q-CNSR and Q-CNSI, thereby contributing to the field of algebraic analysis and its application in handling uncertainty and vagueness.

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Doi: https://doi.org/10.54216/IJNS.220402

Vol. 22 Issue. 4 PP. 29-35, (2023)

SEE Transform in Difference Equations and Differential-Difference Equations Compared With Neutrosophic Difference Equations

Eman A. Mansour , Emad A. Kuffi

The Sadiq-Emad-Emann (SEE) transform, also known as operational calculus, has gained significant importance as a fundamental component of the mathematical knowledge necessary for physicists, engineers, mathematicians, and other scientific professionals. This is because the SEE transform offers accessible and efficient resources for resolving several applications and challenges encountered in diverse engineering and science domains. This study aims to introduce the fundamental principles of SEE transformation and establish the validity of two statements and associated attributes. The objective of this study is to use the aforementioned qualities in order to determine the solution of difference and differential-difference equations, with neutrosophic versions of difference and differential difference equations. In addition, we are able to get very effective and expeditious precise answers.

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Doi: https://doi.org/10.54216/IJNS.220403

Vol. 22 Issue. 4 PP. 36-43, (2023)

On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts

Luis Albarracín Zambrano , Fabricio Lozada Torres , Bolívar Villalta Jadan , Nabil Khuder Salman

This paper is dedicated to studying the foundations of 7-plithogenic and 8-plithogenic number theory, where the central concepts about symbolic 7-plithogenic/8-plithogenic integers will be discussed such as symbolic 7-plithogenic/8-plithogenic Pythagoras triples and quadruples, symbolic 7-plithogenic/8-plithogenic linear Diophantine equations, and the divisors. On the other hand, we prove that Euler's theorem is still true in the case of the symbolic 7-plithogenic/8-pithogenic number theory.

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Doi: https://doi.org/10.54216/IJNS.220404

Vol. 22 Issue. 4 PP. 44-55, (2023)

A Note on Invertible Neutrosophic Square Matrices

P. Prabakaran , Gustavo Alvarez G´omez , Rita Azucena Diaz Vasquez , Andr´es Le´on Yacelga

The purpose of this article is to study the adjoint and inverse of neutrosophic matrices, where the inverse of a neutrosophic square matrix is defined and studied in terms of neutrosophic determinant and neutrosophic adjoint. It is shown by examples that, the converse part of the result “M is invertible if and only if detM ̸= 0” is not true, proved by Mohammad Abobala et al. in.2 Also some of the properties of neutrosophic adjoint are discussed.

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Doi: https://doi.org/10.54216/IJNS.220405

Vol. 22 Issue. 4 PP. 56-62, (2023)

Selection of neutral networks using q-rung neutrosophic vague soft set TOPSIS aggregating operator setting multi-criteria group decision making

A. Priya , P. Maragatha Meenakshi , Aiyared Iampan , N. Rajesh , Suganthi Mariyappan

The q-rung neutrosophic vague soft set (q-rung NVSS) is a generalization of the neutrosophic vague soft set (NVSS) and the vague soft set (VSS). The TOPSIS aggregated operation (AO) was used to discuss the q-rung NVSS. As an extension of VSS, the TOPSIS method effectively makes multi-criteria group decision making (MCGDM). With a score function, the goal is to find a positive and negative ideal solution based on q-rung NVSS. Closeness values are determined by presenting optimal alternatives. We provide practical examples to support our conclusions. This results in the outcome of the models for which q is provided. Considering the validity and usefulness of the models under consideration can be achieved by comparing them with those that have been proposed. Recent discoveries have generated quite a bit of interest and fascination.

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Doi: https://doi.org/10.54216/IJNS.220406

Vol. 22 Issue. 4 PP. 63-81, (2023)