International Journal of Neutrosophic Science

This paper introduces a broadened concept of fuzzy semi-open sets by framing them in the context of fuzzy ideals. Where many of their elementary properties will be presented in terms of theorems and lemmas. Also, many related examples about the validity of semi-open sets and their relationships with fuzzy ideals will be provided and discussed.

Various educational barriers have negative impacts on teachers, organizations, and students. Identify these barriers and introduce some strategies that give benefits to organizations.   There are different conflicting barriers, so the concept of multi-criteria decision-making (MCDM) is used to deal with these barriers. We proposed an MCDM Framework to evaluate the education barriers and rank strategies to select the best one. We suggest a TOPSIS method to rank the alternatives. The TOPSIS method is integrated with the neutrosophic set to deal with uncertain information. The weights of the criteria are computed with the mean method. We collected ten barriers and nine strategies in this study. The results show that Promoting teacher motivation is the best of the nine strategies. We created a sensitivity analysis to show the model's effectiveness and the results' stability. The sensitivity analysis is made by changing the criteria weights and ranking the strategies. The results show that promoting teacher motivation is the best in all cases in sensitivity analysis.   

In this paper, we have studied for the first time the concept of n-potent fuzzy groups and n-potent anti-fuzzy groups. Many related properties will be proved such as the intersection of n-potent fuzzy groups, the product of n-potent anti-fuzzy groups, and the factor groups formed by these structures.

A field is a fundamental algebraic structure that finds extensive applications in algebra and various mathematical domains. On the other hand, a Q-complex neutrosophic soft set (Q-CNSS) is a unique hybrid model that combines the characteristics of soft sets and neutrosophic sets within a complex number framework. It utilizes the effectiveness of Q-set as a powerful tool in the domain of this particular model. In this article, we leverage this model to define fields under uncertainty. We present the Q-complex neutrosophic soft field (Q-CNSF) and examine the unique algebraic properties associated with this model. Additionally, we explore the relationships between Q-CNSF and Q-neutrosophic soft field (Q-NSF). Furthermore, we define the Cartesian product of QCNSFs and delve into the relevant properties. Through this comprehensive exploration, our aim is to enhance the understanding of Q-CNSFs and their properties, ultimately contributing to the field of algebraic analysis and its practical applications in handling uncertainty and vagueness.

The notion of neutrosophic nil radicals of neutrosophic ideals in rings is introduced, and related properties are investigated. In addition, we study some relations between the nil radical of the neutrosophic polynomial ideal of the polynomial ring R[x] induced by a neutrosophic ideal of a ring R and the nil radical of a neutrosophic ideal of R. Finally, we find the result of neutrosophic nil radicals of neutrosophic ideals from the epimorphism of rings.

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.

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.

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.

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.

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.

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].