International Journal of Neutrosophic Science

The goal of this paper is to study complex fuzzy soft graph (CFSG). We introduce the concept of complex fuzzy soft graph from apply complex fuzzy set on fuzzy soft graph. The notations and definitions of some operations on two complex fuzzy soft graphs presented such as union, cartesian product, tensor product, normal product and composition of two complex fuzzy soft graphs. Also, a decision-making (DM) problem on supply chain management is discussed.

This project aims to concretize Ronald Dworkin's theory of legal integrity via Plithogenic n-SuperHyperGraphs. Therefore it investigates how such mathematical entities metaphorically and multidimensionally formulate moral coherence in legal interpretation. Using a mixed-method approach, this work will assess documents through a documentary assessment of Dworkin's written works (Law’s Empire and Taking Rights Seriously) to formulate a Plithogenic n-SuperHyperGraph of a case study featuring n-dimensional nodes as moral principles, moral assertions, and past decisions with hyperedges symbolizing the relationship between them generated by degrees of truth, falsity, or indeterminacy. Tools of graph visualization and neutrosophic computing will provide the legal assessment of characterization for coherence. The results will discuss whether the model intentionally visualizes the connections among the principles and how it assessed which characterizations would make the law most morally coherent under Dworkin's theory while acknowledging the indeterminacy in certain complicated cases. Thus, this study seeks to find correlations between which nodes function as the primary principles consistent with Dworkin's metaphor of the law's "chain." Ultimately, this research intends to present Plithogenic n-SuperHyperGraphs as a viable application to formally express Dworkin's theory for the sake of more moral legal determinations applicable to legal education or judicial assistive software, although generalizability will require cross-jurisdicDworkin; Legal Integrity; N- Superhypergraphs; Moral Coherence; Judicial Interpretation; Neutrosophic; Plithogenictional applications of the model.

The purpose of the study was to implement a patient classification for cleft lip and palate (CLP) patients according to their overall etiopathogenic risk profile given the multifactorial yet uncertain etiology of the disorder. To do this, a novel approach was made based on Plitogenic Fuzzy Soft Set Theory, which accommodates the simultaneous inexactness of clinically and epidemiologically derived information, ambiguous relationships of risk factors and indeterminacy of absent or conflicting information. A series of etiopathogenic parameters (genetic, environmental, and behavioral) were proposed as attributes and a set of plitogenic membership functions was used to assess each patient. Major findings enabled the classification of patients into certain risk levels (e.g. , high genetic risk, environmental dominance with less caution, mixed risk but dominantly high indeterminacy) and reveal factor composition patterns that would otherwise be invisible to classical statistical analyses. It was concluded that this model provides a superior clinical decision support system that is personalized since it quantifies the uncertainty of FLAP's etiology for more accurate risk stratification and preventative or early intervention planning more applicable to the complicated reality of all patients.

The research problem of this endeavor was how to comprehend subjective meanings based upon qualitative research—a uniform methodological concern of the social sciences for phenomena perpetually occurring in ever-changing environments. The significance of the study is based upon a methodological necessity that transcends natural human capability to engage what it means to be "uncertain" now that so much social reality has been rendered tainted, in addition to cultural and contextual amalgamation. Nonsensical articles provide one form of understanding but fail to equip uncertainty—acknowledgement of where something can go one way or the other, or multiple—and multivalent perspectives ultimately render ineffective opportunities for researchers to adopt a quantifiable, absolute reality. Therefore, this endeavor applies the Iadov Plithogenic Neutrosophic approach, compounded of plithogenic logic with neutrosophic meaning to successfully navigate qualitative research with high uncertainty. Ultimately, findings support that this approach empowers researchers to remove layers and find meaning in more original and texture-based fashions than the traditional A/B/C option. Ultimately, this work contributes theoretically to qualitative researches with an integrative new approach to render subjectivity, while practically providing those who want to understand a complicated world, the works to be effective. This endeavor illustrates that the most effective flexible approach to render meaning knowledge is the only way to go when the undertaking exists in comprehensive arenas.

There has been an unending debate about the effect of WhatsApp on students’ performance globally. This paper seeks to contribute to this debate by investigating the extent of WhatsApp usage and its’ effect on Uttarakhands’ post-graduate students’ academic performance. Estimation tools such as simple descriptive statistics, the difference in difference, and ordinary least square regression analyses were applied to a survey of 250 post-graduate students. At the top of the study, we found that most MBA students in India use WhatsApp during academic activity, connect with their professor via WhatsApp, and spend between 1 – 2 hours each day on WhatsApp. We also found a significant difference between the GPAs of students who are connected with their professors and those who are not connected with their professors. Again, we found a low level of addiction to WhatsApp but severe threats to circulating and withholding information by post-graduate students. It was also discovered that student connection with the professors via WhatsApp and spending 3 – 5 hours on WhatsApp increases ones’ academic performance. Therefore, we recommend that; school management put policies that will promote a positive and healthy relationship between professors and students, primarily via WhatsApp. The Indian Ministry of Information should enact laws that frond on sending false information on social media and possible punishment. Finally, we recommend that school management institutions have strict policies to prevent students from using WhatsApp during academic activity

This paper introduces and investigates a new class of bi-univalent functions constructed through the Neutrosophic 𝓆-Poisson distribution series. The study focuses on estimating the upper bounds of the basic coefficients |a_2 |and |a_3 |   in the Taylor series expansion of these functions.

Applying Chebyshev polynomial approximate results, this paper applies the idea of neutrophilic logic to the approach to partially differential equations (FPDEs).  Three elements make up the Neutrosophic technique: Indeterminacy (I), Falsehood (F), and Truth (T).  These three elements are appropriate for issues where precise values or distinct limits are lacking since they are utilized to represent ambiguity, vagueness, and imperfect truth in mathematical models.  We improve the depiction of real-world occurrences that could contain unclear or ambiguous information by adding these values to the coefficients of FPDEs.  In domains like material science, mechanical engineering, and biological phenomena, where uncertainty is inevitable, the use of neutrophilic logic enables a more thorough and precise approximation of approaches to complicated fractional differential equations. The findings show that when working with systems that have unknown characteristics, the Neutrosophic technique increases the accuracy and dependability of computations.

In this research, we introduce and develop new concepts in the field of Neutrosophic Topology (NCT). Particularly our study is focusing on the filter and its properties. Also, we present the properties of convergence of -filter, a specialized filter that incorporates neutrosophic values, providing a robust approach to handle uncertainty in topological spaces. Additionally, we explore the concept of adherent points in neutrosophic crisp triple topological spaces, offering a new perspective on the study of these spaces. Moreover, our findings contribute to expanding the understanding and application of neutrosophic theories in topology that will provide a solid foundation for future research in this area. Furthermore, this work opens new avenues for the study of topological spaces under uncertainty, with potential Applications in various domains, including data analysis, decision-making, and artificial intelligence, among others.

Oral cancer is presently a growing health concern at the global level, with intense incidences of lifestyle factors. The increasing mortality rates of the diseased shall be controlled with effective early detection mechanisms. However, the traditional statistical approaches in practice fail to deliver in making a precise diagnosis of this cancer due to the intricate and interdependent prevalence of symptoms. This research work provides a solution approach using the potency of neutrosophic statistics in developing neutrosophic-integrated models of random forests and decision trees. Neutrosophic representation of data considering the indeterminacy, values of truth, and falsity facilitates healthcare experts in handling the conflicting patient data. The proposed random forest decision model with neutrosophic logic identifies the significant features, and the neutrosophic decision tree classifier predicts the stages of cancer. The findings are compared with conventional modelling of random forest and decision trees, and it demonstrates the efficiency and precision of neutrosophic statistical analysis in predicting oral cancer. This proposed neutrosophic decision framework will assist and support the medical practitioners and research experts in gaining more insights and deeper comprehension of the cancer progression and suggesting suitable treatment plans to minimize the morbidity rate.

Recent years have witnessed remarkable developments in fuzzy logic, with interval-valued fuzziness and negative structures emerging as powerful tools for modeling inaccurate phenomena. The crossing cubic structures (CCs), as a generalization of the bipolar fuzziness structures, represent a comprehensive mathematical framework capable of dealing with a wide range of fuzziness and contradictory data, thus expanding research prospects in this area. This paper has made a new contribution to some algebraic structures by investigating the concept of CCs on algebraic substructures in a hoop algebra. The concepts of crossing cubic sub-hoops (CC − SHs) and crossing cubic filters (CCFs) are introduced, and a deeper understanding is sought to analyze their characteristics. The effect on the relationship between CC − SHs and CCFs is revealed, and the characterizations of CC − SHs and CCFs are analyzed.

This paper introduces new acceptance sampling plans for situations where the life test is terminated at a predetermined time. The minimum sample sizes needed to guarantee a specified average lifetime are determined for different acceptance numbers, confidence levels, and ratios of the fixed test duration to the defined average lifetime. The Shanker distribution is adopted to represent the lifetimes of test units, with its mean serving as the quality indicator. Furthermore, the operating characteristic function values for the proposed sampling plans, along with the associated producer's risk, are provided. Examples are included to demonstrate how to use the tables effectively. An application of a real data set is used to illustrate the usefulness of the suggested acceptance sampling plans.

Nonlinear programming is one of the most important methods used to obtain the optimal solution to many real-world problems. Given the importance of this method, numerous studies and research have been conducted in recent years with the aim of providing methods that help find the optimal solution. These studies and research have resulted in a basic structure used to find these solutions. This structure initially indicates that the optimal solution can be found at any boundary point in the feasible region, at a point within the feasible region, or at a discontinuity point. In this research, we present some of the important foundations and principles of nonlinear programming and the gradient projection method used in searching for the optimal solution to unrestricted nonlinear programming problems. We will reformulate these foundations and principles using neutrosophic logic concepts as a complement to our previous research, the aim of which is to provide a new vision for some operations research methods, a neutrosophic vision. Our focus will be on the improvement these concepts offer when used in the field of applied mathematics, through the more accurate and comprehensive solutions we obtain, which provide a margin of freedom commensurate with the Given the reality we live in, and the changes that can occur to the data of the actual issue under study, this requires decision makers to prepare many appropriate alternatives for each change.

A tools and techniques of neutrosophic graph have found many applications in different areas such as topology, networks, computer of science, etc. In addition, neutrosophic graph is a generalization of intuitionistic fuzzy graph. Therefore, in this paper we study some characteristics of neutrosopheic graphs (NTCG) and some basic definitions. Moreover we investigate several kinds of arcs,  -strong, -strong,  -arc, and  -strong, -strong,  –arc in neutrosopheic graphs (NTCG) , Finally we give neutrosophic -bridge and neutrosophic -bridge (NTC -bridge) and some interesting properties of  neutrosophic bridge (NTCB), which is being taught for the first time, and obtain several important properties.

In this paper, two numerical methods that are method of successive approximations and Fredholm’s first fundamental theorem are developed, reformatted, and applied to solve fuzzy second kind Fredholm integral equations with a separable kernel. The fuzziness in the equations is represented utilizing convex normalized triangular fuzzy numbers, which are based on a single and double parametric form of fuzzy numbers. A comparative analysis study between the proposed schemes are discussed through numerical experiment. It was found that Fredholm's first fundamental theorem is more efficient and effective than method of successive approximations. Furthermore, the double parametric form of fuzzy number is a general and more reliable than single parametric form since it reduced the computational cost and provides more certain fuzzy cases.

This paper introduces two new classes of bi-Bazilevic and bi-univalent functions that are defined using Borel distribution and Ruscheweyh operator, which also associated with Legendre polynomials and modified Sig-moid function within the open unit disk D. This paper explores the characteristics and behaviors of these functions, we find estimates for the modulus of the initial Taylor series coefficients a2 and a3 for functions within our newly defined classes and some of their various subclasses. Moreover, this paper explores the classical Fekete-SzegÖ functional problem concerning functions f that are classified within our specific classes. Additionally, we obtain the classical Fekete-SzegÖ inequalities of functions belonging to these classes and some of their various subclasses.