International Journal of Neutrosophic Science

In This paper, we develop the Runge-Kutta numerical method to be applied on neutrosophic problems of high orders, where we present generalized neutrosophic versions of Runge-Kutta methods of rank five, six and seven to use them in finding numerical solutions for some neutrosophic differential problems. In addition, we apply our generalized methods to some solid problems with many illustrated examples and numerical tables for comparing the results and the absolute errors.

This study reviews a comprehensive mathematical framework known as neutrosophic soft sets, which combines neutrosophic theory with the soft set theory. Also, we review neutrosophic fractional order functions. For decision making, this framework effectively conveys ambiguity and uncertainty. The developments in soft set theory and neutrosophic set theory are thoroughly examined in this article. We review the advancements of both theories in general. We examine the qualities, applications, and theoretical underpinnings of both theories. We study the combination of neutrosophic soft set theory and logic. The study talks about important new developments and techniques that make neutrosophic soft suites better at solving difficult real-world problems that aren’t always clear. To promote the advancement of the discipline, we also provide a comprehensive overview of the theories derived from literature methodologies, and propose potential avenues for future research. This review serves as an important resource for researchers and practitioners wishing to utilize neutrophil suites in their work. It provides a deeper understanding of the potential effects and applications. This review also addresses a discussion on fractional order neutrosophic sets (FONS). The fractional order component offers an additional degree of freedom, enhancing the adaptability of neutrosophic sets for many applications.

In this study, we introduce fixed point theorems related to integral type contractions, framed within the advanced context of neutrosophic fuzzy metric spaces. Additionally, we derive multiple fixed point results that are relevant to this particular setting.

The notions of neutrosophic IUP-subalgebras, neutrosophic IUP-ideals, neutrosophic IUP-filters, and neutrosophic strong IUP-ideals of IUP-algebras are introduced, and their basic properties are investigated. Conditions for neutrosophic sets to be neutrosophic IUP-subalgebras, neutrosophic IUP-ideals, neutrosophic IUPfilters, and neutrosophic strong IUP-ideals of IUP-algebras are provided. Relations between neutrosophic IUP-subalgebras (resp., neutrosophic IUP-ideals, neutrosophic IUP-filters, neutrosophic strong IUP-ideals) and their level subsets are considered.

The study of geometric properties within the subclass of analytic functions has garnered significant attention in recent years due to its complex and intricate interplay between geometric function theory and complex analysis. This area of study provides deep insights into both mathematical theory and its practical applications. The exploration of these properties is not only of theoretical interest but also offers valuable implications for various applications in mathematical and engineering disciplines. In particular, this paper focuses on a detailed examination of the inclusion, neighborhood, and partial sums properties within a broad and general subclass of analytic functions. This class of functions is defined through a generalized multiplier transformation operator, which adds a layer of complexity to their analysis. By investigating these specific properties, this study aims to validate and build upon many existing findings documented in the literature, offering new perspectives and contributing to a deeper understanding of the field.

Multi-criteria decision-making is essential for resolving issues in the real world. The choice of cloud computing services on the basis of service quality is solved in this paper using bipolar-neutrosophic circumstances. The removal area approach is used to carry out the de-bipolarization technique. The results have been compared with other methods found in the research to determine which method provides better cloud service.

In this study, a rational cubic Ball function has been used to preserve the shape of monotonic and convex data. Conditions for shape preservation were drawn from the data and imposed on the free parameters of the interpolant function in such a way as to preserve the shape of the data. The interpolant is C1, which is continuous and visually pleasant function. The outputs of a number of numerical examples are presented.

This paper aims to introduce a new concept which is Fermatean Neutrosophic Soft Set (FNSS), which is a combination of the Neutrosophic soft sets and Fermatean Fuzzy Sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of FNSS is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the most attractive laptop based on a computer simulation report. Finally, a comparative analysis between the initiated FNSS model and some existing approaches is provided to show its reliability.

The object of the present paper is to introduce a new class of soft functions called soft regular-closed functions. This class contains the class of soft closed functions. Numerous theorems that give properties of such soft functions are presented. Moreover, sufficient conditions for a soft function to be soft regular-closed are given. In addition, several preservation theorems of soft separations axioms using soft regular-closed are given. Finally, the correspondence between this class of soft functions and the class of regular-closed functions in classical topology is studied.

The objective of this paper is to introduce the concept of Weak Fuzzy Complex differential equations. We have defined the general solution of the n-th order Weak Fuzzy Complex ordinary differential equation. That we have used a special isomorphism transformation function to write the WFC-ODE as two Real ODEs and solved them with respect to their own variables. Then, by the inverse of the transformation function, we have got the general solution in F (J) as a structure of two general solutions in R. Therefore, we have shown some types of first-order first-degree separable, exact, and linear WFC-ODEs. Also, we have found their general solutions with examples to demonstrate them.

In this paper, a new subclass of bi-univalent functions linked to Lucas-Balancing polynomials is introduced. Bounds for the coefficients in the Taylor-Maclaurin series, denoted as |a2| and |a3|, are determined for these functions. The Fekete-Szeg¨o functional problems are also addressed, and bounds for the second Hankel determinant for functions in this specific subclass are established. Additionally, it is shown that by adjusting the parameters in the main findings, several new results can be derived.

In order to solve hyperbolic fractional partial differential equations, this paper develops the Sumudu decomposition method. This method is based on solving time-fractional hyperbolic partial differential equations either individually or in systems using the Sumudu transform. Adomian polynomials whose values are chosen by a specific formula are used to solve the non-linear terms. The developed method’s convergence and stability are discussed. Example such as the shallow water equations, which serve as illustrations of the fractional derivatives as defined by Caputo, is used to show the validity and applicability of the proposed method. It is discovered that the procedure is rapid and precise

Today's educational assessment strategies require innovation and digital transformation in order to overcome biases towards data orientation in uncertain, ambiguous, and fuzzy conditions. Neutrosophic-based analysis techniques in educational assessment provide a thoughtful and highly effective approach to calibrating student learning abilities. However, there is a lack of access to resources and complete guidance on implementing soft computing methods like neutrosophic sets, resulting in a gap in knowledge and practice. Research and development have shown that neutrosophic-based analysis techniques can explain the formulation and algorithms used in multi-criteria decision-making approaches. Since educational assessment also involves decision making, this paper proposes a neutrosophic-based analysis assessment framework aimed at transforming assessment strategies in education to promote soft computing. The development of this paper will begin by reviewing the literature and conducting a preliminary study, highlighting the benefits of the neutrosophic set, and then forming a framework and operational design for the assessment strategy in a systematic manner. Illustrations with numbered data will be used to explain the suitability and usability of this framework for real educational assessment. The implications of calibrating the factors that have the strongest influence on students' mathematics learning demonstrate that this assessment framework can be expanded as an innovative and flexible approach to assessment, capable of improving the efficiency of data analysis in real learning environments. This framework and initiative can be used synergistically to improve the quality of education by incorporating digital elements and providing strong support for the Sustainable Development Goal (SDG).

In this paper, the notion of hesitant fuzzy norm based on the Bag-Samanta’s Type Fuzzy Norm on linear space has been introduced. Further the concepts of ascending family of semi-norms, convergence and fuzzy continuous linear operators are studied in hesitant fuzzy normed linear space.

This work focuses on nth-locally compact spaces, which are topologies with locally compactness properties. Furthermore, the properties of these spaces will be studied in terms of locally compact spaces. Theoretical conclusions have been given and proven, and well-known theorems for locally compact spaces have been extended to nth-topologies. An instance case is offered to back up the findings.