The Frechet distribution is a versatile probability distribution that is used within a loose range in many important statistical fields, such as image processing, data analysis, and pattern recognition. It aims to explore and study the estimation of the parameters of the Frechet distribution using the noise-robust least squares method, as in the research paper, and it also has uses. There are many real-world scenarios. It is known that there is a growing challenge in estimating the parameter because of the noisy data. Depending on rigorous simulations and experimental analysis, we provide a novel powerful way to estimate the parameters for the Frechet Distribution Robust Least Squares approach to be flexible. Also, the results approach of this work will be very helpful in estimating the Frechet distribution parameters for diverse statistical applications. Also, we generalize our results to include the generalized neutrosophic case of this distribution dealing with neutrosophic numbers.
Read MoreDoi: https://doi.org/10.54216/IJNS.250301
Vol. 25 Issue. 3 PP. 01-13, (2025)
We employ the Laplace Residual Power Series Method to approximate analytical solutions for differential equations and neutrosophic differential equations with associated parameters, including non-homogeneous equations and fractional formulas in partial differential equations (PDEs). This approach showcases the method's simplicity, effectiveness, and robustness in deriving analytical series solutions for PDEs that involve associated parameters, especially in the context of fractional differential equations. Several practical uses of LRPSM with an emphasis on non-homogeneous and partial differential equations and neutrosophic equations with fractions (PDEs). These applications are significant in a variety of scientific and engineering domains that simulate complicated dynamic system such as anomalous diffusion in physics, viscoelastic material modeling in engineering and signal processing.
Read MoreDoi: https://doi.org/10.54216/IJNS.250302
Vol. 25 Issue. 3 PP. 14-24, (2025)
This paper uses finite difference methods to study the numerical solution for neutrosophic Sine-Gordon system in one dimension. We use the explicit method and Crank-Nicholson method. Also, an effective comparison between the results of the two methods has been made, where we obtain the result that Crank-Nicholson method is more accurate than the explicit method, but the explicit method is easier. We also study the stability analysis for each method by using Fourier (Von-Neumann) method and get that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition 𝑟2≤1𝑐2 and 𝑟2≤1.
Read MoreDoi: https://doi.org/10.54216/IJNS.250303
Vol. 25 Issue. 3 PP. 25-36, (2025)
In this study, we define time-fuzzy soft set (T-FSS) as an extension of fuzzy soft set. We will also define and investigate the features of its main operations (complement, union intersection, ”AND” and ”OR”). Finally, we’ll apply this approach to decision-making difficulties.
Read MoreDoi: https://doi.org/10.54216/IJNS.250304
Vol. 25 Issue. 3 PP. 37-50, (2025)
This study develops a new version of the lognormal distribution, the neutrosophic lognormal distribution (NLND), to address uncertainties commonly exist in reliability studies within the engineering field. The NLND is suitable for analyzing complex data with symmetrical or right-skewed patterns. The paper discusses the mathematical characteristics of the NLND, including concepts of reliability like mean time failure, hazard rate, cumulative failure rate, and reliability function. The model is based on real-life examples from life-test data and uses the maximum likelihood method to determine two key parameters. A simulation experiment was conducted to evaluate the accuracy of the estimated parameters, showing that maximum likelihood estimators can effectively estimate unknown parameters, especially with a large sample size. Finally, a real-world data is used to demonstrate the adequacy of the proposed model in a practical scenario.
Read MoreDoi: https://doi.org/10.54216/IJNS.250305
Vol. 25 Issue. 3 PP. 51-59, ()
In this paper, the basic properties of the convex fuzzy metric space will be presented. In particular, the proof of the fixed-point theorem for the fuzzy contraction single valued functions will be discussed. Furthermore, the solution system of linear equations, Volterra equations and Fredholm integral equations will be obtained as a direct application of the fixed-point theorem.
Read MoreDoi: https://doi.org/10.54216/IJNS.250306
Vol. 25 Issue. 3 PP. 60-69, (2025)
The research started from Salama's generalization to both ideal and local function through NCSs. We presented some results and properties to reinforce the concept of the generalized local function, which though its properties was used to deduce the properties of the 𝜓Ν𝐶- operator that we generalized through NCSS.
Read MoreDoi: https://doi.org/10.54216/IJNS.250307
Vol. 25 Issue. 3 PP. 70-75, (2025)
This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms the Runge-Kutta method in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Runge-Kutta method. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods. In conclusion, the proposed method consistently outperforms the Runge-Kutta method experimentally in all practical problems.
Read MoreDoi: https://doi.org/10.54216/IJNS.250308
Vol. 25 Issue. 3 PP. 76-91, (2025)
We present the neutrosophic interval-valued set applied to the q-rung logarithmic operator (q-RLOANIVS). One might develop a q-rung neutrosophic interval-valued set by extending the Pythagorean interval-valued fuzzy set (PIVFS) and neutrosophic set (NS). We discuss the q-Rlogarithimic operator applied neutrosophic interval-valued weighted averaging (q-RLOANIVWA), q-Rlogarithimic operator applied neutrosophic intervalvalued weighted geometric (q-RLOANIVWG), extended q-Rlogarithimic operator applied neutrosophic intervalvalued weighted averaging (q-RELOANIVWA) and extended q-Rlogarithimic operator applied neutrosophic interval-valued weighted geometric (q-RELOANIVWG). Several algebraic attributes have been established, including distributivity, idempotency, and associativity of q-RLOANIVSs.
Read MoreDoi: https://doi.org/10.54216/IJNS.250309
Vol. 25 Issue. 3 PP. 92-105, (2025)
In light of the great development witnessed by our contemporary world, it has become necessary to focus on scientific methods and use the quantitative method to reach more accurate decisions, appropriate to the surrounding circumstances and factors. The process of decision-making and choosing the optimal alternative depends on the type and quality of data that describes the issue for which the decision is to be made. Regarding it, in this chapter we present a study of the issue of determining the ideal advertising medium to display a company’s products. This issue is considered one of the issues of decision-making in the case of confirmed data, so we build the appropriate mathematical model and through the optimal solution to it we can make the ideal decision through which the company achieves its goal from the campaign. Informative, we will divide this study into two parts. In the first section, we will develop a general formula for this issue, and the data will be classical values. We will obtain a linear mathematical model. In the second section, we will formulate the issue from the perspective of neutrosophic science, meaning we will take the data as neutrosophic values, obtaining a linear neutrosophic model.
Read MoreDoi: https://doi.org/10.54216/IJNS.250310
Vol. 25 Issue. 3 PP. 106-114, (2025)
The aim of this study is to compare common and previously used numerical algorithms for nonlinear problems under different conditions. This study proposes a parallel implementation of two free derivative optimization methods, Powell's method and Nelder-Mead's method, combined with two restart strategies to achieve a global search. In terms of total time, the Powell method converges faster than the Nelder-Mead method. The final function value obtained by the Powell method is slightly lower. Both are optimization techniques used to find the minimum of an objective function in multidimensional space, without requiring derivatives. Also, we extend our results to apply to some neutrosophic non-linear problems under different neutrosophic-based conditions with many examples that explain the validity of our approach.
Read MoreDoi: https://doi.org/10.54216/IJNS.250311
Vol. 25 Issue. 3 PP. 115-122, (2025)
In this investigation, we present a new collection of analytic functions that includes Touchard polynomials. We then aim to calculate the Maclaurin coefficients |𝑎2 | and |𝑎3 | and address the Fekete-Szegö functional problem within this specific subfamily. Additionally, we demonstrate several new outcomes by specifying the parameters used in our main findings.
Read MoreDoi: https://doi.org/10.54216/IJNS.250312
Vol. 25 Issue. 3 PP. 123-131, (2025)
The cyclical nature of credit is a pivotal component of the broader business cycle, with credit expansion serving as a crucial mechanism for economic resurgence post-crisis. This paper delves into the ramifications of stringent financial regulations implemented in the wake of the 2007–2008 financial crisis, which notably decelerated the credit expansion phase, culminating in an anomalously extended period of credit contraction within the non-financial private sector. From a Neutrosophic Science perspective, this study posits that the typical progression of the credit cycle was significantly altered due to the heightened requirements under Basel III and the overhaul of the United States financial system. Distinct from prior crises, the post-2007–2008 period witnessed a more languid recuperation in credit activity, with the credit volume to the non-financial private sector yet to attain pre-crisis levels. This article offers a comparative analysis, scrutinizing the temporal dynamics of credit recovery following various crises. Drawing on Minsky’s financial instability hypothesis, Crotty’s theory of endogenous credit standard formation, and the Neutrosophic Science framework, the research investigates the phenomenon termed "credit paralysis." It hypothesizes that banking credit standards are intrinsically linked to macroeconomic variables such as GDP levels, interest rates, and loan volumes. Employing a vector autoregressive model, the study examines the alterations in credit activity vis-à-vis shifts in credit standards and explores the genesis of these standards in relation to macroeconomic indicators. The analysis leads to the conclusion that the augmented credit standards, necessitated by Basel III's implementation in crisis response, disrupted the normal trajectory of the credit cycle. The research culminates in the development of a stylized model of the U.S. credit cycle, which incorporates specific factors from the 2007–2008 crisis, including pre-crisis financial innovations, the subsequent intensification of financial regulations, and the principles of Neutrosophic Science.
Read MoreDoi: https://doi.org/10.54216/IJNS.250313
Vol. 25 Issue. 3 PP. 132-143, (2025)
In this paper, we explore the theoretical foundations of neutrosophics type-2 fuzzy sets by investigating its algebraic properties, demonstrating how neutrosophics type-2 fuzzy sets can generalize and extend existing operations in Type-1 and traditional Type-2 fuzzy sets. We also provide illustrative examples to clarify the practical applications of these operations, showcasing the potential of neutrosophics type-2 fuzzy sets in areas requiring sophisticated decision-making tools and uncertainty management.
Read MoreDoi: https://doi.org/10.54216/IJNS.250314
Vol. 25 Issue. 3 PP. 144-154, (2025)
In this study, I introduce time-fuzzy soft expert set (T-FSES) as an extension of fuzzy soft set. I will also define and investigate the features of its main operations (complement, union intersection, AND and OR). Finally, I’ll apply this approach to decision-making difficulties.
Read MoreDoi: https://doi.org/10.54216/IJNS.250315
Vol. 25 Issue. 3 PP. 155-176, (2025)
In this manuscript, we present the concept of E -Geraghty contractions, demonstrating several fixed point results.Additionally, we provide an illustrative example to highlight our principal findings.
Read MoreDoi: https://doi.org/10.54216/IJNS.250316
Vol. 25 Issue. 3 PP. 177-186, (2025)
The generalization for interval fuzzy set name as neutrosophic set employed to construct a measurable space in this work. The measurable space with respect to a ring of sets that is closed under difference and union, is studied. The objective of this study is to extend the notion of a ring of sets by using neutrosophic sets. Neutrosophic set concept has gained popularity in various fields of mathematics, probability, and other sciences due to its many uses, especially when dealing with uncertainties. Several different properties of neutrosophic ring are studied. Examples and characterizations to the proposed extension are given.
Read MoreDoi: https://doi.org/10.54216/IJNS.250317
Vol. 25 Issue. 3 PP. 187-193, (2025)
In decision-making, NS permits the representation of information with three membership functions: indeterminacy (I), false (F), and truth (T). All components in an NS have indeterminacy, non-, and membership degrees that are autonomous and vary from (0-1). This generates NS particularly appropriate in composite decision-making situations where information is incomplete, ambiguous, or contradictory, which allows strong and more complex solutions and analysis. Detecting road damage accurately and quickly enables the capability of road maintenance agencies to generate timely maintenance to road surfaces, retain optimum road conditions, enhance the safety of transportation, and reduce transportation charges. Research on road damage detection using AI models achieved more attention at present, particularly in smart cities. This paper develops a Boosting Road Damage Detection using DEMATEL with Bipolar Neutrosophic Dombi and Siberian Tiger Optimization (BRDD-DBNDSTO) algorithm. The presented BRDD-DBNDSTO technique is mainly intended to improve the accuracy and reliability of road damage classification for intelligent smart city infrastructure. To accomplish this, the BRDD-DBNDSTO technique employs adaptive bilateral filtering (ABF) using image preprocessing to effectively enhance image quality by reducing noise. Then, the SqueezeNet method was used to create a collection of feature vectors. For the classification and detection of road damage, the DEMATEL with bipolar neutrosophic Dombi model is exploited. At last, the Siberian tiger optimization (STO) algorithm is used to adjust the parameters related to the classifier model. To guarantee the improved performance of the BRDD-DBNDSTO method, an extensive experimental study was carried out and the gained outcomes illustrate the improvement of the BRDD-DBNDSTO model across the existing techniques.
Read MoreDoi: https://doi.org/10.54216/IJNS.250318
Vol. 25 Issue. 3 PP. 194-205, (2025)
Neutrosophic set (NS) is particularly appropriate in applications where data is incomplete, unclear, or inconsistent, which offers an effectual means for analyzing and exhibiting complex mechanisms. An NS is a mathematical technique to manage uncertainty, indeterminacy, and imprecision. It enlarges classical sets, IF sets, and fuzzy sets by presenting three degrees such as indeterminacy (I), false (F), and truth (T). Financial technology (Fintech) plays an essential part in advancing modern society, technology, economies, and various fields. Financial crisis prediction (FCP) plays a crucial role in shaping economic outcomes. Past research has predominantly focused on using deep learning (DL), machine learning (ML), and statistical methods to forecast the financial stability of business. In this manuscript, we focus on the development of Effective Data Classification using Interval Neutrosophic Covering Rough Sets based on Neighborhoods and Multi-Strategy Improved Butterfly Optimization (EDCINCRS-MSIBO) Algorithm for FinTech Applications. It contains distinct kinds of stages such as data normalization, feature selection, classification, and parameter tuning. In the EDCINCRS-MSIBO technique, a min-max normalization-based data pre-processing model to scale the raw data into a uniform format. For feature subset selection, the whale optimizer algorithm (WOA) is employed to reduce the dimensionality and improve model efficiency by selecting the most relevant features. In addition, the EDCINCRS-MSIBO technique takes place interval neutrosophic covering rough sets (INCRS) classifier is utilized for detection and classification of a financial crisis. Finally, a multi-strategy improved butterfly optimization algorithm (MSIBOA) is exploited for the optimum parameter adjustment of the INCRS model. To confirm the better predictive solution of the EDCINCRS-MSIBO model, a wide range of simulations are executed on the two benchmark databases. The comparative result analysis displays the encouraging outcomes of the EDCINCRS-MSIBO method on the existing techniques
Read MoreDoi: https://doi.org/10.54216/IJNS.250319
Vol. 25 Issue. 3 PP. 206-218, (2025)
Neutrosophy is the neutralities study and prolongs the discussion of the truth of opinions. Neutrosophic logic might be used in all sectors, to provide the solution for the indeterminate challenges. Some real-time data experience issues like inconsistency, incompleteness, and indeterminacy. A fuzzy set (FS) offers an uncertain solution, and an intuitionistic fuzzy set (IFS) processes partial data, but both fail to handle uncertain data. Financial fraud, believed as a deceptive strategy to gain financial assistance, has recently become a common threat in organizations and companies. Traditional methods namely manual inspections and verifications are costly, time-consuming, and imprecise to identify such fraudulent actions. With the development of artificial intelligence (AI), machine learning (ML)-based algorithms are applied logically to identify fraud transactions by investigating a larger amount of financial data. Therefore, the study offers an Optimizing Financial Fraud Detection using Bayesian Optimization and Variable Selection with Neutrosophic Vague Soft Set (OFFDBO-VSNVS) Algorithm. The OFFDBO-VSNVS model presents an optimized framework for fraud detection by integrating advanced variable selection techniques and classification models. Initially, the OFFDBO-VSNVS technique applies the Z-score data normalization technique to transform input data into a compatible layout. Next, the grey wolf optimizer (GWO)--based feature selection to effectively reduce dimensionality and highlight the most relevant features. For the classification and detection of financial fraud, the neutrosophic vague soft set (NVS) model can be employed. Eventually, the Bayesian optimization (BO) model adjusts the hyperparameter values of the NVS algorithm optimally and outcomes in greater classification performance. The stimulated outcome study of the OFFDBO-VSNVS model occurs and the outcomes are examined in terms of changing features. The experimental study represented the superiority of the OFFDBO-VSNVS method across the existing state-of-the-art methods
Read MoreDoi: https://doi.org/10.54216/IJNS.250320
Vol. 25 Issue. 3 PP. 219-230, (2025)
To handle incomplete and indeterminate data, neutrosophic logic/set/probability was recognized. The neutrosophic falsehood, truth, and indeterminacy modules show symmetry as the truth and the falsehood appear the similar and perform in a symmetrical method with esteem to the indeterminacy module which aids as a line of the symmetry. Soft set is a general mathematical device to deal with uncertainty. Sentiment analysis (SA) is the foremost task of natural language processing (NLP), where judgments, opinions, thoughts, or attitudes toward an exact subject are removed. Web is a rich foundation of information and unstructured covering numerous text documents with reviews and opinions. The detection of sentiment will be useful for governments, discrete business groups, and decision-makers. With this motivation, this study develops a Data Analytics Framework for Sentiment Classification Using Pythagorean Neutrosophic Bonferroni Mean (DAFSC-PNBM) technique on Product Reviews. The presented DAFSC-PNBM technique mainly aims to determine the nature of sentiments based on product reviews. Primarily, data preprocessing is performed to increase the product review qualities. For the word embedding process, word2vec model is used. Besides, the DAFSC-PNBM model uses the Pythagorean Neutrosophic Bonferroni Mean (PNBM) technique for classification. To enhance the SA performance of the PNBM model, the grey wolf optimizer (GWO) model has been applied as a hyperparameter tune process. The experimentation outcome analysis of the DAFSC-PNBM method occurs and the outcomes are investigated under several features. The experimental study indicated the improvement of the DAFSC-PNBM method across the modern techniques
Read MoreDoi: https://doi.org/10.54216/IJNS.250321
Vol. 25 Issue. 3 PP. 231-241, (2025)
Decision-making theory is an effective way to help the decision-maker take the right path to solve a problem. Among the applications of this theory is the medical field, i.e. allowing the decision maker (doctor) to analyze patient data and judge the result of this analysis as to whether the patient is infected or not. In this path and to enrich this theory with more flexible mathematical methods, we present in this work a more flexible expanded method for a previous concept called Interval-valued Q-neutrosophic soft matrix (IV-Q-NSM) as a new generalization of previous mathematical tools. These tools deal with the two-dimensional uncertainty issues that exist in many areas of life. Next, some ordinary algebraic properties and matrix operations have also been studied. After that, we present a new methodology for the decision-making (DM) selection problems in medical diagnoses.
Read MoreDoi: https://doi.org/10.54216/IJNS.250322
Vol. 25 Issue. 3 PP. 242-257, (2025)
This manuscript presents a novel approach for solving first-order initial value problems by leveraging the Fuzzy Kamal Transform within a Neutrosophic framework. By integrating fuzzy logic with Neutrosophic set theory, the method adeptly addresses uncertainties inherent in differential equations. The efficacy of this method is demonstrated through the exposition of various illustrative examples.
Read MoreDoi: https://doi.org/10.54216/IJNS.250323
Vol. 25 Issue. 3 PP. 258-264, (2025)
Let R be a G-graded ring and M be a G-graded R-module. The graded second spectrum of M, denoted by Specs G(M), is the set of all graded second submodules of M. In this paper, we define a topology on Specs G(M) which is analogous to that for SpecG(R), and investigate several topological properties of this topology.
Read MoreDoi: https://doi.org/10.54216/IJNS.250324
Vol. 25 Issue. 3 PP. 265-279, (2025)
Wireless Body Area Networks (WBANs) play a pivotal role in modern healthcare by enabling continuous monitoring of physiological data through sensors placed on or around the human body. Despite their significant benefits, WBANs face challenges such as data uncertainty, complex decision-making processes, and dynamic network conditions. These challenges can lead to inaccuracies and inefficiencies in health monitoring and diagnostics. The paper's main aim is to incorporate neutrosophic theory into Wireless Body Area Networks to provide enhancements in decision-making. In modern healthcare, the use of WBANs for monitoring physiological data by sensors, which are attached to or around the human body, can be continuous. Despite huge advantages, the main challenges that WBANs face are the uncertainties in data, complex decision-making processes, and dynamic network conditions, making health monitoring and diagnostics inaccurate and inefficient. In this paper, authors propose a robust framework to map sensor data into the neutrosophic domain and apply neutrosophic logic for enhanced accuracy and reliability of decision-making. In this paper, a Neutrosophic Decision-Making Algorithm is proposed, and its performance is compared with other decision-making techniques in terms of accuracy, response time, energy efficiency, and reliability. Experimental results show major improvements of around 95.3% in accuracy and a reduction of up to 25% in response time and energy consumption. Results underline the potential of neutrosophic theory for revolutionizing decision-making processes within WBANs to ensure more reliable and efficient health monitoring. This approach enables not only operational life but also improves patient outcome, avoiding a wrong diagnosis, during long-term health monitoring applications using WBAN devices.
Read MoreDoi: https://doi.org/10.54216/IJNS.250325
Vol. 25 Issue. 3 PP. 280-295, (2025)
This paper is dedicated to studying for the first time the building of a topological space based on the intervals defined over 4-refined neutrosophic real numbers and 5-refined neutrosophic real numbers, where we define a special partial order relation on these rings, and we use it to study the structure of the corresponding intervals generated from this relation. Also, we characterize the formula of open sets through these two topological spaces with some illustrated examples.
Read MoreDoi: https://doi.org/10.54216/IJNS.250326
Vol. 25 Issue. 3 PP. 296-306, (2025)
In this paper, we prove new spectral radius inequalities for sums, differences and commutators involving accretive-dissipative matrices of Hilbert space. Earlier well-known results used the spectral radius for its importance for general matrices. In our paper, we focus on some results related to spectral radius for special kind of matrices which are accretive-dissipative. A particular example is also presented in this work.
Read MoreDoi: https://doi.org/10.54216/IJNS.250327
Vol. 25 Issue. 3 PP. 307-311, (2025)
The study of chemical compounds’ molecular structures is one of the most cutting-edge uses of graph theory, along with computer science, nanochemistry, network design in electrical and electronic engineering, and the depiction of graphs in Google Maps. The degree and distance between vertices of a graph are the basis for examining topological indices. The formula for computing the Weighted Padmakar Ivan index (WPI) of a graph G is PIw(G) = P e∈E(G) [(dG(u) + dG(v)][|V (G)| − NG(e)].
Read MoreDoi: https://doi.org/10.54216/IJNS.250328
Vol. 25 Issue. 3 PP. 312-321, (2025)
One of the traditional problems in survey sampling is to estimate the population parameter like mean variance etc. This article investigates the mathematical derivations and application of neutrosophic statistics to address the challenges posed by imprecise, indeterminacies or ambiguous data, such as daily stock prices, weather forecast, social media sentiment and temperatures. The suggested estimators are highly useful for computing results while working with unclear, hazy, and neutrosophic-type data. These estimators produce answers that are interval-form rather than single-valued, which may give our population parameter a better chance of being off. We propose three novel neutrosophic exponential ratio-type estimators for the population mean, utilizing information of neutrosophic auxiliary variables. Expressions for bias and mean square error (MSE) of these estimators are derived using first-order approximations to assess their performance in terms of accuracy. To demonstrate their effectiveness, we apply the proposed estimators to real-life neutrosophic data sets. Additionally, a simulation study shows that our estimators outperform existing methods in terms of MSEs and percentage relative efficiency (PREs). This study further expands its originality by including pre-existing estimators into the neutrosophic framework, showcasing its versatility and adaptability. The results suggest that neutrosophic statistics provide a robust framework for analyzing uncertain data, facilitating more reliable decision-making in various applications.
Read MoreDoi: https://doi.org/10.54216/IJNS.250329
Vol. 25 Issue. 3 PP. 322-338, (2025)
In this study, the lindel”of property of spaces will be examined across nth topologies, referred to as nthlindel” of spaces. Furthermore, the characteristics of these spaces will be analyzed in relation to lindel¨o]f spaces and tri-Lindelf spaces. Several theoretical results have been presented and proven, and various well-known theorems concerning Lindel?f spaces have been extended to accommodate nth topologies. An illustrative examples are provided to support the findings.
Read MoreDoi: https://doi.org/10.54216/IJNS.250330
Vol. 25 Issue. 3 PP. 339-348, (2025)
In this article, we introduce and establish a novel concept called ’cubic spherical linguistic neutrosophic topological spaces’ by employing cubic spherical linguistic neutrosophic sets and topological frameworks. Various foundational definitions, theorems, and properties are provided along with illustrative examples.
Read MoreDoi: https://doi.org/10.54216/IJNS.250331
Vol. 25 Issue. 3 PP. 349-362, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250332
Vol. 25 Issue. 3 PP. 363-372, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250333
Vol. 25 Issue. 3 PP. 373-384, (2025)
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).
Read MoreDoi: https://doi.org/10.54216/IJNS.250334
Vol. 25 Issue. 3 PP. 385-397, (2025)
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
Read MoreDoi: https://doi.org/10.54216/IJNS.250335
Vol. 25 Issue. 3 PP. 398-416, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250336
Vol. 25 Issue. 3 PP. 417-434, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250338
Vol. 25 Issue. 3 PP. 450-468, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250337
Vol. 25 Issue. 3 PP. 435-449, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250339
Vol. 25 Issue. 3 PP. 469-488, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250340
Vol. 25 Issue. 3 PP. 489-500, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250342
Vol. 25 Issue. 3 PP. 511-539, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250341
Vol. 25 Issue. 3 PP. 501-510, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250343
Vol. 25 Issue. 3 PP. 540-560, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250344
Vol. 25 Issue. 3 PP. 561-572, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250345
Vol. 25 Issue. 3 PP. 573-592, (2025)
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.
Read MoreDoi: https://doi.org/10.54216/IJNS.250346
Vol. 25 Issue. 3 PP. 593-600, (2025)