This paper introduces a novel approach to the concept of neutrosophic Lie algebra by leveraging the AH isometry framework. We establish foundational properties of neutrosophic Lie algebra, demonstrating that each neutrosophic algebra inherently fulfills the criteria of a Lie algebra. Moreover, we introduce distinct neutrosophic Lie algebraic structures, providing illustrative examples to support these constructs. By integrating neutrosophic logic, our approach effectively addresses indeterminacy, ambiguity, and imprecision, enhancing the classical algebraic structures with new dimensions of flexibility. The potential applications of neutrosophic Lie algebra are vast, particularly in fields requiring nuanced treatments of uncertainty.
Read MoreDoi: https://doi.org/10.54216/IJNS.250401
Vol. 25 Issue. 4 PP. 01-09, (2025)
In this paper, we present a numerical approach to the seventh rank refined neutrosophic Runge-Kutta numerical method, where we provide the theoretical basis of this formula to be applicable on refined neutrosophic differential equations. In addition, we provide numerical tables to compare the validity of this new method with other methods, as well as a clear computation of absolute errors in terms of refined neutrosophic numbers.
Read MoreDoi: https://doi.org/10.54216/IJNS.250402
Vol. 25 Issue. 4 PP. 10-17, (2025)
In this paper, we study a novel numerical method for finding the neutrosophic numerical solutions to some neutrosophic boundary values problems in differential equations of high orders. The proposed method based on neutrosophic numerical collocations of higher degree polynomials as an approximation to solve the problems. In addition, we provide many mathematical proofs about the existence of the solutions with many different examples and numerical tables that clarify the validity of the proposed method.
Read MoreDoi: https://doi.org/10.54216/IJNS.250403
Vol. 25 Issue. 4 PP. 18-25, (2025)
In this paper, we introduce a new weak form of soft continuity called soft weak θ-continuity in soft topological spaces and investigate the relationships between soft weak θ-continuity and θ-continuity (resp. soft weak continuity and soft δ-continuity). We obtain several characterizations of soft weak θ-continuity. Also, we give sufficient conditions for the equivalence between soft weak θ-continuity and soft θ-continuity (resp. soft δ-continuity). Moreover, we investigate the link between soft weak θ-continuity and weak θ-continuity in classical topology. Furthermore, via soft weak θ-continuity, we obtain preservation theorems of soft hyperconnectedness and soft near compactness. Finally, we obtain soft restriction, soft product, and soft graph theorems of soft weak θ-continuity.
Read MoreDoi: https://doi.org/10.54216/IJNS.250404
Vol. 25 Issue. 4 PP. 26-41, (2025)
This paper presents a modified Laplace Adomian decomposition method (MLADM) to solve the nonlinear time-fractional coupled Jaulent–Miodek system. The proposed approach provides convergent series solutions with easily computable components, demonstrating both accuracy and simplicity in its application. By employing the Caputo fractional derivative, this study establishes a robust framework for analyzing nonlinear behavior in fractional differential equations. The effectiveness of the method is validated through comparisons with previous studies, with results illustrated using graphical representations. The solutions proposed herein are significant for modeling complex and dynamic real-world phenomena across various scientific disciplines. All computations and graphical results were carried out using Mathematica, emphasizing the method’s reliability, precision, and ease of application to nonlinear fractional systems. The study of fractional nonlinear systems is crucial for modeling complex, dynamic, and uncertain processes, which are core aspects of neutrosophic science. By addressing the intricate behavior of the nonlinear time-fractional coupled Jaulent–Miodek system, this work advances mathematical models that encapsulate uncertainty, indeterminacy, and complex interactions. Such an alignment with the principles of neutrosophic science underscores the relevance of our approach to the objectives of the International Journal of Neutrosophic Science, highlighting its potential to enhance the understanding and practical applications of complex systems.
Read MoreDoi: https://doi.org/10.54216/IJNS.250405
Vol. 25 Issue. 4 PP. 42-57, (2025)
In this paper, we continue the studyWd-fuzzy implication algebras which are subalgebras of fuzzy implication algebras. Properties and axiomatic systems for Wd-fuzzy implication algebras are presented, then a few new results on Wd-fuzzy implication algebras have been added. We showed that there are relations between Wdfuzzy implication algebras and some of other fuzzy logical algebras such as FI-algebras, RFI-algebras, CFIalgebras, HFI-algebras. In particular, the relations between Wd-fuzzy implication algebras and L-algebras are investigated, and we prove that every Wd-fuzzy implication algebras is a proper subclass of L-algebras. Finally, we introduce the notions of GWd-FI algebras, whose some properties of it are investigated. The relations between distributive GWd-FI-algebras, Hilbert algebras, BE-algebras and W-eo algebras have been obtained.
Read MoreDoi: https://doi.org/10.54216/IJNS.250406
Vol. 25 Issue. 4 PP. 58-72, (2025)
Let G be a group with identity e and let W be a G-graded ring. In this paper, we introduce and study the concept of Gr-2-nil ideals of W. We obtain many results concerning gr-2-nil ideals. Some characterizations of gr-2-nil ideals and their homogeneous components are given. A proper graded ideal I of W is said to be a gr-2-nil ideal of W if whenever rg, sh, ti ∈ h(W) with rgshti ∈ I, then either rgsh ∈ Gr (0) or rgti ∈ I or shti ∈ I.
Read MoreDoi: https://doi.org/10.54216/IJNS.250407
Vol. 25 Issue. 4 PP. 73-79, (2025)
Based on the concept of Atanassov’s intuitionistic fuzzy set on a universe X, we introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy filters on an intuitionistic fuzzy lattice. More specifically, we provide characterizations of these concepts in terms of the intuitionistic fuzzy lattice meet and join operations, in terms of some associated fuzzy sets, as well as, in terms of their crisp level sets. Furthermore, we introduce the concepts of prime intuitionistic fuzzy ideals (resp. filters) as interesting kinds, and investigate their various properties and characterizations.
Read MoreDoi: https://doi.org/10.54216/IJNS.250408
Vol. 25 Issue. 4 PP. 80-100, (2025)
Finally In this study, we define parameterized time fuzzy soft expert set (PTFSES) as an extension of fuzzy soft set. Additionally, we will clarify and investigate the characteristics of its primary operation (complement, union intersection, ”AND” and ”OR”). , we’ll apply this approach to decision-making difficulties.
Read MoreDoi: https://doi.org/10.54216/IJNS.250409
Vol. 25 Issue. 4 PP. 101-121, (2025)
In this paper we aims to provide a clear definition of Neutrosophic Fuzzy Soft Sets and explain its fundamental operations through relevant examples. This work examines the computation of static Expected Time of Arrival (ETA) utilizing neutrosophic fuzzy soft set values and the fundamental Expected Time of Arrival. Our research also investigates the incorporation of sophisticated artificial intelligence (AI) methods to create reliable and adaptable dynamic Expected Time of Arrival(ETA) prediction models. Through the utilization of many types of data, such as current traffic statistics, weather conditions, road conditions, vehicle status, and driver behavior, we suggest a comprehensive system that adapts to changing circumstances and consistently enhances its ability to make accurate predictions. Our methodology utilizes cutting-edge machine learning algorithms to analyze and interpret vast amounts of diverse data. In addition, we tackle the difficulties of managing uncertainty and indeterminacy in data by utilizing Neutrosophic Fuzzy Soft Sets, which improve the model’s resilience and dependability.
Read MoreDoi: https://doi.org/10.54216/IJNS.250410
Vol. 25 Issue. 4 PP. 122-134, (2025)
This paper investigates the theoretical basis of fermatean neutrosophic sets, which were first introduced by Smarandache, to clarify the relationship between single-valued fermatean neutrosophic sets and their role as specific subsets in the wider context of fermatean neutrosophic sets, particularly in science and engineering. This study investigates fermatean neutrosophic INK-ideals within INK-algebras using the translation concept, which is proposed as an extension of intuitionistic fuzzy sets. First, translation fermatean neutrosophic INKalgebras are presented and their fundamental features are studied. Furthermore, the research investigates properties related to the translation of INK-subalgebras and INK-ideals, as well as the dynamics of their unions, intersections, and multiplications for fermatean neutrosophic INK-ideals. The article adds definitions and theorems to provide a complete grasp of the problems of fermatean neutrosophic INK-algebras.
Read MoreDoi: https://doi.org/10.54216/IJNS.250411
Vol. 25 Issue. 4 PP. 135-146, (2025)
In this article, we combined the Epanechnikov kernel function with the pareto distribution to produce the Epanechnikov-Pareto distribution (EPD). Some properties of this distribution are studied, like the moments, MLEs, reliability analysis functions, ordered statistics, and quintile function.
Read MoreDoi: https://doi.org/10.54216/IJNS.250412
Vol. 25 Issue. 4 PP. 147-155, (2025)
This article introduces the idea of neutrosophic ideal of a near algebra and provides a definition and example. A few fundamental features related to this approach are also explored. We also present the topics neutrosophic near algebra homomorphism, kernel of a neutrosophic near algebra and coset of a neutrosophic ideal of a near algebra. It is been briefed with the appropriate definitions and theorems on it. It is been proved that sum of the right neutrosophic ideal of a near algebra is also a right neutrosophic ideal of a near algebra over a neutrosophic field.
Read MoreDoi: https://doi.org/10.54216/IJNS.250414
Vol. 25 Issue. 4 PP. 169-175, (2025)
Accurately representing the complex linkages and inherent uncertainties included in huge datasets is still a major difficulty in the field of data clustering. We address these issues with our proposed Unified Neutrosophic Clustering Algorithm (UNCA), which combines a multifaceted strategy with Neutrosophic logic to improve clustering performance. UNCA starts with a full-fledged similarity examination via a λ-cutting matrix that filters meaningful relationships between each two points of data. Then, we initialize centroids for Neutrosophic K-Means clustering, where the membership values are based on their degrees of truth, indeterminacy and falsity. The algorithm then integrates with a dynamic network visualization and MST (Minimum Spanning Tree) so that a visual interpretation of the relationships between the clusters can be clearly represented. UNCA employs Single-Valued Neutrosophic Sets (SVNSs) to refine cluster assignments, and after fuzzifying similarity measures, guarantees a precise clustering result. The final step involves solidifying the clustering results through defuzzification methods, offering definitive cluster assignments. According to the performance evaluation results, UNCA outperforms conventional approaches in several metrics: it achieved a Silhouette Score of 0.89 on the Iris Dataset, a Davies-Bouldin Index of 0.59 on the Wine Dataset, an Adjusted Rand Index (ARI) of 0.76 on the Digits Dataset, and a Normalized Mutual Information (NMI) of 0.80 on the Customer Segmentation Dataset. These results demonstrate how UNCA enhances interpretability and resilience in addition to improving clustering accuracy when contrasted with Fuzzy C-Means (FCM), Neutrosophic C-Means (NCM), as well as Kernel Neutrosophic C-Means (KNCM). This makes UNCA a useful tool for complex data processing tasks.
Read MoreDoi: https://doi.org/10.54216/IJNS.250415
Vol. 25 Issue. 4 PP. 176-192, (2025)
Cold transportation is one among the unquenching needs of people around the globe. Although cost sensitive, refrigerated transportation is preferred globally as it ensures the quality of perishable items in pharmaceutical, food and beverages, chemicals and certain other industries during transportation. However, many refrigerated vehicles fail in offering consistent preservation as most of their cooling units depend on the vehicle’s engine. It is also important to acknowledge that operating a vehicle unceasingly to maintain temperature is impossible in real life. This set up of poor cold logistics and supply chain leads to an increased deterioration of sensitive items. The paper overcomes this complication by adjoining an extra power source that supports freezing during the shutdown time of the vehicle engine by proposing improved mathematical models on Multi-Objective Cold Fuzzy Solid Transportation Problem (MOCFSTP) with an extra time parameter relating to the static and delay condition of the vehicles during various preservation modes (zero, semi, full) and defends them with comparable scrutinizing. The objectives contemplated in the problem are minimizing the cost, time and rate of deterioration. Numerical examples are discussed in detail and solved using reknown methods in LINGO (19.0) to stress on the effectiveness of the models.
Read MoreDoi: https://doi.org/10.54216/IJNS.250416
Vol. 25 Issue. 4 PP. 193-202, (2025)
Decision-making theory serves as an effective framework to guide decision-makers in solving problems. One notable application of this theory is in the medical field, where it aids doctors in analyzing patient data to determine whether a patient is infected. To enhance this theory with more adaptable mathematical methods, we propose an expanded approach based on previously introduced matrixes of Q-neutrosophic soft under an Interval-valued setting (IV-Q-NSM). This represents a new finding of existing mathematical tools to address the two-dimensional uncertainty prevalent in various life domains. This work explores several algebraic properties and matrix operations associated with IV-Q-NSM. Subsequently, we introduce a new methodology for decision-making (DM) in medical diagnosis selection problems. This approach aims to provide a more flexible and comprehensive framework for evaluating complex medical data and improving diagnostic accuracy.
Read MoreDoi: https://doi.org/10.54216/IJNS.250413
Vol. 25 Issue. 4 PP. 156-168, (2025)
A novel technique to produce complicated tangent trigonometric (ζ,∂,e) neutrosophic sets is presented in this study. Complex tangent trigonometric (ζ,∂,e) neutrosophic weighted averaging, geometric, generalized weighted averaging, and generalized weighted geometric will all be discussed in this article. We calculated the weighted average and geometric using an aggregating model. The following algebraic methods will be used to further study several sets having significant properties.
Read MoreDoi: https://doi.org/10.54216/IJNS.250417
Vol. 25 Issue. 4 PP. 203-217, (2025)
Neutrosophy has developed as a generalization to fuzzy logic and is being employed in the research field in many areas such as set theory, logic, and others. Neutrosophic Logic is one of the neonate study regions and its intention is assessed to have the percentage of truth in a subset T, the percentage of falsity in a subset F, and the percentage of indeterminacy in a subset I. Recently, financial fraud has become a highly major issue, which results in severe consequences across firm sectors and affects people’s everyday lives. Therefore, financial fraud recognition is critical for the prevention of the regularly overwhelming effects of financial fraud. It includes differentiating fraudulent financial data from accurate data and permitting decision-makers to progress suitable plans to reduce the effect of fraud. Over the past few years, Artificial intelligence (AI), mainly machine learning (ML) systems, turned out to be the highest thriving model in fraud detection. This study presents a novel Intelligent Decision Support System for Financial Fraud Detection Using Pythagorean Neutrosophic Bonferroni Mean (IDSSFFD-PNBM) model. The main intention of the IDSSFFD-PNBM algorithm is to enrich the detection model for financial fraud using advanced optimization models. Initially, the z-score normalization is applied in the data normalization stage for converting input data into a beneficial format. Besides, the proposed IDSSFFD-PNBM designs a grasshopper optimization algorithm (GOA) for the selection of feature processes to enhance the efficiency and performance of the model. For the detection and classification procedure, the pythagorean neutrosophic bonferroni mean (PNBM) model has been employed. Additionally, the firefly optimization algorithm (FFOA)-based hyperparameter range method has been done to heighten the recognition outcomes of the PNBM system. The experimental evaluation of the IDSSFFD-PNBM technique takes place using a benchmark dataset. The experimental results indicated an enhanced performance of the IDSSFFD-PNBM technique compared to recent approaches
Read MoreDoi: https://doi.org/10.54216/IJNS.250418
Vol. 25 Issue. 4 PP. 218--229, (2025)
This paper investigates the 𝔓𝕞ℵ operator, constructed from the Neutrosophic 𝓆-Poisson distribution series. The study examines this operator within the realm of geometric function theory, focusing on key characteristics such as coefficient bounds, growth and distortion behavior, and the determination of convexity and star likeness radii. Additionally, the paper explores the weighted and arithmetic means of functions associated with this operator and analyzes its closure properties under the Hadamard product.
Read MoreDoi: https://doi.org/10.54216/IJNS.250419
Vol. 25 Issue. 4 PP. 230-239, (2025)
In this paper, we study the applications of block method to find the numerical solutions of some neutrosophic differential problems, where we discuss the approximated n-refined neutrosophic solutions and absolute n-refined neutrosophic errors in two special cases for n=2, and n=3. In addition, we list the numerical tables of our results.
Read MoreDoi: https://doi.org/10.54216/IJNS.250420
Vol. 25 Issue. 4 PP. 240-249, (2025)
Neutrosophic set (NS) is a novel devise to handle uncertainty considering the memberships of truth T, indeterminacy I, and falsity F satisfying. It is employed to illustrate the indefinite data more appropriately and precisely than an intuitionistic fuzzy set. The search for cost information over the supply chain is very significant for controlling costs that aid in enhancing and beginning activities in organizations in the value chain. In today’s intricate supply networks, sharing data among suppliers and buyers is important for sustainable competitive benefit. Particularly, for both business partners, cost information is extremely appropriate in buying conditions. As per experimental analyses in literature, artificial neural networks (ANNs) are probable to have a great latent to expose cost structures by machine learning (ML). This study presents a novel Interpretation of Kernel Regression Neutrosophic Set using Enhanced Coati Optimization for Cost Estimation Model (KRNSECO-CEM). The main goal of the presented KRNSECO-CEM technique is to analyze and interpret the multi-product of Supply Chain Management Systems. At first, the KRNSECO-CEM approach applies Z-score normalization to pre-process the input data. For the regression process, the kernel regression based neutrosophic set (KRNS) model can be used. Eventually, the enhanced coati optimization algorithm (ECOA) has been applied for the fine-tuning of the best hyperparameter of the KRNS model. The experimental evaluation of the KRNSECO-CEM algorithm can be tested on a benchmark dataset. The extensive outcomes highlighted the significant solution of the KRNSECO-CEM approach over other recent approaches
Read MoreDoi: https://doi.org/10.54216/IJNS.250421
Vol. 25 Issue. 4 PP. 250-261, (2025)
Using three machine knowledge models that utilise Neutrosophic Logic (NL)—Linear Regression, Random Forest, and Gradient Increasing—this study studies the possibilities of refining financial result forecast. The cognitive behind this is that NL recovers the prediction power of these models across dissimilar organisations by accounting for the inherent uncertainty, unpredictability, and lack of sureness in financial numbers. In this study, the models' presentation is evaluated using a variety of financial factors, including interest rates and stock prices. F1 score, recall, correctness, and exactness are some of the metrics used by this drive. When likened to other models, NL with Gradient Cumulative consistently outperforms them in terms of correctness and robustness. You might think of Abu Dhabi Islamic Bank and the National Bank of Bahrain as two such examples. Companies like Emirates Islamic Bank reap some benefits from Chance Forest's combination of cheap computation with precision, but only to a lower degree. Complex datasets used by businesses like Al Rajhi Bank are beyond the capabilities of Linear Reversion, even when combined with NL. By proving that cooperative techniques combined with NL positively reduce financial data volatility, our results lay the groundwork for improved financial forecasting and decision-making. The exercise has demonstrated that NL has great potential to enhance financial prediction models, which could have future applications in investment planning and risk organization.
Read MoreDoi: https://doi.org/10.54216/IJNS.250424
Vol. 25 Issue. 4 PP. 282-294, (2025)
Real data modelling of extreme events, such as rainfall, temperature, financial costs is very important in neutrosophic statistical methods. The Cauchy distribution is one of statistical models used for modelling such extreme events in natural processes. In cases of imprecise data which most often involve vague, incomplete and ambiguous information, standard statistical methods cannot fully describe the spectrum of uncertainty. In this study, we have considered a new Cauchy distribution under neutrosophic context to deal with uncertain data. The proposed neutrosophic Cauchy distribution (NCD) may analysis extreme events data involving incomplete observations. We provide basic mathematical characteristics and important statistical functions of the Cauchy model under neutrosophic framework. A complete procedure of random numbers generation using neutrosophic quantile function is discussed. The unknown parameters of the proposed are estimated using the maximum likelihood approach. Numerical results show that the proposed model adequately fits the data involving extreme and imprecise values. The performance and flexibility of the model are also supported by an application to a real data set.
Read MoreDoi: https://doi.org/10.54216/IJNS.250422
Vol. 25 Issue. 4 PP. 262-271, (2025)
The Burr distribution is one of the most important and commonly used probability distribution in statistical analysis. In this study, a new class of univariate distribution based on the Burr random variable is proposed. Characteristics of the proposed neutrosophic Burr distribution (NBD) are discussed. The neutrosophic form of the proposed distribution is particularly advantageous for handling the imprecise and uncertain information commonly present in real-world problems. The statistical properties and the shapes of corresponding probability density and cumulative density functions are illustrated. Some important functions commonly utilized in survival studies are formulated within neutrosophic structures. General expressions for other distributional properties of the proposed NBD are developed under neutrosophic framework. The inverse cumulative method is used to find random numbers from the suggested model. Maximum likelihood method for estimating the model parameters is described, and the performance of estimated parameters are assessed using a Monte Carlo simulation experiment. Finally, the paper demonstrates the practical use of the proposed model through a real-world application of malaria cases per thousand population at risk.
Read MoreDoi: https://doi.org/10.54216/IJNS.250423
Vol. 25 Issue. 4 PP. 272-281, (2025)
The most widely used distribution for risk management data for modeling longevity is the one-parameter inverse exponential distribution. Among alternative models, we suggest the neutrosophic inverse exponential (NIE) model, which generalizes the extended inverse exponential distributions and the classical structure. For the suggested model, we derive explicit formulations for the quantile functions, median, mode, cumulative distribution function, and probability density function. Data generating process of the proposed model under neutrosophic environment is discussed. To estimate the model parameters, we use the maximum likelihood approach. Using the proposed model, we run the simulation setup for randomly generated data. A genuine data set is also used to support the proposed model applicability.
Read MoreDoi: https://doi.org/10.54216/IJNS.250425
Vol. 25 Issue. 4 PP. 295-304, (2025)