International Journal of Neutrosophic Science

This work analyzes the econometric efficiency in the use of finance instruments applied by microfinance institutions, using a Neutrosophic methodological framework; it develops with emphasis in terms of financial performance and social impact for 2018-2023. The study aims to fill important gaps in understanding how alternative financial instruments affect operational efficiency, poverty mitigation and institutional sustainability within a changing regulatory and development context. The mixed-methods was used by combining the N-MCDM and DEA technique with panel data regression analysis techniques. The sample consisted of 89 MFIs (including traditional and alternative-finance-based ones) in all 14 administrative regions. The method used for efficiency estimation was two-stage DEA, GMM was used to estimate the dynamic panel model, and Tobit regression model a set of key explanatory variables for performance. Input data were institutional annual financial reports, operation indicators, borrower information as well as macro-prudential regulatory metrics from central financial authorities. The outcomes indicate that microfinance institutions (MFIs) using alternative finance have higher social efficiency at 0.863 compared with their Conventional counterparts (at 0.741), while they conserve the same financial efficiency (0.694 versus 0.708). Murabaha-type financing models had a 26% better portfolio quality so that portfolio-at-risk percentages were as high as 2.6% compared to conventional frameworks of 3.5%. Musharaka-utilizing systems captured 21% higher likelihoods of loan recovery, whereas Ijarah-based models showed 18% lower odds of default. Moreover, rural outreach efficiency improved by 34% and women’s participation ratio became 81% instead of 64%, in conventional institutions. With marginally lower average ROA (1.97% compared to 2.24%), alternative-finance players revealed a higher level of alignment with priorities on value-creating expansion and impact on society. In conclusion, the results highlight the power of neutrosophic econometric analysis for assessing trade-offs among complex financial and social decisions, providing a strong decision-support system for policymakers and financial regulators aiming to design the optimal balance between profitability, efficiency and social welfare in microfinance schemes.

The research analyses the impact of digitalisation levels on structural transformations in regional economies and the education sector, highlighting their reciprocal relationship in generating sustainable and inclusive growth. This study assesses the multi-dimensional mediation of digitalization with economic performance and learning modernization in education. It also analyzes the efficacy and efficiency of digital policies and institutional strategies as data, as well as offers databased policy recommendations for a more balanced and knowledge based regional development. A full mixed-methodological approach is employed consisting of statistical (correlation and regression between regional digitalization and economic variables) and neutrosophic multi-criteria evaluation of the education system dynamics. Crosscutting comparisons between regions and higher education end-users with various degrees of digital maturity are analysed, enabling to understand more in depth how digital infrastructure and the enactment of policies can contribute to structural transformation as both economy and educational institutions move forward. Under the light of the findings, the paper calls for focused digital and educational policies to strengthen regional and institutional capabilities through increased investment in digital infrastructure, the professional capacities of educators and the integration of digital competences into curricula. The study also offers a strategic approach to align educational digitalization with regional innovation systems, so that the benefits of digital transformation truly and in a balanced way support both economic modernisation and the development of human capital. A strategic framework, based on neutrosophy, is contributed for policymakers, university managers and development planners to formulate sustainable digitally enabled-smart ecosystems building up the link between economic growth and education development.

We develop a neutrosophic framework for the 1-D transient heat equation that treats key thermal parameters as indeterminate rather than fixed or strictly probabilistic. Thermal diffusivity and source strength are represented by neutrosophic intervals; two extreme forward solves yield guaranteed envelopes u_min and u_max , from which we compute a core field u_mean =1/2 (u_min+u_max ), an absolute width W=u_max-u_min, and a relative indeterminacy index I=W/(|u_mean  |+ε). Using an explicit FTCS discretization with stability enforced by α_max , we report decision-oriented diagnostics: spatio-temporal maps of u_mean ,W, and I; band plots along space/time sections; percentile trajectories of I over time; coverage curves quantifying the fraction of space-time with I≤τ; and response surfaces showing sensitivity of u(x^( ^* ),T) to (α,S). Results demonstrate that, even when absolute spreads remain small, localized reliability losses can occur where u_mean  crosses zero, a regime routinely obscured by point-estimate modelling. The framework is transparent (envelopes + core), computationally light (two extreme runs), and compatible with neutrosophic statistics for data-driven interval setting. Beyond thermal diffusion, the method provides a conservative, explainable backbone for transport-driven decisions in materials, interfaces, and infrastructure subject to incomplete or evolving information.

This paper introduces the novel concept of a Neutrosophic Signed Domination Function (NSDF) of graphs, generalizing classical domination by assigning each vertex a triple-valued influences (truth, indeterminacy, falsity) from {−1, 0, 1}. We define the Neutrosophic Signed Domination Number γns(G) as the optimal weighted sum under neighborhood constraints ensuring net positive influence. Fundamental properties and sharp bounds for general graphs are established. Exact values for γns(G) are determined for paths and cycles. This work bridges neutrosophic logic with domination theory, enabling sophisticated modeling of complex networks with uncertainty.

Assessing investor trust is inherently complex, involving multiple interrelated factors and expert opinions that are often uncertain or inconsistent. Traditional Multi-Criteria Decision-Making (MCDM) methods face limitations in addressing such ambiguity, whereas Neutrosophic Sets provide a more robust alternative by separately modeling truth, indeterminacy, and falsity. This study proposes a three-stage Neutrosophic MCDM approach, consisting of NS-Delphi to consolidate expert input, NS-DEMATEL to analyze causal relationships, and NS-COCOSO to rank trust-related criteria, aimed at evaluating the determinants of investor trust in Vietnam’s supply chain finance (SCF) ecosystem. A case study demonstrates how this integrated model effectively captures expert hesitancy and causal interdependence. The findings highlight transparency, regulatory reliability, technological adoption, and ethical conduct as the most influential drivers of trust. Building on these insights, the study recommends several practical and policy-oriented strategies to enhance investor confidence: advancing digital transparency through blockchain and traceability systems, establishing legal safeguards to prevent financial fraud and protect investors, and promoting diversification in logistics investments to attract long-term capital and mitigate systemic risks. These implications provide a structured roadmap for policymakers, financial institutions, and SCF stakeholders seeking to foster a resilient and investor-friendly supply chain finance environment in Vietnam.

This research introduces a novel approach to the non-polynomial spline dependent method for solving fuzzy partial differential equations. The tensor product of non-polynomial spline functions is derived in order to obtaining a solution to fuzzy partial differential equations, such as fuzzy hyperbolic and parabolic equations. The advantage of this method is that it simplifies the complex procedure that arises from the term of the typical product of a fuzzy number by fuzzy functions. Examples are presented to show that the outcomes of the research indicate that the technique is extremely useful to construct the solution to the desired fuzzy partial differential equations.

This paper tackles the difficulty of accurately modeling uncertainty in complicated DM settings, where conventional FS models frequently fail. The IVFS theory, a broadening FS theory, is a potent tool that can offer the potential to approach uncertain data in vague environment in order to get over these restrictions. This paper presents an application of IVFS in a DM challenges, where on CV and WCV of an IVFS are used to select a qualified applicant for the HR manager position. Additionally, sensitivity analysis has demonstrated the stability of the final decision.

Classical statistical methods assume that data are precise and free from uncertainty, which may not hold in many real-world applications. Neutrosophic statistics provides a flexible framework for handling indeterminacy, vagueness, and inconsistency in data. In this paper, we propose a new formulation of one-way analysis of variance (ANOVA) within the neutrosophic framework. The method treats membership, indeterminacy, and non-membership components separately, with explicit F -tests for each, and employs a maximum-based decision rule to determine significance. We also compare the proposed method with the classical one-way ANOVA. The results demonstrate that the neutrosophic ANOVA is more sensitive in detecting group differences, particularly in cases where the classical approach yields smaller F -values and may fail to reject the null hypothesis. These findings highlight the potential of neutrosophic ANOVA as a more robust alternative to classical ANOVA for analyzing data with inherent uncertainty and indeterminacy.

This paper introduces the class Mε,4L, defined through a convex combination of starlike and convex functions associated with a four-cusped epicycloid domain, where the parameter satisfies 0 ≤ ε ≤ 1. Unlike earlier studies that focused on circular or conic domains, this work extends the geometric framework to epicycloidal domains. Within this framework, sharp estimates for the first coefficients are obtained, together with the Fekete-Szeg¨o inequality and the second Hankel determinant evaluations. These findings extend several classical results for starlike and convex functions and offer new perspectives on analytic function theory related to epicycloidal domains.

Artificial neural networks have become a cornerstone of modern artificial intelligence, powering progress in a wide range of fields. Their effective training heavily depends on techniques from unconstrained optimization, with iterative methods based on gradients being especially common. This study presents a new variant of the conjugate gradient method tailored specifically for unconstrained optimization tasks. The method is carefully designed to meet the sufficient descent condition and ensures global convergence. Comprehensive numerical testing highlights its advantages over traditional conjugate gradient techniques, showing improved performance in terms of iteration counts, function evaluations, and overall computational time across a variety of problem sizes. Additionally, this new approach has been successfully used to improve neural network training. Experimental results show faster convergence and better accuracy, with fewer training iterations and reduced mean squared error compared to standard methods. Overall, this work offers a meaningful contribution to optimization strategies in neural network training, displaying the method is potential to tackle the complex optimization problems often encountered in machine learning.

In this work, we introduce the notion of best proximity point for a non-self map defined in a neutrosophic complete metric space. Moreover, we define the class of neutrosophic proximal contraction of first kind and second kind, and we prove theorems which ensures existence and uniqueness of best proximity point for such mappings in neutrosophic complete metric spaces. Additionally, a technique to identify an optimal approximation solution intended as a best proximity point is demonstrated.

As a generality of fuzzy sets (FS) and intuitionistic FS (IFS), neutrosophic sets (NS) was progressed by F. Smarandache for signifying incomplete, inaccurate, and uneven data present in the real world. Neutrosophic Logic (NL) is a neonate research field in which every proposition was projected to have the proportion of truth in a sub-set T, I, and F. Neutrosophic sets (NS) have been well employed for indeterminate information handling, and determine benefits to tackle indeterminate data. A NS is categorized by indeterminacy-, truth-, and a falsity- membership functions. Atanassov as a major simplification of FS presented the notion of IFS. IFS are very beneficial in conditions when problem description by linguistic variables, assumed with only a membership function, appears to be difficult. In recent times, IFS have been employed to numerous areas like medical diagnosis, logic programming, decision-making issues, etc. An interval NS (INS) is an example of NS, which is employed in real engineering and scientific applications. Owing to the competition in the banking industry and the importance, access to customer information is vital to establish a successful relationship that benefits both parties. Representing longer-term customer relationships and building brand equity are essential in modern banking, and therefore increasing relationship quality plays a significant part in the development of new services and customer lifetime value (CLV) approximation.  CLV is an estimated profit that can be achieved by the organization from a customer for some time. Presently, the development of Machine Learning (ML) methods has resulted in better precision and effectiveness. Therefore, by utilizing ML methods of real-time customer data, predictions of a more precise future value of the customer are gained by businesses, which helps in establishing a more personal marketing approach. In this manuscript, we propose a Customer Lifetime Value Estimation using Interval-Valued Neutrosophic Set and Parameter Optimization Algorithms (CLVE-IVNSPOA). The foremost main of this paper is to progress a predictive analytics model for estimating customer lifetime value in digital banking utilizing advanced optimization methods. Initially, the data pre-processing phase was employed by using the Z-score method. Moreover, the pelican optimization algorithm (POA) is mainly executed by the feature subset selection in order to select the most optimal features from a dataset. For CLV prediction, the Interval-Valued Neutrosophic Set (IVNS) technique is exploited. At last, the model parameter adjustment process is performed through improved shark optimization (ISHO) algorithm for improving the prediction performance. The experimental evaluation of the CLVE-IVNSPOA occurs using benchmark database. The experimental outcomes indicated out an improved performance of CLVE-IVNSPOA compared to existing systems.

A vast amount of Internet of Things (IoT) devices deployment has created huge issues about trust management and reliability guarantees in heterogeneous, dynamic and often uncertain ecosystems. Available probabilistic or fuzzy-logic-based models do not hold water to deal with indeterminacy and contending data in distributed IoT networks. The current paper proposes a brand new framework to model trust and reliability in IoT systems by implementing Neutrosophic Logic to build quantification and strengthen trust and reliability in IoT systems. Incorporating the semantic understanding of data and node behavior in uncertainty using three dissimilar elements to represent trust: truth, indeterminacy and falsity, the model commands a wider range of semantics in the relationship of data and nodes during the phase of uncertainty. A mathematical solution is established to measure trust scores and reliability indexes based on Neutrosophic membership functions. Further, a new dynamic trust assessment and anomaly detection algorithm is presented based on a multi-layered decision-making process. This simulation and case- study definition shows the effectiveness of the proposed framework in having less false positives, better reliability estimation, and the solid optimization of decision support in a very uncertain environment of IoT. The work therefore further develops the process of Neutrosophic systems integration with IoT and its setting up of basis of more intelligent, context-aware and robust trust management systems.

A mathematical model consists of decision variables, a goal function, and constraints. The region of possible solutions for a nonlinear mathematical model is the set of vectors whose components satisfy all constraints. The optimal solution is the vector whose components satisfy all constraints, and at which the function reaches an optimal value (maximum or minimum). Nonlinear programming constitutes an important and fundamental part of operations research and is more comprehensive than linear programming. Its applications have spread across all branches of science, including engineering, physics, chemistry, management, economics, and military fields, among others. Nonlinear programming can also be used in forecasting, estimation, applied statistics, and determining the costs resulting from the production, purchase, and storage of goods. Given this importance, and in order to obtain a more accurate solution that takes into account all the changes that the system under study may be exposed to, we have previously presented a neutrosophic study of nonlinear models and some of the methods used to find the optimal solution. In addition to what we have previously done, in a research we present an improvement to the gradient projection method used to find the optimal solution for nonlinear models constrained by equal constraints, enabling us to obtain the optimal solution in fewer steps. We will then apply it to find the solution. Optimization of nonlinear neutrosophic models.

The fuzzy reliability estimate for the Benktander distribution, a model appropriate for heavy-tailed data, is investigated in this work. By adding membership functions and α-cuts, we extend the Benktander distribution to a fuzzy framework and compute its probability density function and reliability function. The fuzzy reliability is estimated using two methods: maximum likelihood and Bayesian approaches. The Bayesian method uses special loss functions, gamma priors, and squared error. The effectiveness of these estimators is examined in a simulated study using varying sample sizes and parameter values. The findings show that, especially for smaller samples, Bayesian techniques—in particular, the cautious Bayes estimator—perform better in terms of accuracy and stability than maximum likelihood estimation. The results emphasize how crucial it is to choose suitable prior distributions and loss functions while doing reliability analysis.