International Journal of Neutrosophic Science

Set-based theories have become key tools to address uncertainty and imprecision in complex systems. Fuzzy sets model gradual membership, soft sets add flexibility through parameterization, and neutrosophic sets generalize both by incorporating truth, indeterminacy, and falsity degrees. In this manuscript, a fuzzy-soft expert system is described to determine the efficiency of different fertilizations in lettuce (Lactuca sativa L.) crops considering agronomic variables such as fresh weight (FW), number of leaves (NL), and crown diameter (CD). The model, based on fuzzy membership functions and soft set operations, effectively manages the un- certainty inherent in agricultural data and provides a novel decision-support tool. Although this work focuses on fuzzy and soft sets, its extension to the neutrosophic framework could further enrich the analysis by ex- plicitly modeling indeterminacy and inconsistency, offering a more comprehensive approach to agricultural decision-making.

This study introduces the innovative idea of associating a possibility measure with the membership of an element in a set, and further proposes the structure of quadripartitioned neutrosophic cubic sets (PQNCS). Within this framework, the authors define four distinct components—truth, contradiction, ignorance, and falsity—each in two modes: internal and external. They explore the corresponding sets (truth-internal, contradiction-internal, ignorance-internal, falsity-internal and truth-external, contradiction-external, ignorance-external, falsity-external) and uncover their interrelated properties. Moreover, the work emphasizes the role of a score function as a central instrument for multi-attribute decision-making, and examines how measures of PQNCS—through score, accuracy and certainty functions grounded in the possibility concept—can be employed to support and guide decision-making in the quadripartitioned neutrosophic cubic setting.

This paper introduces and systematically studies new classes of mappings and set-theoretic structures in the context of neutrosophic soft topological structures. In particular, this study introduces and examines neutrosophic soft semi closed and semi open sets, generalized semi-mappings, and semi-continuous generalized mappings, highlighting their interrelationships and key topological properties The neutrosophic soft generalized semi-closure and semi-interior operators are also formulated, and their principal algebraic and topological characteristics are derived. These developments generalize and unify several existing notions in classical, fuzzy, and neutrosophic soft topologies. Unlike previous studies, this work provides a comprehensive mapping-based approach that clarifies how generalized semi-properties behave under neutrosophic soft transformations. The findings not only extend the theoretical foundations of NST but also open potential directions for modeling and analyzing uncertainty in advanced topological systems.

This paper presents the Fractional Maxwell-Weibull Copula (FMWC) distribution to deal with the heavy tails, extended memory, and nonlinear dependence of price returns of Bitcoins, as the existing financial models face limitations in this aspect. The FMWC provides a flexible model that allows incorporating fractional Weibull distributions to capture persistent autocorrelation, Maxwell components to model significant price changes, and a Student-t copula to capture multivariate dependencies to discuss the volatile returns of Bitcoin. The FMWC was applied to historical Bitcoin data between January 2020 and May 2025 and showed better results than other models, such as Weibull, GARCH-t, and Maxwell-Log Logistic, with an MAE of 0.034374, RMSE of 0.0335, and log-likelihood of 4200.0. Its risk measures (VaR 95% = -0.07983, CVaR 95% = -0.10882) improve tail risk estimation, which is important in risk measurement and portfolio management. Robustness tests also validate its performance over periods and proper handling of outliers. Nevertheless, the FMWC is an excellent tool, despite its computational complexity issues, and can be used by investors, traders, and regulators. Further studies on the computational efficiencies and applications to other cryptocurrencies are required to increase their application in dynamic financial markets.

This work presents a neutrosophic stance detection model to bridge computational assessment and logic of indeterminacy in artificially intelligent (AI)-mediated learning and its outcomes. Utilizing the BART-large-MNLI model, a causal assessment was made of five hypotheses stemming from AI-supported learning between teacher-student relationships. These stances were then transformed into refined neutrosophic values (truth (T), partial support (P_S), indeterminacy (I), partial opposition (P_O) and falsity (F)). Ultimately, findings suggest that partial support is the most prevalent stance applied to any of the hypotheses, revealing that AI is, largely, a boon to education. However, this valence is tempered by indeterminacy among axes as well as stance magnitude. The largest partial support in rank order came from personalized education and access to AI tutors, while the most importance was given to opposition of relying on AI as support and replacement AI learning. Such findings confirm neutrosophic stance analysis and causal graph modeling as increasingly successful for applying measurable patterns to epistemically ambiguous fields. The neutrosophic causal graph integrates the above findings with a visualization of proposed dynamics between each vertex based on both quantitative patterns and epistemic uncertainty trends. The current research holds implications for educational theory, policy and instructional design integrity in 21st century learning. Uncertainty became a tangible concept; instead of devaluing AI in the classroom, it must be present as an enhancing supplemental tool, never replacement, for ethical considerations and equitable access. The potential for neutrosophic to transform apparent truths that are at times contradictory is confirmed through the human-machine interactive learning process, with subsequent suggestions for future research into AI-mediated education's causal relationships and decision-making potential.

In an increasingly multicultural world, workforces become more diverse, and the challenge of internal communications exacerbates. What one group deems clear communication can easily be reinterpreted, countered or found invalid by another group valuing different cultural mores, norms, and expectations. As these issues grow, not only does organizational coherence suffer, but also strategic impact potential fails as globalized realities emerge. There becomes a need for a model that successfully implements the nuance and indeterminacy of such communicative interactions. While models of intercultural communications exist, they often operate on a binary method of understanding that fails to acknowledge the simultaneous presence of varying levels of truth, indeterminacy, and untruths. This is where neutrosophic plitogenic logic intervenes as the advanced form through which these properties can be modeled to suggest cognitive/emotional/symbolic determination as a single potentialized system of assessment. Thus, the challenge emerges to neutralize indeterminacy by fluidly responding to the communicative elements relative to what is present at any given moment over time. Neutrosophic Plitogenic Logic emerges as a viable interdisciplinary approach to understanding internal communication by theoretical and practical means - using epistemology through organizational studies fields and management feasibility - as it successfully presents the shifting and multivalent form of such a communicative process within increasingly multicultural dynamics when existing reconciled methods fail. This contribution is theoretical - as it creates a tool for fields of study to manage structural ambiguity - and practical - for management purposes - as it fosters a model for inclusion in resilient, contextually viable messaging design.

This paper responds to the problem of establishing criteria priority for microcredential implementation in Latin American universities, a developing topic with great momentum and the need to professionalize traditional learning models. Amid rapid digital and labor developments, microcredentials emerge as an efficient way of certifying targeted skills and fostering adaptability to market demand. Still, implementation in higher education lacks a clear pathway of systematic substantiation. The state-of-the-art demonstrates that few mixed-method studies have attempted to prioritize institutional, pedagogical, and technological aspects of this endeavor. This paper applies the Analytic Hierarchy Process (AHP) to a criterion for criteria relative assessment as a method for qualitative and quantitative study. This approach assesses relative importance between seemingly equal criteria—digital infrastructure, teacher training, curriculum relevance, and external validity, for example—for better implementation within higher education systems. Results assess teacher training and platform interoperability as the two most important criteria for successful microcredential implementation. This study is relevant theoretically for multicriteria approaches to the assessment of learning flexibility and practically speaking, supports university administrative decisions for more adaptable, equity-driven and sustainable learning options.

The goal of the study is to provide the context, substantiation and formation of a strategic model for development of an innovative educational environment in higher education based on application network interaction principles. The study adopts a holistic systems theoretical approach that integrates systemic, institutional and network theories within a neutrosophy based decision-making model to deal with uncertainties and indeterminacy involved in innovation management at HEI level. The study is based on data collected from different universities and institutions with different profiles in terms of innovation potential. The results lead to a strategic model of networked scientific and innovative activity, including mechanisms for knowledge exchange, technology transfer, and collaborating with industry and government. The model together enabling universities’ effectiveness in producing, disseminating and applying new knowledge proposes three levels of interacting channels. This study is new in merging neutrosophic logic with network interaction theory to develop a flexible decision-making model for strategic development of higher education sector. The paper offers policy consolidators, university heads and academic consultants with practical tips aimed at improving innovation-management as well as educational quality, deepening the synergies between education-sciences-business worlds at Universities.

This study aims to apply Neutrosophic Theory in analyzing monolingual and bilingual lexical entries as an approach capable of accurately representing semantic ambiguity, phonological values, and developmental values. This is because lexical meaning is a vital component of the semantic system, responsible for conveying and clarifying meaning. However, despite its importance, it is insufficient for fully conveying meaning. Lexical entries lack crucial values, especially the recognition of probable meanings. The network of semantic relationships in any dictionary addresses meaning in a binary way. In a language that relies heavily on metaphor or derivation, like Arabic, dictionaries tailored to the Arabic language fail to provide probable meanings for words such as (eye - heart - hand), whose contextual and metaphorical meanings sometimes do not align with the body-part indication but include other potential meanings. This study is based on the hypothesis that the linguistic dictionary in general and Arabic in particular, still require an approach that allows observing the meanings across three dimensions: truth (T), indeterminacy (I), and falsehood or negation (F). By integrating phonological, semantic, and evolutionary analysis within a neutrosophical framework, a more comprehensive lexical model can be developed that captures the interaction between language, usage, context, and history. This research adopted a mixed descriptive–analytical method, combining qualitative linguistic analysis with quantitative Neutrosophic modeling.

Transportation optimization remains a critical challenge in international businesses, particularly given the inherent uncertainties of supply chain networks. This paper proposes a novel machine learning-based model for solving multi-objective, multi-item solid transportation problems that fundamentally advances beyond existing fuzzy and neutrosophic approaches. Our key innovation lies in the synergistic integration of neutrosophic Z-numbers (NZNs) with adaptive machine learning techniques, creating a framework that simultaneously captures value vagueness, information reliability, and dynamic uncertainty patterns capabilities absent in conventional fuzzy transportation models. Unlike traditional fuzzy methods that treat all uncertainty uniformly, our NZN representation provides a three-dimensional structure incorporating truth, indeterminacy, and falsity measures, each with associated reliability metrics. This enriched uncertainty modeling enables three ground breaking advancements over existing approaches: (1) a neural scoring system that autonomously learns optimal NZN comparison functions from historical decision patterns, overcoming the limitations of static aggregation operators in fuzzy systems; (2) LSTM networks that jointly forecast demand values and their reliability evolution under uncertainty; and (3) reinforcement learning optimizers that dynamically balance economic efficiency with information quality in routing decisions. Computational experiments demonstrate superior performance compared to six established baseline methods, including traditional fuzzy, intuitionistic fuzzy, neutrosophic, and pure machine learning approaches. Our hybrid framework achieves a 23.4% reduction in transportation costs and 35.4% improvement in uncertainty handling compared to conventional fuzzy transportation models, with statistically significant improvements (p < 0.001) across all evaluation metrics. By coupling the theoretical rigor of neutrosophic mathematics with the adaptive power of machine learning, this study provides businesses with a transformative decision-support system for transportation planning under real-world uncertainty conditions.

In this paper, we introduce and investigate new generalized subclasses of neutrosophic n-fold symmetric bi-univalent functions defined in the open unit disk U . These subclasses are characterized via four neutrosophic multi-parameters κ, ρ, γ, and β, which provide a flexible framework to capture the truth, indeterminacy, and falsity components inherent in geometric and analytic behaviors. Within this neutrosophic setting, we derive upper bounds for the initial coefficients |dn+1| and |d2n+1|, and establish generalized Fekete–Szeg˝o inequalities for the considered classes. The results obtained extend and unify several existing results in classical and neutrosophic bi-univalent function theory. Examples and corollaries are presented to demonstrate the sharpness and applicability of the results.

Many of the problems that we face in our lives and daily work are how to directly and accurately select candidates or categories from multiple sets of candidates (categories). The ranking and selection approach is a modern and direct method for selecting categories easily, which is associated with a probability of correct selection. In this paper, we employ the neutrosophic Bayes procedure for decision to select multinomial population. Select a mid-range category for multiple categories and employ neutrosophic logic to define a modern Bayesian procedure that incorporates parameters with some indeterminacy and has a prior distribution, which we call the neutrosophic prior distribution.

The sophisticated statistical methods known as Bayesian EWMA and DEWMA control charts are intended to track process performance and identify changes in data over time. They improve the capacity to monitor minute changes in the process by combining conventional smoothing methods with Bayesian inference. By integrating the idea of neutrosophic approaches into Bayesian EWMA and DEWMA models, the suggested approach seeks to address and get beyond this restriction. In this study, neutrosophic approaches are utilized to provide the manufacturing process with two tolerance limits instead of a set value for upper and lower control limits, particularly when all observations are uncertain, imprecise, or fuzzy. By combining the Exponential, Inverse Rayleigh, and Weibull distributions, five symmetric loss functions are examined while taking uniform prior into account. Additionally, for mean, variance, and control limits of the proposed work have been derived. Simulation studies were conducted and compared with previous work as well as all projected works. This study significantly advances the subject of control chart technique, especially when it comes to managing hard, vast, and complicated information.

The primary goal of the article is to examine the data s shape and crack higher-order graph structures in cell complex topology. Further simplical complex-based kernel estimation methods are explored and discussed.

The concentration of linear operators is unpretentious to prove in measurable space   but there is few works in weighted space, here we will include characteristics of approximate of unrestrained functions in measured space by lined operators via direct and converse approximation theorems. In addition, the relationship between modulus of softness and K- functional where, we proven are together tools equivalence.