Search Results (442)

This thesis pioneers the development of q-Rung Neutrosophic Fuzzy Rough Sets (q-RNFRSs), establishing the first theoretical framework that integrates q-Rung Neutrosophic Sets with rough approximations to break through the conventional ${\mu }^q+{\eta }^q+{\nu }^q\le 1$ constraint of existing fuzzy–rough hybrids, achieving unprecedented capability in extreme uncertainty representation through our generalized model (${\mathcal{T}}^q+{\mathcal{I}}^q+{\mathcal{F}}^q\le 3$). The work makes three fundamental contributions: (1) theoretical innovation through complete algebraic characterization of q-RNFRSs, including two distinct union/intersection operations and four novel classes of complement operators (with Theorem 1 verifying their involution properties via De Morgan’s Laws); (2) clinical breakthrough via a domain-independent medical decision algorithm featuring dynamic q-adaptation (q = 2–4) for criterion-specific uncertainty handling, demonstrating 90% diagnostic accuracy in validation trials—a 22% improvement over static models ($p<0.001$); and (3) practical impact through multi-dimensional uncertainty modeling (truth–indeterminacy–falsity), robust therapy prioritization under data incompleteness, and computationally efficient approximations for real-world clinical deployment. Full article

In engineering and decision sciences, trapezoidal-valued neutrosophic fuzzy numbers $(TzVNFNs)$ have become effective tools for managing imprecision and uncertainty in multi-attribute group decision-making (MAGDM) problems. This work introduces accumulation operators based on the Dombi t-norm $(D{T}_n)$ and Dombi t-conorm $(D{T}_{cn})$ specifically designed for $TzVNFNs$. These operators enhance the flexibility, consistency, and fairness of the aggregation process. To demonstrate their practical applicability, we propose three novel geometric aggregation operator’s namely, the trapezoidal-valued neutrosophic fuzzy Dombi weighted geometric ($TzVNFDWG$), the trapezoidal-valued neutrosophic fuzzy Dombi ordered weighted geometric ($TzVNFDOWG$), and the trapezoidal-valued neutrosophic fuzzy Dombi hybrid Geometric ($TzVNFDHG$) operators. These are incorporated into a systematic MAGDM framework to support the selection of optimal locations for charging stations. Comparative analysis with current decision-making methodologies highlights the efficacy and benefits of the suggested method. The suggested method provides a flexible and mathematically based choice framework designed for uncertain condition. Full article

Graph theory models relationships by representing entities as vertices and their interactionsas edges. To handle directionality and multiple head–tail assignments, various extensions—directed, bidirected, and multidirected graphs—have been introduced, with the multidirected graph unifying the first two. In this work, we further enrich this landscape by proposing the Multidirected hypergraph, which merges the flexibility of hypergraphs and superhypergraphs to describe higher-order and hierarchical connections. Building on this, we introduce five uncertainty-aware Multidirected frameworks—fuzzy, neutrosophic, plithogenic, rough, and soft multidirected graphs—by embedding classical uncertainty models into the Multidirected setting. We outline their formal definitions, examine key structural properties, and illustrate each with examples, thereby laying groundwork for future advances in uncertain graph analysis and decision-making. Full article

Instead of measuring the distance between two points with a positive real number, determining the degree to which the distance between these two points is close, not close, or uncertain allows for more detailed measurement. Recently, researchers have overcome this grading problem by using probability distribution functions, along with fuzzy, intuitionistic fuzzy, and neutrosophic sets. This study pioneers neutrosophic quadruple metric spaces as a powerful new tool for quantifying distances under complex, multi-dimensional uncertainty. It provides a comprehensive mathematical structure, including topology, convergence theory, and completeness, and handles both symmetric and asymmetric cases, generalising previous neutrosophic metric results. For this purpose, neutrosophic quadruple metric spaces were derived from neutrosophic metric spaces in order to better model situations involving uncertainty. Also, we generalised the findings obtained with the neutrosophic metric to the quadruple neutrosophic metric. Full article

Past experiences and memory significantly contribute to self-learning and improved decision-making. These can assist decision-makers in refining their strategies for better outcomes. Fractional calculus is a tool that captures a system’s memory or past experience through its repeating patterns. In the realm of uncertainty, neutrosophic set theory demonstrates greater suitability, as it independently assesses membership, non-membership, and indeterminacy. In this article, we aim to extend the theory further by introducing fractional calculus for neutrosophic-valued functions. The proposed method is applied to an economic lot-sizing problem. Numerical simulations of the lot-sizing model suggest that strong memory employment with a memory index of 0.1 can lead to an increase in average profit in memory-independent phenomena with a memory index of 1 by approximately 44% to 49%. Additionally, the neutrosophic environment yields superior profitability results compared to both precise and imprecise settings. The synergy of fractional-order dynamics and neutrosophic uncertainty modeling paves the way for enhanced decision-making in complex, ambiguous environments. Full article

A neutrosophic set is an important tool for handling vagueness and impreciseness in real-world problems, and distance measures are also exhibited in neutrosophic set theory. The (m,a,n)-fuzzy neutrosophic set is more flexible and efficient than the existing extensions of neutrosophic sets when discussing the distance between multiple objects. This paper invents ten distance measures for comparing (m,a,n)-fuzzy neutrosophic sets. Moreover, the created distance measures are applied in pattern classifications and multi-criteria decisions. Additionally, numerical examples demonstrate these distance measures in practical and scientific applications involving classifying materials and investment problems. The comparative analysis, along with graphical interpretations, further illustrates the effectiveness and superiority of the proposed measures. Full article

This study addresses the challenge of effectively modeling uncertainty and hesitation in complex decision-making environments, where traditional fuzzy and vague set models often fall short. To overcome these limitations, we propose the Fermatean neutrosophic vague soft set (FNVSS), an advanced extension that integrates the concepts of neutrosophic sets with Fermatean membership functions into the framework of vague sets. The FNVSS model enhances the representation of truth, indeterminacy, and falsity degrees, providing greater flexibility and resilience in capturing ambiguous and imprecise information. We systematically develop new operations for the FNVSS, including union, intersection, complementation, the Fermatean neutrosophic vague normalized weighted average (FNVNWA) operator, the generalized Fermatean neutrosophic vague normalized weighted average (GFNVNWA) operator, and an adapted Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. To demonstrate the practicality of the proposed methodology, we apply it to a solar panel selection problem, where managing uncertainty is crucial. Comparative results indicate that the FNVSS significantly outperforms traditional fuzzy and vague set approaches, leading to more reliable and accurate decision outcomes. This work contributes to the advancement of predictive decision-making systems, particularly in fields requiring high precision, adaptability, and robust uncertainty modeling. Full article

Humanity faces significant challenges in achieving internationally agreed sustainable development goals, particularly in reducing public health risks and improving the environmental quality. Measuring and comparing performance across regions requires a systematic and transparent framework. This study explores the application of sustainable development indicators, including a mortality rate attributed to exposure to unsafe WASH services (SDG 3.9.2), a mortality rate attributed to household and ambient air pollution (SDG 3.9.1), and a mortality rate attributed to unintentional poisoning to assess regional health outcomes. Using data from 50 countries across five sub-regions of Asia, this research applies a weighted neutrosophic similarity measure based on the Hausdorff metric to evaluate regional alignment with an ideal benchmark. The results reveal significant disparities across regions, highlighting Central Asia as the closest to the benchmark, while South and West Asia exhibit substantial gaps. These findings provide actionable insights for policymakers to improve public health infrastructure and address environmental challenges, promoting equitable and sustainable development. Full article

This paper introduces two concepts, subcompatibility and subsequential continuity, which are, respectively, weaker than the existing concepts of occasionally weak compatibility and reciprocal continuity. These concepts are studied within the framework of neutrosophic metric spaces. Using these ideas, a common fixed point theorem is developed for a system involving four maps. Furthermore, the results are applied to solve the Volterra integral equation, demonstrating the practical use of these findings in neutrosophic metric spaces. Full article

In this study, we introduced non-Newtonian neutrosophic numbers and non-Newtonian neutrosophic complex numbers by combining two recently popular approaches and examined some of their properties. Furthermore, we presented the non-Newtonian neutrosophic triangle inequality and some properties of the non-Newtonian neutrosophic norm, which can be frequently used in analysis and geometry. Thus, compared to existing studies, we provided a broader perspective for fields such as artificial intelligence, quantum mechanics, medicine, analysis, and geometry. Full article

Contemporary ports are facing a variety of challenges due to technological advancements, economic pressures, and changing policies. Key issues include the effects of globalization, rapid advancements in information and communication technologies (ICTs), and the changing nature of port services. In order to tackle these challenges and achieve operational excellence, adapt to the shifting of activities, and meet new business demands, smart ports have been proposed as a comprehensive solution. These challenges arise because port success is often measured by traditional metrics such as port size and performance. To accurately assess the intelligence of a port, there is a need for a systematic and scientifically sound smart port evaluation method. This paper provides an overview of the concept of a smart port and develops a multi-criteria assessment framework of port smartness based on neutrosophic cognitive maps (NCMs). The unique and valuable characteristic of NCMs lies in their ability to manage the uncertainty associated with the relationship between two concepts, indicating their effects on each other in neutral states. This structure enables the NCM to provide results with a greater degree of sensitivity than fuzzy cognitive maps (FCMs) and allows for a greater degree of freedom of intuition for an expert to express not only the potential impacts but also the uncertainty associated with those impacts. Our methodology can make decisions using incomplete, uncertain, and inconsistent data during the assessment process, providing a rigorous quantitative framework for the assessment of port “smartness”. The proposed solution has the potential to act as a valuable tool in a group decision support environment and can be used to accelerate an organization’s development, improve productivity, and reinforce efforts to achieve strategic and sustainability objectives. To achieve this, an appropriate framework for such a methodology is demonstrated through an illustrative example offering actionable insights for improving port operations. Full article

Fuzzy topology has long been celebrated for its ability to address real-world challenges in areas such as information systems and decision making. However, with ongoing technological advancements and the increasing complexity of practical requirements, the focus has gradually shifted toward neutrosophic topology, a broader and more inclusive framework than fuzzy topology. While neutrosophic topology is primarily rooted in neutrosophic open sets, other related families, including neutrosophic pre-open sets, neutrosophic semi-open sets, and neutrosophic beta-open sets, have also proven instrumental in driving progress in this field. This study introduces neutrosophic $\delta$-open sets as a significant enhancement to the current theoretical framework. In addition, we propose a novel category of separation axioms, termed neutrosophic $\delta$-separation axioms, which are derived from the concept of neutrosophic $\delta$-open sets. Moreover, we explore the interplay between these separation properties and their characteristics within subspaces. Our findings confirm that neutrosophic $\delta$-separation axioms are reliably upheld in neutrosophic regular open subspaces. Full article

In this manuscript, we present the classical Hutchinson–Barnsley theory on the product neutrosophic fractal spaces by utilizing an iterated function system, which is enclosed by neutrosophic Edelstein contractions and a finite number of neutrosophic b-contractions. Further, we provide a sequence of sets that, under appropriate conditions and in terms of the Hausdorff neutrosophic metric, converge to the attractor set of specific neutrosophic iterated function systems. Furthermore, we present a fuzzy variant of α-dense curves that can accurately approximate the attractor set of certain iterated function systems with barely noticeable and controlled errors. In the end, we make a connection between the above-discussed concepts of neutrosophic theory and α-density theory. Full article

: In this study, we introduce a novel class of generalized neutrosophic open sets, referred to as neutrosophic strongly preopen sets. Building on this foundation, we propose a new type of continuity and several new types of mappings. These concepts aim to inspire future research in the scientific community and are rooted in this newly defined class. Additionally, we explore the properties and characteristics of these concepts within neutrosophic spaces. Furthermore, this study investigates the connections between the newly introduced types of mappings and those defined in earlier research, thereby establishing relationships that can serve as a foundation for further scientific exploration. Full article

Uncertainty-aware soft sensors in sign language recognition (SLR) integrate methods to quantify and manage the uncertainty in their predictions. This is particularly crucial in SLR due to the variability in sign language gestures and differences in individual signing styles. Managing uncertainty allows the system to handle variations in signing styles, lighting conditions, and occlusions more effectively. While current techniques for handling uncertainty in SLR systems offer significant benefits in terms of improved accuracy and robustness, they also come with notable disadvantages. High computational complexity, data dependency, scalability issues, sensor and environmental limitations, and real-time constraints all pose significant hurdles. The aim of the work is to develop and evaluate a Type-2 Neutrosophic Hidden Markov Model (HMM) for SLR that leverages the advanced uncertainty handling capabilities of Type-2 neutrosophic sets. In the suggested soft sensor model, the Foot of Uncertainty (FOU) allows Type-2 Neutrosophic HMMs to represent uncertainty as intervals, capturing the range of possible values for truth, falsity, and indeterminacy. This is especially useful in SLR, where gestures can be ambiguous or imprecise. This enhances the model’s ability to manage complex uncertainties in sign language gestures and mitigate issues related to model drift. The FOU provides a measure of confidence for each recognition result by indicating the range of uncertainty. By effectively addressing uncertainty and enhancing subject independence, the model can be integrated into real-life applications, improving interactions, learning, and accessibility for the hearing-impaired. Examples such as assistive devices, educational tools, and customer service automation highlight its transformative potential. The experimental evaluation demonstrates the superiority of the Type-2 Neutrosophic HMM over the Type-1 Neutrosophic HMM in terms of accuracy for SLR. Specifically, the Type-2 Neutrosophic HMM consistently outperforms its Type-1 counterpart across various test scenarios, achieving an average accuracy improvement of 10%. Full article