Search Results (297)

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

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

The exponential growth in global student mobility has resulted in a corresponding increase in demand for international student fairs. Education fairs serve as pivotal platforms for the acquisition of information and the formulation of decisions pertaining to academic pursuits, with a considerable number of students ultimately enrolling in undergraduate, graduate, and language programs abroad. By reaching a large number of students at international education fairs, students from underdeveloped or developing countries benefit from educational opportunities in developed countries, providing significant contributions to social sustainability and socio-economic opportunities. The success of these events is reliant upon the selection of an appropriate location, which necessitates a multifaceted process that considers a range of factors and potential risks. This initial study on the location selection of international education fairs addresses the existing literature gap by employing the interval-valued neutrosophic fuzzy TOPSIS (IVN Fuzzy TOPSIS) method, a novel approach to the location country selection decision problem faced by a fair company operating in Türkiye for international education fairs. IVN Fuzzy TOPSIS is an advanced decision-making method that incorporates interval-valued neutrosophic sets—using high and low values for truthiness (T), indeterminacy (I), and falsity (F)—to more effectively handle uncertainty and indeterminacy in evaluating alternatives. The study demonstrates the efficacy of this method in addressing uncertainty through a real-world case analysis, which provides a balanced assessment of various criteria. The findings, in which Poland was identified as the optimal fair location among five alternatives, demonstrate the efficacy of the method in facilitating expeditious and precise decision-making, particularly through the incorporation of linguistic expressions that simplify the complexities of decision-making processes. This research not only advances the understanding of site selection for education fairs but also offers a practical tool for decision-makers navigating similar challenges in event planning. Full article

To improve the accuracy of choosing restoration materials for repairing ancient Chinese buildings and to mitigate the risk of decision-making, this paper establishes a novel selection model of compositions and proportions of additive lime mortars for the restoration of ancient Chinese buildings. The selection process is influenced by multi-criteria and determined by a group of experts through comprehensive judgment. Thus, it is a multi-criteria group decision-making (MCGDM) problem. Firstly, considering subjective and objective criteria simultaneously, establish a selection index system for compositions and proportions of additive lime mortars in the restoration of ancient Chinese buildings. Secondly, applying a neutrosophic set to characterize experts’ evaluation information and quantify the evaluation information. Thirdly, the best–worst method (BWM) is implemented to obtain criteria weights, and the entropy weight method is utilized to obtain index weights. Finally, obtaining the priority of each alternative solution by using the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) ranking technique. The practicality of the proposed model was demonstrated through a specific case of the selection of repair materials for a decorative window in one ancient Chinese building. The comparative analysis was carried out to verify the reliability and validity of the model. Full article

Interval-valued linguistic neutrosophic sets (IVLNSs), Z-numbers, and the trapezium cloud model are powerful tools for expressing uncertainty and randomness. This paper aims to combine these methodologies. First, we review relevant concepts and operators, introducing a novel combination of IVLNSs and Z-numbers, which establishes a new form of expression. Subsequently, we propose the Z-interval-valued linguistic neutrosophic set-trapezium–trapezium cloud (Z-IVLNS-TTC) model, designed to minimize information loss and distortion during quantification. A novel method for calculating the objective weight vector is then developed using multi-objective programming (MOP). Drawing inspiration from the TOPSIS method, we propose a new approach for calculating the distance between Z-IVLNS-TTCs based on the p-norm. Finally, a group decision-making problem is presented to demonstrate the practical application of the proposed method. To validate the effectiveness and feasibility of the method, sensitivity analysis and comparisons with existing approaches are conducted. Full article

This research aims to introduce and explore the theory of neutrosophic soft hyperalgebras $(NSHA$s), focusing on their core principles and potential applications in decision-making under uncertainty. By defining key operations such as intersection and union, we clarify the foundational characteristics of $NSHA$s and their relationship to soft hyperalgebras. The concepts of ${\xi }_{\beta }$-identity $NSHA$ and $\xi$-absolute $NSHA$ are also examined to better understand their properties. The practical relevance of $NSHA$ is demonstrated through applications in various fields, highlighting its adaptability in addressing complex decision-making scenarios. This approach offers a novel, more precise method for navigating uncertainty in areas such as project methodology selection, sensitivity analysis, and AI chatbot selection. Full article

This study introduces the notion of complex t-neutrosophic graphs (CTNGs) as a powerful tool for understanding and displaying complex interactions that are sometimes difficult to understand. It demonstrates that CTNGs may accurately reflect complicated interactions involving several components or dimensions within a particular scenario. It also instructs the basic set operations of CTNGs and analyzes notions like homomorphism and isomorphism within this framework. Furthermore, the research describes a practical application of CTNGs. It illustrates their value in addressing biodiversity conservation by taking into account a variety of relevant factors. The paper uses this application to highlight the flexibility and effectiveness of CTNGs as a tool for decision-makers to visualize and prioritize activities targeted at improving biodiversity conservation. Full article

This paper contains several novel definitions including neutrosophic $E_{\beta }$ metric space, neutrosophic quasi-$S_{\beta }$-metric space, neutrosophic pseudo-$S_{\beta }$-metric space, neutrosophic quasi-$E$-metric space and neutrosophic pseudo-$E_{\beta }$-metric space. Further, we present some generalized fixed point results with non-trivial examples and the decomposition theorem in the setting of the neutrosophic pseudo-$E_{\beta }$-metric space. Moreover, by using the main result, we examine the existence and uniqueness of the solution to an integral equation, a system of linear equations, and nonlinear fractional differential equations. Full article

The use of acrylonitrile butadiene styrene (ABS) in additive manufacturing applications constitutes an elucidating example of a promising match of a sustainable material to a sustainable production process. Lean-and-green datacentric-based techniques may enhance the sustainability of product-making and process-improvement efforts. The mechanical properties—the yield strength and the ultimate compression strength—of 3D-printed ABS product specimens are profiled by considering as many as eleven controlling factors at the process/product design stage. A fractional-factorial trial planner is used to sustainably suppress by three orders of magnitude the experimental needs for materials, machine time, and work hours. A Gibbs sampler and a neutrosophic profiler are employed to treat the complex production process by taking into account potential data uncertainty complications due to multiple distributions and indeterminacy issues due to inconsistencies owing to mechanical testing conditions. The small-data multifactorial screening outcomes appeared to steadily converge to three factors (the layer height, the infill pattern angle, and the outline overlap) with a couple of extra factors (the number of top/bottom layers and the infill density) to supplement the linear modeling effort and provide adequate predictions for maximizing the responses of the two examined mechanical properties. The performance of the optimal 3D-printed ABS specimens exhibited sustainably acceptable discrepancies, which were estimated at 3.5% for the confirmed mean yield strength of 51.70 MPa and at 5.5% for the confirmed mean ultimate compression strength of 53.58 MPa. The verified predictors that were optimally determined from this study were (1) the layer thickness—set at 0.1 mm; (2) the infill angle—set at 0°; (3) the outline overlap—set at 80%; (4) the number of top/bottom layers—set at 5; and (5) the infill density—set at 100%. The multifactorial datacentric approach composed of a fractional-factorial trial planner, a Gibbs sampler, and a neutrosophic profiler may be further tested on more intricate materials and composites while introducing additional product/process characteristics. Full article

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the “optimal” solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads. Full article

A mathematical method of combining several elements has emerged in recent times, providing a more comprehensive approach. Adhering to the foregoing mathematical methodology, we fuse two extremely potent methods, namely graph theory and neutrosophic sets, and present the concept of neutrosophic graphs ($\aleph G$). Next, we outline many ideas, such as union, join, and composition of $\aleph G$s, which facilitate the straightforward manipulation of $\aleph Gs$ in decision-making scenarios. We provide a few scenarios to clarify these activities. The homomorphisms of $\aleph Gs$ are also described. Lastly, understanding neutrosophic graphs and how Japan responds to earthquakes can help develop more resilient and adaptable disaster management plans, which can eventually save lives and lessen the effects of seismic disasters. With the support of using an absolute score function value, Hokkaido (H) and Saitama (SA) were the optimized locations. Because of its location in the Pacific Ring of Fire, Japan is vulnerable to regular earthquakes. As such, it is critical to customize reaction plans to the unique difficulties and features of Japan’s seismic activity. Examining neutrosophic graphs within the framework of earthquake response centers might offer valuable perspectives on tailoring and enhancing response tactics, particularly for Japan’s requirements. Full article

Maritime shipping is a crucial method of transporting goods internationally and is vital in supporting global trade. However, due to its global scope, the international shipping market is susceptible to political and economic disturbances. The recent escalation in the Israeli–Palestinian conflict has severely impacted the international shipping market, particularly in the tense Red Sea region. Previous research has neglected the significance of evaluating international shipping companies, particularly their origins, within their evaluation frameworks. A fuzzy multi-attribute decision-making (MADM) approach is necessary to address the complexity of evaluating shipping companies with unclear criteria and uncertain expert opinions. Symmetry is crucial in various mathematical fields, with recent applications in hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs), which are frequently employed to solve complex MADM problems. The consideration of symmetry in decision-making processes can enhance the robustness and fairness of evaluations, ensuring a balanced and unbiased approach. The neutrosophic–hesitant fuzzy set (NHFS) considers both the uncertainty of membership degrees of elements (hesitancy in HFSs) and the performance of membership degrees in the true, false, and neutral aspects (the ternary relation in NSs). NHFSs can be seen as a generalization of HFSs and NSs, providing a flexible mathematical framework to more effectively describe and analyze the uncertainties, hesitancies, and fuzziness involved in MADM problems. This study presents single-valued neutrosophic power Hamy mean (SVNPHM) operators and single-valued neutrosophic weighted power Hamy mean (SVNWPHM) operators, which are derived from power aggregation operators (AOs) and the Hamy mean (HM), within the framework of single-valued neutrosophic sets (SVNS). Some properties were investigated via these operators. Furthermore, SVNWPHM operators were employed to address single-valued neutrosophic MADM issues. The proposed methodology was validated by conducting a case study on international shipping provider selection, showcasing the methodology’s relevance and efficiency. Full article