Search Results (145)

An upgrade to the quasi-Newton (QN) family of methods for solving unconstrained optimization problems is proposed. This research focuses on a detailed investigation of the Barzilai and Borwein (BB) gradient methods. The upgrade involves the use of neutrosophic logic to determine an additional parameter that will be incorporated into an appropriate step size for the BB iterations. Unlike previous research, which incorporated neutrosophic concepts into gradient methods by using only two objective-function values to calculate the input parameter during the neutrophication phase, this study determines the input parameter using three consecutive objective-function values. The main idea is to use appropriately defined membership functions to perform neutrosophication and de-neutrosophication. The set of if–then rules is based on two or more successive values of the objective function. This strategy also directly influences the design of the newly proposed method. Numerical comparisons demonstrate superior performance of the proposed methods with respect to Dolan–Moré performance profiles including the number of iterations, central processing unit (CPU) time, and number of function evaluations. Furthermore, experimental results confirm that the proposed algorithms can be effectively applied to image restoration tasks, particularly for image denoising, where they achieve competitive reconstruction quality and stable convergence behavior. Full article

Uncertainty is the biggest issue when modeling real-world multi-level fractional optimization problems. In this paper, a fully intuitionistic fuzzy multi-level multi-objective fractional programming problem (FIF-MLMOFPP) is tackled via two different approaches. Because of the ambiguity introduced in the model, all the parameters and decision variables in each objective function and feasible domain are intuitionistic fuzzy numbers (IFNs). Firstly, FIF-MLMOFPP is converted into a non-fractional fully intuitionistic fuzzy multi-level multi-objective programming problem (FIF-MLMOPP) utilizing a series of transformations. The accuracy functions and ordering relations of IFNs are employed to transform the non-fractional FIF-MLMOPP into a deterministic variant. An interactive approach is first applied to solve the problem by transforming it into discrete multi-objective optimization problems (MOOPs). Each separate MOOP addresses the ϵ-constraint methodology and the goal of satisfactoriness. Neutrosophic fuzzy goal programming (NFGP) is the second approach applied to solve the FIF-MLMOFPP, as the marginal evaluations of predetermined neutrosophic fuzzy objectives for all functions at each level are attained through various membership functions, including degrees of truth, indeterminacy, and falsehood, within neutrosophic uncertainty. The NFGP algorithm is presented to achieve optimal levels for each marginal evaluation objective by minimizing their deviation variables, thus yielding a suitable solution. To confirm and approve the two suggested approaches, a numerical example and a comparison between them are presented. Finally, recommendations for additional research are given. Full article

The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets assume full independence of such information. In view of this, this paper proposes a new neutrosophic set, namely the q-type semi-dependent neutrosophic set (QTSDNS), based on the classical neutrosophic set, whose membership and non-membership degrees are interrelated. QTSDNS is a generalized form of classical semi-dependent fuzzy sets, such as the intuitionistic neutrosophic set. It contains a regulatory parameter, which allows for decision-makers to flexibly adjust the model. Furthermore, a multi-attribute group decision-making (MAGDM) algorithm is proposed by integrating QTSDNS with evidence theory to solve the supplier selection problem. The algorithm first utilizes QTSDNS to represent the preference information of experts, then employs the q-TSDNWAA (or q-TSDNWGA) operator to aggregate the evaluation information of individual experts. Following the analysis of the mathematical relationship between QTSDNS and evidence theory, evidence theory is used to aggregate the evidence from each expert to obtain the group trust interval. Then, the best supplier is determined using interval number ranking methods. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method. 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

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

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

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

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

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

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

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical. Full article

Social media platforms have allowed many people to publicly express and disseminate their opinions. A topic of considerable interest among researchers is the impact of social media on predicting the stock market. Positive or negative feedback about a company or service can potentially impact its stock price. Nevertheless, the prediction of stock market movement using sentiment analysis (SA) encounters hurdles stemming from the imprecisions observed in SA techniques demonstrated in prior studies, which overlook the uncertainty inherent in the data and consequently directly undermine the credibility of stock market indicators. In this paper, we proposed a novel model to enhance the prediction of stock market movements using SA by improving the process of SA using neutrosophic logic (NL), which accurately classifies tweets by handling uncertain and indeterminate data. For the prediction model, we use the result of sentiment analysis and historical stock market data as input for a deep learning algorithm called long short-term memory (LSTM) to predict the stock movement after a specific number of days. The results of this study demonstrated a predictive accuracy that surpasses the accuracy rate of previous studies in predicting stock price fluctuations when using the same dataset. Full article

Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to solve problems with inconsistent, ambiguous, and inaccurate data. In this article, we demonstrate some basic fixed-point theorems for any even number of compatible mappings in complete neutrosophic metric spaces. Our primary findings expand and generalize the findings previously established in the literature. Full article