Search Results (63)

In this paper, we present the notion of fuzzy $\mathcal{R}-F-$contractive mappings and provide some fuzzy fixed point results in the setting of fuzzy metric spaces, which are endowed with binary relations. Furthermore, we apply our newly established fuzzy fixed point results to solve certain boundary value problems for nonlinear fractional differential equations involving the Caputo fractional derivatives. Also, we provide some examples to show the utility of our new results. Full article

This study presents an experimental and comprehensive data-driven framework to gain deeper insights into the effect of acidic pretreatment in enhancing the biomethane yield of Xyris capensis. The experimental workflow involves subjecting the Xyris capensis to different concentrations of HCl, exposure times, and digestion retention time in mesophilic anaerobic conditions. Key insights were gained from the experimental dataset through correlation mapping, feature importance assessment (FIA) using the Gini importance (GI) metric of the decision tree regressor, dimensionality reduction using Principal Component Analysis (PCA), and operational cluster analysis using k-means clustering. Furthermore, different clustering techniques were tested with an Adaptive Neuro-Fuzzy Inference System (ANFIS) tuned with particle swarm optimization (ANFIS-PSO) for biomethane yield prediction. The experimental results showed that HCl pretreatment increased the biomethane yield by 62–150% compared to the untreated substrate. The correlation analysis and FIA further revealed exposure time and acid concentration as the dominant variables driving biomethane production, with GI values of 0.5788 and 0.3771, respectively. The PCA reduced the complexity of the digestion parameters by capturing over 80% of the variance in the principal components. Three distinct operational clusters, which are influenced by the pretreatment condition and digestion set-up, were identified by the k-means cluster analysis. In testing, a Gaussian-based Grid-Partitioning (GP)-clustered ANFIS-PSO model outperformed others with RMSE, MAE, and MAPE values of 5.3783, 3.1584, and 10.126, respectively. This study provides a robust framework of experimental and computational data-driven methods for optimizing the biomethane production, thus contributing significantly to sustainable and eco-friendly energy alternatives. Full article

As technological progress and population growth continue to drive rising energy demand, renewable energy has emerged as a key focus of the global energy transition due to its environmental sustainability. However, in suitability assessments and site selection for green energy projects such as photovoltaic (PV) power generation, key criteria such as supply–demand balance and land price are often inadequately considered, despite their direct impact on decision outcomes. Moreover, excessive reliance on expert judgment for weighting, along with the neglect of inter-criterion relationships, introduces uncertainty. Combined with the presence of ill-posed problems, these issues limit the practical value of the evaluation results. This study integrates economic cost–benefit analysis into the evaluation criteria system alongside climatic and geographical criteria, constructing a set of 11 spatial indicators, including global horizontal irradiation (GHI), land prices, and regional power demand, to support PV site selection. Furthermore, a comprehensive evaluation framework is proposed that combines geographic information systems (GIS), multi-criteria decision analysis (MCDA), fuzzy comprehensive evaluation (FCE), and machine learning (ML). The framework enables the collaborative optimization of expert-constrained and data-driven criteria weighting. A national suitability zoning map for PV power plants was developed and validated against actual construction cases. The results demonstrate that the proposed methodology outperforms traditional approaches, achieving a 0.1178 improvement in weight determination compared to expert-based methods, producing a photovoltaic suitability map that more accurately reflects actual construction trends, thereby providing better and more effective support for PV site planning. Full article

Watersheds are threatened by numerous issues, such as climate change, population growth, urban expansion, and industrial development. These issues are complex and interconnected, and effectively addressing them requires integrating the values, knowledge, and expertise of various governing bodies, local organizations, and community members, all of whom have their own viewpoints and priorities. The current study employs a participatory approach and systems lens to engage different stakeholders in the complexity of watershed issues and management approaches. Using participatory modeling and semi-quantitative scenario analysis techniques, the study identifies relationships among watershed values, challenges, and strategies as well as the dynamics of these relationships. A fuzzy cognitive map was developed, which consists of 53 nodes (i.e., 13 values, 12 challenges, and 28 strategies) and 113 connections. Biodiversity, mental health, and sense of place emerged as key values, as they exhibited high centrality values when analyzing the system, and challenges like invasive species and urban sprawl were found to exert considerable impacts on these values. Strategies such as establishing and expanding greenspace, community stewardship, and governance-based interventions were identified as critical for addressing watershed challenges and enhancing watershed values. The study identified a series of governance-based strategies that focus on resource allocation, participatory governance, and institutional collaboration to address watershed management challenges as well as a set of engagement-based strategies that focus on environmental communication and public awareness. The study demonstrates the potential that participatory modeling and semi-quantitative analysis techniques can have for integrating both tangible, measurable values and intangible, difficult-to-measure values into planning and policymaking. The research reinforces the idea that local governments play a critical role in fostering inclusive and collaborative watershed management strategies. Full article

To enable early identification of failure risks in ship systems and equipment, a dynamic cloud center of gravity model is developed for real-time system-level health assessment. First, the Functional Analysis System Technique (FAST) was applied to decompose the operational functions and dependencies of the intelligent machinery room system, enabling the structured establishment of a hierarchical evaluation index system. The comprehensive weight is derived through synergistic application of the fuzzy set (FS) theory and entropy weight. This process integrated expert-defined functional boundaries with measurable parameters critical to system performance. Then, an improved cloud center of gravity method based on the Gaussian cloud model and sliding time window method is used for the system’s adaptive health value calculation. The dynamic health model can achieve continuous online assessment and track the further evolution of the system. Finally, the proposed model is applied to the Fuel Oil Supply System (FOSS). The integration of system performance output and disassembly inspection results demonstrates that the method proposed in the article more accurately reflects the true health status changes in the system when mapping health values. Full article

This study presents new fuzzy adaptations of Ostrowski’s integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-valued Ostrowski inequalities. Their formulations incorporate integrability concepts for fuzzy-valued mappings (FVMs), applying the Kaleva integral and a Kulisch–Miranker fuzzy order relation. The fuzzy order relation is constructed via a level-wise approach based on the Kulisch–Miranker order within the fuzzy number space. Additionally, numerical examples illustrate the effectiveness and significance of the proposed theoretical model. Various applications are explored using different means, and some complex cases are derived. Full article

In this study, trapezoidal-type inequalities in fuzzy settings have been investigated. The theory of fuzzy analysis has been discussed in detail. The integration by parts formula of analysis of fuzzy mathematics has been employed to establish an equality. Trapezoidal-type inequality for functions with values in the fuzzy number-valued space is proven by applying the proven equality together with the properties of a metric defined on the set of fuzzy number-valued space and Höler’s inequality. The results proved in this research provide generalizations of the results from earlier existing results in the field of mathematical inequalities. An example is designed by defining a function that has values in fuzzy number-valued space and validated the results numerically using the software Mathematica (latest v. 14.1). The p-levels of the defined fuzzy number-valued mapping have been shown graphically for different values of $p\in \left[0,1\right]$. Full article

In the industrial sector, accurate fault identification is paramount for ensuring both safety and economic efficiency throughout the production process. However, due to constraints imposed by actual working conditions, the motor state features collected are often limited in number and singular in nature. Consequently, extending and extracting these features pose significant challenges in fault diagnosis. To address this issue and strike a balance between model complexity and diagnostic accuracy, this paper introduces a novel motor fault diagnostic model termed FSCL (Fourier Singular Value Decomposition combined with Long and Short-Term Memory networks). The FSCL model integrates traditional signal analysis algorithms with deep learning techniques to automate feature extraction. This hybrid approach innovatively enhances fault detection by describing, extracting, encoding, and mapping features during offline training. Empirical evaluations against various state-of-the-art techniques such as Bayesian Optimization and Extreme Gradient Boosting Tree (BOA-XGBoost), Whale Optimization Algorithm and Support Vector Machine (WOA-SVM), Short-Time Fourier Transform and Convolutional Neural Networks (STFT-CNNs), and Variational Modal Decomposition-Multi Scale Fuzzy Entropy-Probabilistic Neural Network (VMD-MFE-PNN) demonstrate the superior performance of the FSCL model. Validation using the Case Western Reserve University dataset (CWRU) confirms the efficacy of the proposed technique, achieving an impressive accuracy of 99.32%. Moreover, the model exhibits robustness against noise, maintaining an average precision of 98.88% and demonstrating recall and F1 scores ranging from 99.00% to 99.89%. Even under conditions of severe noise interference, the FSCL model consistently achieves high accuracy in recognizing the motor’s operational state. This study underscores the FSCL model as a promising approach for enhancing motor fault diagnosis in industrial settings, leveraging the synergistic benefits of traditional signal analysis and deep learning methodologies. Full article

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra. Full article

The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval $[0, 1]$, but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results. Full article

The aim of this paper is to present new existence results for solutions to a generalized quasi-equilibrium problem with set-valued mappings and moving cones. The key to this approach is a new Browder-type fixed point theorem, which permits working in a new direction with the milder condition of transfer open-valued mapping and considering weaker assumptions on the coving cone. These results are applied to some generalized vector quasi-equilibrium problems with trifunctions and to a vector quasi-equilibrium problem with fuzzy mappings in a fuzzy environment. Full article

This paper introduces a semi-automated approach for the prioritization of software features in medium- to large-sized software projects, considering stakeholders’ satisfaction and dissatisfaction as key criteria for the incorporation of candidate features. Our research acknowledges an inherent asymmetry in stakeholders’ evaluations, between the satisfaction from offering certain features and the dissatisfaction from not offering the same features. Even with systematic, ordinal scale-based prioritization techniques, involved stakeholders may exhibit hesitation and uncertainty in their assessments. Our approach aims to address these challenges by employing the Binary Search Tree prioritization method and leveraging the mathematical framework of Intuitionistic Fuzzy Sets to quantify the uncertainty of stakeholders when expressing assessments on the value of software features. Stakeholders’ rankings, considering satisfaction and dissatisfaction as features prioritization criteria, are mapped into Intuitionistic Fuzzy Numbers, and objective weights are automatically computed. Rankings associated with less hesitation are considered more valuable to determine the final features’ priorities than those rankings with more hesitation, reflecting lower indeterminacy or lack of knowledge from stakeholders. We validate our proposed approach with a case study, illustrating its application, and conduct a comparative analysis with existing software requirements prioritization methods. Full article

Hybrid contractions serve as a flexible and versatile framework for establishing fixed-point Theorems and analyzing the convergence of iterative algorithms. This paper demonstrates the adapted form of the admissible hybrid fuzzy $\mathfrak{Z}$-contraction in the perspective of £-fuzzy set-valued maps for extended ♭-metric spaces. Sufficient criteria for obtaining £-fuzzy fixed points for this contraction have been established. In addition, the hypotheses of its main result are endorsed by some nontrivial supportive examples featuring graphical illustrations. Consequently, the concept of graphical extended ♭-metric spaces is introduced and a £-fuzzy fixed point result in the context of newly defined space is derived. Illustrative examples, incorporating relevant graphs, are provided with the support of a computer simulation to validate the established results, enhancing the understanding of the underlying notions and investigations. The concepts presented here not only considerably improve, enrich, and extend a number of well-known pre-existing fixed-point results but also assemble and merge several ones in the corresponding domain. Full article

Mathematical expression retrieval is an essential component of mathematical information retrieval. Current mathematical expression retrieval research primarily targets single modalities, particularly text, which can lead to the loss of structural information. On the other hand, multimodal research has demonstrated promising outcomes across different domains, and mathematical expressions in image format are adept at preserving their structural characteristics. So we propose a multi-modal retrieval model for mathematical expressions based on ConvNeXt and HFS to address the limitations of single-modal retrieval. For the image modal, mathematical expression retrieval is based on the similarity of image features and symbol-level features of the expression, where image features of the expression image are extracted by ConvNeXt, while symbol-level features are obtained by the Symbol Level Features Extraction (SLFE) module. For the text modal, the Formula Description Structure (FDS) is employed to analyze expressions and extract their attributes. Additionally, the application of the Hesitant Fuzzy Set (HFS) theory facilitates the computation of hesitant fuzzy similarity between mathematical queries and candidate expressions. Finally, Reciprocal Rank Fusion (RRF) is employed to integrate rankings from image modal and text modal retrieval, yielding the ultimate retrieval list. The experiment was conducted on the publicly accessible ArXiv dataset (containing 592,345 mathematical expressions) and the NTCIR-mair-wikipedia-corpus (NTCIR) dataset.The MAP@10 values for the multimodal RRF fusion approach are recorded as 0.774. These substantiate the efficacy of the multi-modal mathematical expression retrieval approach based on ConvNeXt and HFS. Full article

This paper discusses some properties of complex-valued fuzzy metric spaces and introduces the $\alpha$-admissible mappings in the setting of complex-valued fuzzy metric spaces. We establish fixed point theorems for mappings satisfying symmetric contractive conditions with control functions. The results of this paper generalize, extend, and improve several results from metric, fuzzy metric, and complex-valued fuzzy metric spaces. Several examples are presented that verify and illustrate the new concepts, claims, and results. Full article