Clustering is an unsupervised learning technique used to discover hidden structures in data. By identifying patterns and similarities among objects, this methodology enables the organization of datasets into homogeneous groups. This work presents a new perspective on a specific class of partition-based algorithms for unsupervised discrete clustering in complete finite-dimensional Riemannian manifolds by introducing statistical shape analyses to classify clusters and improve label selection. To achieve this aim, we extend the statistical concepts of skewness and kurtosis to Riemannian settings, based on vector operations in the tangent plane at each point of the manifold. Assumptions regarding the injectivity radius and the boundedness of the sectional curvature are initially adopted to enable local convex analysis. Nevertheless, the well-posedness of Riemannian weighted centroids is ensured by analyzing the coercivity and quasiconvexity properties of the distance function’s powers. In addition, we demonstrate that well-posedness and continuity extend to any positive power of the distance function, rather than being limited to powers greater than or equal to 1. Computational experiments involving diffusion tensor imaging and hyperspectral image segmentation are performed. We also present a statistical analysis to demonstrate the practical applicability and computational performance of our technique compared with leading clustering approaches. Ultimately, our methodology is applicable to any field where data modeling resides in a complete finite-dimensional Riemannian manifold.
Advances in deep learning have led to significant progress in the field of speech processing, particularly in applications such as speaker recognition systems (SRSs). Additional information such as gender, accent, and age of the speaker can improve the performance of the SRS. This paper focuses on the influence of speaker gender on the performance of speaker recognition systems, specifically by analyzing the frequency domain using neural computations inspired by the human auditory system. To achieve this goal, four types of well-known filters—rectangular, gammatone, cascade, and all-pole, derived from audio filter models—are utilized in the first convolutional layer of a Convolutional Neural Network (CNN). A comprehensive analysis of the filterbank learned in this layer provides valuable insights into the importance of different frequency ranges in this application. The analysis is performed on two datasets, TIMIT and LibriSpeech, for speaker identification and speaker verification tasks by training distinct models for males and females. Experimental results indicate that, in our setting, knowing the speaker’s gender does not guarantee improved performance in the recognition system. Moreover, recognition of female speakers is more challenging than that of male speakers, and the frequency importance of the learned filterbanks does not align with the Mel-scale.
Multi-objective flexible fuzzy job shop scheduling problem(MOFFJSSP) is a combination of scheduling problem and fuzzy system, which simulates the uncertainty in the actual production. Due to the high complexity of MOFFJSSP, it has received widespread attention. In this work, a mixed integer linear programming model of MOFFJSSP is considered and a Q-learning antibody evolution algorithm(QAEA) is proposed to minimize fuzzy makespan and fuzzy total machine load. In this approach, (1) a reinforcement learning-based parameter adaptive adjustment(RLPAD) method is adopted to improve the diversity performance; (2) inspired by artificial immune algorithms(AIA), the antibody neighborhood density(AND) operator is proposed to further maintain population diversity; (3) four problem-specific neighborhood structures are designed to enhance exploitation ability and convergence performance. Finally, to verify the effectiveness of QAEA, it is compared with other state-of-art algorithms on 23 benchmarks, the results demonstrate that QAEA can obtain the best pareto solution set in the most of benchmarks.
The aim of the paper is to construct the nontrivial monadic operators on finite linearly ordered perfect IMTL-algebras. We propose the notion of cutting IMTL-algebras and obtain some of their properties. We list all monadic operators on linearly ordered IMTL-algebras with less than 7 elements. The necessary and sufficient conditions for some finite linearly ordered perfect IMTL-algebras having nontrivial monadic operators are also established. Furthermore, we explore the nontrivial monadic operators on cutting IMTL-algebras and verify that if the square of coatom is not greater than the cutting point, then each cutting algebra with more than 10 elements has nontrivial monadic operators. When the square of coatom is greater than the cutting point, we give examples to show that there are cutting IMTL-algebras only having trivial monadic operators. We further analyze the structure of cutting IMTL-algebras and achieve the conditions for cutting IMTL-algebras having nontrivial monadic operators. In addition, we give some characterizations of monadic IMTL-algebras.
The basic tool for comprehending transport processes in a physical system is the advection–diffusion equation. A new numerical scheme is proposed in this work to compute accurate numerical solutions of the considered equation. This study introduces a non-polynomial sextic spline technique for addressing Advection–diffusion equation exhibiting oscillatory behaviour. This method applies the sextic spline as an interpolation function in the space dimension, while discretising the time derivative using a finite difference approach. From a computational perspective, this strategy yields a solution that is both efficient to use and in great agreement with those found by previous research. The efficiency and practical relevance of the proposed method are validated through several numerical experiments, while its unconditional stability is proven through rigorous stability analysis. Error analysis demonstrates that the suggested approach has second-order accuracy in time variables and fourth-order convergence in space.
This paper is dedicated to the development of a new compact numerical method tailored for solving the variable order time fractional mobile–immobile convection–dispersion equation with variable convection coefficient, a model widely applicable to intricate systems in engineering and science. The proposed scheme is established with a fourth-order compact exponential discretization in space, a fourth-order multistep cubic C^1 -spline collocation method for integer time discretization, and Caputo numerical techniques to approximate the fractional time derivative. The theoretical study shows that the proposed scheme is unconditionally stable and uniquely solvable. Several numerical results are presented to illustrate the accuracy of the proposed scheme.
In this paper, we introduce three novel relations, Bonding relation B, Neighborhood relation N and Connected relation C, on the soft approximation space, and study their important properties. On this basis, we first establish three new soft rough set models and then establish three enhanced soft rough fuzzy set models. The new models have advanced properties such as stability, duality, and better approximations than existing models. We compare their properties with existing ones in detail, and compare their applications with practical examples, which show that the new models are more powerful than the existing models.
Generalized three-way decision (G3WD) offers flexible adjustment of decision strategies based on varying backgrounds and demands. Pythagorean fuzzy sets (PFSs) exhibit higher sensitivity and accuracy in handling intricate data scenarios. However, decision-makers’ behaviors can be influenced by psychological factors. Regret theory (RT) elucidates the psychological mechanisms underlying human choices. To address this, we endeavor to develop a novel G3WD model by introducing PFSs and RT. Firstly, an entropy weight method based on Pythagorean fuzzy entropy is proposed to objectively calculate attribute weights. Secondly, we define Pythagorean fuzzy rejoicing and regret functions by incorporating RT. From these functions, Pythagorean fuzzy superiority and inferiority flows are derived. Leveraging the above knowledge, a G3WD model using RT is built in Pythagorean information fuzzy systems by defining trisection and ranking rules. Finally, the effectiveness, superiority, and stability of the model are further verified through numerical and experimental analyses.
Here, the notions of connectivity factor node, weakest weak inverse fuzzy mixed cycles, abandoned edge, cycle associativity set, simple cycle associated graph, and inverse simple cycle associated graph are defined and studied in the context of inverse fuzzy mixed graphs. These concepts provide new perspectives for examining the interaction between vertices, edges, and cyclic structures within such graphs. Based on these newly introduced ideas, several properties and results related to cycles in inverse fuzzy mixed graphs are established. Various theoretical results are derived to analyze the behaviour of inverse fuzzy mixed graphs under different cycle configurations, highlighting their structural and connectivity properties. An application has also been presented to demonstrate the practical relevance of the proposed concepts.
Climate change has become a severe problem that requires global attention and has resulted in increasingly frequent occurrences of extreme weather events such as drought, floods, cyclones, and heat waves. These weather disasters are sometimes compounded by earthquakes, resulting in incalculable loss of life and property. The delivery of relief supplies is a critical part of the emergency response following a disaster. Most previous studies have considered either the selection of distribution centers or the design of a relief supply chain network; by contrast, this study attempts to optimize both problems with a proposed hybrid multiple-criteria decision-making model. Fuzzy theory was applied to model uncertainties and inconsistencies among decision-makers. First, distribution centers for relief material distribution were selected using fuzzy best–worst method and the reference ideal method; then, transportation within the supply chain network was examined using fuzzy multiple-objective decision-making. A case study for actual data collected from the Taipei region was performed. Our results show that the population density is the critical factor while selecting the distribution centers. The best distribution network identified in this study can be provided to decision-makers as a reference when drafting emergency response plans.
This paper introduces the concept of ℐ -lacunary statistical soft convergence of order α for sequences of soft points in soft topological spaces. This new framework unifies ideal convergence, lacunary methods, and statistical convergence of variable order within the soft set setting. We investigate the fundamental properties of this notion, including the uniqueness of the underlying limit point in soft Hausdorff spaces and the inclusion relations between convergence classes for distinct orders satisfying 0 < α≤β≤ 1 . Furthermore, we establish a connection between lacunary and ordinary statistical soft convergence. Specifically, for the ideal of finite sets ℐ_fin , we prove that ℐ -lacunary statistical soft convergence of order α implies statistical soft convergence of the same order, provided the lacunary sequence satisfies a bounded ratio condition. Counterexamples are provided to demonstrate that the converse implications and general inclusions do not hold without additional assumptions.
Abstract In this paper, the arranged element is introduced in MV -algebras, and its characteristics are studied. It is proved that an MV -algebra A is an MV -chain if and only if every nonzero element is an arranged element. In the continuation, weak $$Z^{\circ }$$ Z ∘ -ideals are defined and equivalent definitions of weak $$Z^{\circ }$$ Z ∘ -ideals are provided. Their relationships with existing notions such as $$Z^{\circ }$$ Z ∘ -ideals and $$Z^{\circ }_{J}$$ Z J ∘ -ideals are examined. This analysis makes it possible to establish new classifications of prime and minimal prime ideals. Additionally, properties of annihilators in MV -algebras are investigated.
In this paper, the arranged element is introduced in MV-algebras, and its characteristics are studied. It is proved that an MV-algebra A is an MV-chain if and only if every nonzero element is an arranged element. In the continuation, weak Z^∘ -ideals are defined and equivalent definitions of weak Z^∘ -ideals are provided. Their relationships with existing notions such as Z^∘ -ideals and Z^∘_J -ideals are examined. This analysis makes it possible to establish new classifications of prime and minimal prime ideals. Additionally, properties of annihilators in MV-algebras are investigated.
Fully fuzzy linear systems (FFLS) appear in many control problems where data and model parameters are represented by triangular fuzzy numbers. Classic iterative algorithms, such as fuzzy Jacobi and Gauss–Seidel, are usually slow to convergence and amplify uncontrolled spread growth as a result of dependency effects in fuzzy arithmetic. This paper presents two contributions to address these limitations. we propose a polynomially accelerated explicit Gauss–Seidel scheme that, unlike prior work that applies acceleration naively, presently decouples the acceleration logic a three-term min-max polynomial is applied exclusively to the deterministic center system. Second, we provide the rigorous proof that the spread dynamics remain uniformly bounded throughout the iteration process, directly countering the exponential spread inflation endemic to conventional fuzzy arithmetic. This combination of superlinear convergence and provable boundedness is a central contribution of this work. Numerical experiments on medium and large-scale FFLS demonstrate significantly faster convergence and controlled error propagation than current fuzzy iterative and embedding-based methods. The results demonstrate that the proposed framework provides an effective and theoretically based alternative to large-scale fuzzy linear issues.
This research aims to redefine decision-making in Agri-Biotech systems, where dynamic biological behavior, operational uncertainty, and conflicting performance objectives require a more integrated control architecture. To address this need, the study presents a unified framework based on digital twin, neuromorphic interpretation, and multi-objective fuzzy optimization, creating a closed loop between real data, dynamic forecasting, and adaptive decision-making. The results showed that in the base scenario, production efficiency increased to 91.4
Droughts are natural phenomena that affect the health of crops, and owing to changes in climate, they are expected to increase in frequency. Drought has a significant impact on economic and social well-being. Recently, satellite data have emerged as one of the most powerful tools for studying the environment owing to the high availability of data. This paper presents the design and implementation of a system that uses satellite remote sensing data to analyze the impact of drought on agricultural regions. Our approach makes use of Sentinel Hub, a Cloud service that provides access to multi-spectral satellite imagery. In this study, we analyzed the correlation between vegetation health and soil moisture, which was detected using multi-spectral indices. A model was devised to study vegetation cover variations that occur over a period of time and to evaluate whether soil moisture played a role in those changes. The results of the model for a region of lai county in Romania matched the reports from local authorities. Such a system may be useful for farmers, businesses, and local authorities, who could utilize the information provided by the model to make informed decisions that can improve the overall health and performance of crops.
Few-shot learning (FSL) has emerged as an effective approach to tackling data scarcity in real-world applications, such as plant disease classification, where obtaining labeled samples is both costly and labor-intensive. Existing FSL methods often depend on static feature representations and unidirectional adaptation mechanisms. It restricts their capacity to capture task-specific discriminative information in varying environmental conditions. To overcome these constraints, this paper presents TransFeatWalk, a FSL framework that incorporates bidirectional prototype-query adaptation to enhance feature alignment. The proposed model facilitates mutual refinement between support prototypes and query features, which enhances the model’s capacity to generalize to unseen classes. A multi-head feature fusion module has also been added to capture different feature interactions across different representation subspaces. This enhancement improves robustness against both intra-class variability and inter-class similarity. The framework further employs a cosine-similarity–based classifier for effective decision-making in low-data regimes. The overall architecture works in a transductive setting, using query information during inference to improve class representations. Experiments are conducted on the Cashew–Cassava–Maize–Tomato (CCMT) and PlantVillage datasets under standard 5-way 1-shot, 5-shot, and 10-shot settings. The proposed model achieves 43.29
Rough-fuzzy clustering has been successfully applied in image segmentation owing to its superior capability in handling data uncertainty and ambiguity. However, it still has several shortcomings, including manual determination of threshold parameters, reliance on a single clustering criterion function, sensitivity to initialized cluster centers, and a tendency to fall into local optimum. To address these issues, this paper introduces surrogate-assisted multi-objective optimization into rough fuzzy clustering and proposes an enhanced broad learning system (BLS) guided surrogate-assisted multi-objective evolutionary rough fuzzy clustering (EBLS-MERFC) algorithm. The algorithm employs a genetic algorithm to replace traditional traversal methods for selecting optimal points, constructing an enhanced BLS model with parameter adaptive determination strategy. It predicts fitness function values to substitute real function calculations, ensuring prediction performance while reducing computational costs. An adaptive threshold determination mechanism for rough-fuzzy clustering is established based on differences in fuzzy membership degrees, which effectively divides the lower approximation region and boundary region in rough-fuzzy clustering while minimizing manual intervention. Considering the proportion of cluster boundary regions, a rough-fuzzy intra-class compactness fitness function is constructed, which is synchronously optimized with the rough-fuzzy inter-class separability function to obtain segmentation results. Experimental results on Berkeley and Weizmann natural images demonstrate that compared with other multi-objective evolutionary clustering algorithms, the proposed algorithm exhibits superior segmentation accuracy and robustness.
In both classical graph theory and fuzzy graph theory, the number of nodes and arcs is conventionally considered fixed. As a result, removing one or more nodes from a graph usually results in a structure that cannot maintain its original function or may no longer be analyzed as the intended graph. To address this limitation, in this paper, we introduce, for the first time, a novel structure called the permanent graph (permanent fuzzy graph), utilizing the established concepts of neighborhood and distance between two nodes. By introducing this particular and useful graph structure, we propose a method to revive a graph whose functionality has been compromised due to the loss of nodes, thereby preventing its complete collapse. The application of this permanent graph (permanent fuzzy graph) in decision-making processes (specifically for making appropriate and informed choices within a social network) serves as evidence supporting this claim.
Hereditary Multiple Exostoses (HME) is a rare skeletal disorder characterized by the growth of multiple benign bone tumors. They often lead to orthopedic complications and malignant transformation. Despite advancements in medical imaging, no automated deep learning framework has been specifically developed for detecting HME in hip radiographs. In this study, we propose HME-LiteNet, a lightweight convolutional neural network (CNN) customized to identify HME-related features on pelvic radiographs. To address the challenge of limited data, we performed domain-specific data augmentation to enhance model robustness. The proposed model was benchmarked against a pretrained MobileNetV2, demonstrating its superior performance in terms of computational complexity and inference speed. Furthermore, we conducted acceleration cross-NVIDIA platform training and inference experiments. We used a high-performance GeForce RTX 3050 Graphic Processing Unit (GPU) and an edge-capable Jetson Orin device. The model was further optimized using TensorFlow Lite (TFLite). It achieved an accuracy and area under the receiver operating characteristic curve (AUC-ROC) of 0.99 on the validation set. It also reduces the computational complexity by a factor of 1.64 × compared with MobileNetV2. The inference throughput reached 8.75 GOPS on the RTX3050 and 7.58 GOPS on the Jetson Orin, highlighting its suitability for real-time deployment. Visualization using Grad-CAM confirmed that the model consistently focused on clinically relevant regions in HME-positive radiographs. This approach offers interpretable and reliable prediction. These results demonstrate the potential of AI-assisted diagnosis in enhancing the early detection of HME in both clinical and portable healthcare settings.
