To address the issues of high computational overhead and the inability to capture hierarchical structures when DBSCAN processes data with uneven density distributions, this paper proposes a density-driven clustering framework, namely MSGB based on granular balls (GBs). This method uses the GB as the basic operational unit. First, it automatically determines the initial number of partitions using mean drift and initializes cluster centers based on local density peaks to avoid the sensitivity to initial values inherent in traditional k-means. Second, it designs a radius calculation strategy based on the coefficient of variation-weighted median distance, allowing the GB scale to dynamically adjust according to local density variations, thereby preserving structural information while suppressing noise. Furthermore, by constructing a granular ball topological similarity graph, it transforms the density reachability determination into a search for connected components among granular balls, effectively handling scenarios with multi-density clusters and weak connections. To validate the effectiveness of the proposed method, this paper conducts comparative experiments on 10 synthetic datasets and 10 real-world datasets using ACC, NMI, and ARI as evaluation metrics. Specifically, on the synthetic datasets, MSGB improves ACC by 3.81%, NMI by 2.82%, and ARI by 4.49% compared to DBSCAN. On real-world datasets, it also achieves consistent improvements. The results show that MSGB outperforms several mainstream comparison algorithms on average across all datasets, demonstrating outstanding robustness and consistent advantages, particularly in noisy and non-uniform density scenarios, thereby validating the framework’s strong adaptability to data with complex density structures. The source code of the MSGB algorithm is available via the following network link https://github.com/Z-Lucky-M/MSGB.

With the rapid advancement of intelligent decision-making systems, group decision-making (GDM) suffers from insufficient fairness and defective measurement methods, which leads to consensus quantification deviations and low public recognition, thereby restricting the practical application and efficiency of intelligent GDM. To address this issue, this paper develops a fairness-oriented group consensus method from a multi-relationship interaction perspective to eliminate negative impacts stemming from abnormal decision-maker-alternative correlations and consensus gaming behaviors. In the opinion collection stage, behavioral anomaly identification and regulation rules are established to eliminate interference factors such as potential interest ties and subjective preference biases and purify original decision information. In the consensus negotiation stage, a novel two-dimensional guidance mechanism is constructed. By defining the coordination role of formal leaders based on the group opinions and identifying implicit opinion leaders via social network analysis, the developed method realizes dual opinion anchoring and balances decision fairness and convergence efficiency. Case studies and comparative experiments demonstrate that this method effectively suppresses information distortion and individual gaming, improves consensus fairness and decision rationality, and provides a feasible theoretical and technical basis for the practical deployment of intelligent GDM systems in complex scenarios.

Multivariate time series forecasting plays a vital role in finance, meteorology, energy scheduling, transportation, and environmental monitoring, yet traditional statistical and machine learning methods often failto capture the complex nonlinearities, high-dimensional redundancies, and spatio-temporal dependencies inherent in real-world data. To overcome these limitations, we propose IFCM-DSACNN, a novel deep learning framework that synergistically integrates an improved fuzzy $C$-means clustering algorithm (IFCM) with a dual self-attention mechanism and a one-dimensional convolutional neural network (1D-CNN). The IFCM module first clusters features exhibiting similar temporal dynamics, thereby reducing feature redundancy and mitigating noise interference through a cross-entropy-based suppression strategy, while the alpha evolution algorithm autonomously determines the optimal number of clusters without manual tuning. Within each coherent feature subset, a dual self-attention mechanism is applied in parallel along both the sample and feature dimensions to capture complementary global dependencies, and the resulting relation-aware representations are fused and subsequently refined by a 1DCNN to extract local structural patterns for final prediction. Extensive experiments on six publicly available datasets, comparing against nine state-of-the-art forecasting models, demonstrate that IFCM-DSACNN consistently achieves the lowest RMSE and MAE across all datasets, along with near-zero MBE values, confirming itssuperior accuracy, robustness, and bias control. Ablation studies validate the complementary contributions ofeach module, and Friedman with Nemenyi statistical tests confirm the)significance of our improvements. These results establish IFCM-DSACNN as a powerful and reliable solution for complex multi-feature time series forecasting tasks.

Forecasting the future state of a single target sensor from multi-sensor observations is a critical task in intelligent transportation systems, supporting congestion warning, signal control, and fine-grained traffic management at key locations. Existing methods under this setting often face three limitations: they characterize feature contributions only at the point or window level, rely on reduction-oriented feature processing that may discard complementary information, and rarely transform extracted structural information into relation-aware cues for downstream prediction. To address these issues, this paper proposes TVFI-GST, a spatiotemporal forecasting framework driven by time-varying structural cues. TVFI-GST first constructs target-semantic phase partitions and models phase-level temporal feature importance. It then employs fuzzy information granules (FIG) as carriers of trend evidence and reliability information to enable reliability-aware granular soft fusion, suppressing redundancy while preserving and reconstructing task-relevant information. Finally, the learned fusion structure is converted into dynamic relational cues and lag-aware context for fusion-aware prediction, forming a closed loop between representation learning and downstream forecasting. In this way, FIGs support phase-level importance modeling, reliability characterization, and information-preserving fusion, elevating temporal feature importance from a local explanatory signal to a stable structural interface for subsequent modeling. Experiments on six real-world traffic datasets demonstrate that TVFI-GST achieves strong overall forecasting performance against competitive baselines, while also offering interpretable structural cues under complex traffic conditions.

Spectral clustering has shown strong potential for complex data partitioning, but its application to noisy and large-scale scenarios is limited by the high cost of graph construction and eigendecomposition, as well as the insufficient modeling of boundary uncertainty induced by the separation between continuous relaxation and discrete partitioning. To overcome these limitations, this paper proposes an R-anchor-ball-based dual-scale fuzzy spectral clustering method, termed RAB-DSFSC. The method unifies Poisson-disk-sampled anchor-ball representation, sparse graph construction, and dual-scale fuzzy clustering within a single framework. By constructing coarse-grained R-anchor balls, it obtains a compact and robust representation that alleviates sensitivity to noise and local density variations. On this basis, a sparse graph is built to enhance scalability by avoiding explicit eigendecomposition of large-scale similarity matrices. Furthermore, a dual-scale fuzzy consistency mechanism couples sample-level and anchor-ball-level memberships, allowing prototype-level structural information to regularize sample partitioning and improving the interpretability of uncertain boundary assignments. A theoretical analysis of the approximation error of the proposed representation is further provided to support its local structure preservation capability. Experiments on synthetic and real-world datasets show that RAB-DSFSC delivers more competitive and stable performance in terms of NMI and ARI, together with stronger robustness and scalability in noisy and large-scale settings. The source code is publicly available at https://github.com/hgftgghh/RAB-DSFSC.

In the field of group decision-making (GDM), minimum cost consensus models (MCCMs) have been extensively studied to enhance decision-making efficiency and conserve resources. However, such models generally overlook decision makers' (DMs) demands for fairness, which can easily lead to non-cooperative behavior and thereby hinder the achievement of consensus. In light of this, this study focuses on two core issues under the minimum-cost constraint of MCCMs: first, how to comprehensively characterize individuals' perceptions of fairness; and second, how to design a consensus mechanism that balances efficiency and fairness. As individuals' reliance on social networks increases, this study utilizes fuzzy social networks to quantify DMs' importance and bargaining power, providing a bargaining foundation and weighting basis for subsequent model construction. Specifically, the study first measures the deviation between actual and expected returns based on cost differences arising from individual profit maximization and differentiated bargaining. It then classifies DMs into hierarchical levels based on their trust levels and bargaining power within a fuzzy social network, guiding horizontal fairness comparisons among entities within the same level and thereby quantifying individual perceptions of fairness. Building on this foundation, the study further calculates the maximum achievable fairness level for the group to determine whether it meets the preset fairness threshold requirement. Subsequently, two types of optimization mechanisms are constructed: a fairness-oriented model requiring additional costs, and an efficiency-oriented mechanism based on the deep deterministic policy gradient (DDPG) algorithm, designed to maximize the number of DMs meeting the fairness threshold. Finally, the Taihu Lake cross-regional water pollution control initiative serves as an empirical case study to validate the proposed method's effectiveness. Combined with sensitivity analysis and comparative experiments, its application advantages are thoroughly examined.

In group decision making (GDM) problems, fuzzy social networks (FSNs) provide a new theoretical framework for trust management among decision makers (DMs) and play a key role in weight allocation, opinion dissemination, and consensus building. However, the problem of trust risk still cannot be ignored. To this end, this study proposes an innovative GDM optimization method, TWD-FSN-A-PT, from the perspectives of optimization computation and decision-making application. The method combines the theory of three-way decision (TWD) theory and FSNs, aiming at solving the problem of trust risk and behavioral tendency in fuzzy environments. Specifically, the innovations of the method include: identifying and reducing pseudo-trust risk using the TWD theory; adopting a new mechanism to distinguish between selfish and altruistic behaviors of DMs by considering both group and individual optimization; and maximizing global stability by optimizing the model and respecting individual preferences, which ensures that the adjustment cost is minimized while reaching an efficient consensus. These innovative methods fully rely on the theory and techniques of applied mathematics and ensure the robustness of the model under different parameter settings. Finally, the TWD-FSN-A-PT method is applied to the regional electricity demand analysis, demonstrating the results of ranking the electricity demand at different time periods.

In the era of big data, the integration of data from multiple sources to enhance decision-making processes has become a crucial challenge. Traditional information fusion methods often struggle with incomplete multi-scale information systems, resulting in biased conclusions and an inability to fully leverage the potential connections within the data. This study addresses these limitations by proposing a novel consensus model that integrates asynchronous opinion evolution in the DeGroot model with dynamic trust-driven three-way decision. The method employs adaptive multi-scale clustering partitioning and mutual information to uncover potential associations among the original data, introduces an interval-based neighborhood representation and a weighted aggregation approach to more reasonably impute missing values, and determines the optimal scale through the analysis of the information entropy structure curve. Furthermore, considering the asynchronous behaviors and interactive influences among decision-makers in social networks, the proposed model incorporates a differentiated group consensus regulation method to achieve more flexible and robust group decision-making. The experimental results demonstrate the effectiveness of the method proposed in this paper, with significant improvements in key indicators such as the number of modifications and iterations required to reach a consensus, while maintaining a relatively low adjustment cost.Specifically, the number of modifications and the number of iterations achieved by the proposed method are the lowest among the compared methods, indicating its superior performance in consensus-reaching processes. These findings highlight the model’s ability to efficiently handle incomplete information and enhance the rationality and dynamic adaptability of group decision-making, making it a valuable tool for information fusion.

Three-way decision is a methodology that utilizes human cognitive thinking to handle multi-attribute decision-making with deferral decision-making. The key to achieving this goal is to reasonably fuse evaluation values from multiple attributes of alternatives to extract rules for classifying and ranking alternatives. There have been already lots of literature addressing this issue by considering the regret psychology of decision-makers. However, the regret theory oriented multi-attribute decision-making may lead to irrational or incomplete decision strategies. To tackle such a challenge, this paper introduces the idea of game theory into behavior three-way decision based multi-attribute decision-making (GBMADM) to weighted fuse regret and rejoice values of each alternative across all attributes to extract game rules for classifying and ranking alternatives. Firstly, a decision state set is fuzzified with the idea of TOPSIS and the weight of each attribute is determined based on the self-information of approximate accuracy from generalized fuzzy rough set theory. Secondly, a pair of utility functions is introduced to act as players to play in game. Two pairs of weighted regret functions and weighted rejoice functions are achieved by fusing the regret values and rejoice values of each alternative across all attributes, respectively. A payoff matrix for each alternative is then constructed by fusing the weighted regret value and weighted rejoice value. All decision rules for classification and ranking are thereafter extracted from the payoff matrix through optimal Nash equilibrium solutions. Finally, a practical example and simulation experiments on two benchmark datasets demonstrate the superiority of the proposed method compared to representative methods.

Multi-source information fusion has become the cornerstone of modern intelligent decision systems, yet the explosive volume, heterogeneity and high dimensionality of crowd-contributed data severely challenge the efficiency and fairness of large-scale group decision-making (LSGDM). To transform this “data richness” into “decision wisdom”, dimensionality-reduction technologies have evolved from optional pre-processing modules to indispensable fusion-centric enablers that compress numerous decision makers into a compact but representative subgroup structure while preserving collective knowledge. By systematically reviewing 345 publications (2014-2025) retrieved from the Web of Science, this paper proposes the first information-fusion-oriented taxonomy of LSGDM dimensionality-reduction techniques, clustering them into: (i) clustering-analysis-based fusion of large-scale preference data, (ii) complex-network-based community detection that fuses relational information, and (iii) specialized hybrid methods that fuse multi-modal or semi-supervised cues. This review critically analyzes the above techniques, discusses their roles in alleviating scale dilemmas, improving decision quality and process operability, and establishes an evaluation system covering internal and external validity. Finally, it summarizes key challenges in information fusion, including dynamic streaming preferences, ultra-large sparse networks, and privacy-preserving fusion, and prospects paradigm optimization and key technologies such as semi-supervised granular ball fusion, autoencoder-based deep representation fusion, ensemble learning, and multimodal fusion, providing references for dimensionality reduction to support efficient, reliable, and fair LSGDM in the big data era.

Applied-mathematics and theoretical-computer-science viewpoints jointly frame large-scale group decision-making as a stochastic, graph-constrained optimization problem. Multi-granularity probabilistic linguistic preference relations encode agents’ uncertain utilities via discrete probability distributions over graded linguistic terms. Fuzzy social networks represent trust through real-valued adjacency matrices whose entries are updated by closed-form algebraic operations. A dynamic self-confidence mechanism recasts each agent’s belief mass as a state variable governed by a consensus-error gradient flow. The resulting algorithmic pipeline exhibits poly-logarithmic iteration complexity with respect to agent count, while the worst-case modification cost remains upper-bounded by a constant multiple of the initial inconsistency index. Empirical analysis of 38,900 online tourism reviews delivers a consensus level of 0.9873 within two iterations at a normalized cost of 0.006, outperforming seven state-of-the-art baselines. Beyond tourism, the framework applies to any multi-agent system whose preference topology is representable as an uncertain hyper-graph, including e-commerce recommenders, federated learning aggregators, and distributed medical-diagnosis platforms. Ongoing research incorporates online-learning regret minimizers to adapt model parameters under adversarial, non-stationary conditions.

In the field of group decision-making (GDM), the complex heterogeneous data continuously challenges the traditional single decision-making model, highlighting the limitations of traditional methods in handling multi-dimensional data and dynamic scenarios. Although information fusion is of great significance for GDM, there are still significant deficiencies in existing research within the framework of multi-scale information systems (MSIS). In particular, there is an urgent need to address the challenges of dealing with multi-structural data and managing the complex behaviors of decision-makers (DMs). Firstly, a novel concept, the heterogeneous multi-scale information system (HMSIS), is put forward. This system innovatively integrates utility value quantification analysis, fuzzy preference relation modeling, preference ranking algorithms, and equivalence class partitioning techniques, thereby constructing a highly realistic simulation framework for real-world data. Through this cross-paradigm data integration approach, the HMSIS provides a more adaptable and scalable theoretical foundation for GDM, effectively resolving the limitations of traditional models in handling complex data structures. Building on this foundation, this paper further develops the consensus-trust multi-network opinion interaction mechanism. This mechanism shatters the constraints of one-way information transmission in traditional decision-making processes. By devising an adaptive opinion exchange protocol, it enables multi-round and multi-dimensional information interactions among decision-makers. Additionally, innovative behavior monitoring and intervention rules are introduced, which can detect irrational behaviors of DMs, such as overconfidence and non-cooperation, in real time. Through dynamic weight adjustment, intelligent guidance strategies, and other means, targeted management is implemented to ensure the stability and effectiveness of the group decision-making process. Moreover, this paper constructs an optimized consensus reaching process (CRP). By embedding an optimization model and under the intelligent regulation of a virtual decision-making coordinator, it optimizes both the efficiency of decision-making information transmission and the accuracy of opinion convergence simultaneously. With the core objectives of minimizing the decision adjustment distance and shortening the consensus-reaching time, and combined with a dynamic weight allocation algorithm, this model achieves efficient and fair consensus building in complex decision-making environments. Finally, empirical studies conducted on a real-world dataset demonstrate the remarkable superiority of the proposed method. The experimental results further validate the method’s robust performance in handling heterogeneous data and complex decision-making scenarios.

Multivariate traffic flow forecasting requires accurate multi-horizon prediction with interpretability, while maintaining stable performance under non-stationarity. Recent Gaussian linear fuzzy information granules (GLFIGs) provide compact and explainable representations for traffic forecasting, yet the commonly used “segmentation-granulation-prediction” pipeline still suffers from three key bottlenecks in multivariate and multi-granular settings: (i) heuristic and parameter-sensitive time-domain segmentation may produce unstable boundaries and spurious change points, making trend granules unreliable; (ii) granules across variables and granularities are often misaligned, where dynamic time warping (DTW)-style time warping or splitting and merging alignment can rewrite membership semantics and support structures, causing semantic drift and weakening interpretability; and (iii) granule-level forecasting tends to under-react to short-term details, degrading short-horizon performance. To address these issues, we propose FGT-Net, a multi-granular fuzzy fusion network that improves the FIG forecasting pipeline through three component-level innovations. First, dual-domain enhanced trend representation and analysis (DETRA) performs unsupervised trend discovery via frequency-time co-verification: spectral energy concentration in the frequency domain proposes intrinsic long-term and seasonal candidates, and time-domain boundary consistency validates and refines cut points to suppress spurious segmentation. Second, we develop a semantics-preserving granular alignment strategy that aligns multivariate GLFIG representations through convolution-based count alignment and similarity pooling, avoiding destructive split/merge operations and alleviating granularity mismatch. Third, a horizon-aware adaptive fusion head integrates short-term fluctuations with stable trends using exponentially decayed horizon weights, enabling responsive short-horizon forecasting while emphasizing macro-level trends for long horizons. Experiments on six real-world traffic datasets show that FGT-Net improves predictive accuracy while retaining interpretability: compared with representative baselines, root mean square error (RMSE) is reduced by 20.27% for short horizons and 12.65% for long horizons, indicating fewer large deviations and more stable forecasting errors under challenging conditions. Detailed descriptions and access information are available at https://github.com/Ronghua550/Dataset-2.

The advancement of technology and the rapid developments in the field of artificial intelligence have led to a surge in the research on decision-making in uncertain environments. Furthermore, individual decision-making is too simplistic to solve the complex decision-making problems posed by these challenges, leading to study group decision-making (GDM). Particularly, fuzzy social networks (FSNs) and fuzzy preference relations (FPRs) have important applications in GDM. In addition, probabilistic linguistic term sets (PLTSs) have succeeded as a bridge among natural language, fuzzy reasoning, and probability theory. However, the existing research on GDM under PLTSs faces three key challenges: flaws in PLTSs distance measurement, lack of FSN modeling, and the over-simplified feedback mechanism. These challenges severely impede the effectiveness and reliability of consensus reaching process (CRP) in complex decision-making scenarios. Motivated by these facts, this paper designs a three-way group consensus method based on FSNs under probabilistic linguistic preference relations (PLPRs), namely, the TWD-FSN-PLPR method. This method consists of three successive parts. The first part is the design of an improved consistency method based on the properties of PLTSs. Its main purpose is to ensure that the information on evaluations provided by the decision makers (DMs) maintains internal consistency, paving the way for subsequent GDM. The goal of the second part is to compute the DMs’ weights. Their own familiarity with the PLTS’s cross-entropy and self-confidence are used to construct a directed weighted FSN and then produce the weights from a metric based on social influence. The third part is the consensus reaching process, whose efficiency is improved by a combination of three-way decision and minimum cost, and implementing a penalty mechanism for non-cooperative DMs. In addition, the optimal alternative is selected using regret theory. The methodology is applied to a real case and compared with multiple methods to illustrate its rationality and superiority.

Clustering analysis is a fundamental unsupervised learning paradigm for revealing intrinsic data structures in the era of information explosion. Among various clustering approaches, graph theory-based methods, especially those utilizing minimum spanning trees (MST), have shown remarkable capability in capturing complex data distributions. However, existing MST clustering algorithms face notable limitations when integrated with granular ball (GB) computing. The single-pass GB construction process restricts the quality of the resulting granular structures, while the dependence on predefined parameters compromises the objectivity of clustering. To address these issues, this paper proposes GB-IMST, an MST clustering algorithm that integrates the GB model with the interquartile range (IQR) method through multi-source information fusion. Global sparsity and density indicators are combined to construct a multidimensional evaluation framework for assessing GB quality. By leveraging the IQR method, anomalous GBs are adaptively detected from both global and local perspectives, enhancing the alignment of granular structures with data distributions. An MST is then constructed based on GB centers, and the IQR method is further applied to automatically filter abnormal edge weight thresholds for generating candidate clustering partitions. In addition, an evaluation index tailored to MST clustering principles is developed by integrating intra-cluster cohesion, inter-cluster dispersion, and segmentation validity penalties, facilitating optimal cluster selection. A redistribution strategy ultimately assigns clustering results to original data points. Extensive experiments on ten benchmark datasets demonstrate that GB-IMST outperforms state-of-the-art algorithms such as GB-MST, GB-DP, and GBK-DPC. The source code is available at https://github.com/tingwu99/GB-IMST.

Existing multi-criteria sorting methods predominantly rely on preset classification thresholds or fixed numbers of alternatives for classification, exhibiting strong subjectivity and overlooking potential consensus correlations between classifications. In group decision-making (GDM), the consensus feedback mechanism drives the consensus reaching process (CRP) and gives rise to the problem of adjustment amount allocation among decision-makers (DMs). However, existing studies over-rely on consensus thresholds and neglect differences in DMs’ adjustment capabilities and sequences, which significantly reduces the applicability and accuracy of the methods. To address the above issues, this study proposes a novel group consensus method (NS-FPR-PM) integrating the Nash-Stackelberg game and preference maps within the framework of fuzzy preference relations (FPRs). Specifically, class probability thresholds are objectively derived through an optimization model; the classification results are then converted into preference maps based on these class probability thresholds to explore the inherent consensus relations, thereby eliminating reliance on consensus thresholds. The Nash-Stackelberg game model can characterize the differences in bargaining power among DMs, and an asynchronous adjustment mechanism is designed accordingly to achieve fair allocation of adjustment amount. Finally, we provide an example to illustrate the proposed method, the experimental results and analysis demonstrate that the method exhibits significant advantages over similar methods in terms of consensus reaching efficiency and unit adjustment conversion rate.

In the era of digital transformation, the large-scale deployment of sensors has led to the collection of highly complex and diverse data, posing significant challenges for multivariate time-series forecasting. Traditional forecasting approaches, often based on linear assumptions, are limited in their ability to capture the nonlinear temporal dynamics prevalent in real-world scenarios. To address these challenges, this study proposes an innovative multivariate prediction framework that integrates deep learning with traditional machine learning techniques. The framework incorporates an asymmetric transfer entropy coefficient (ATC) to identify genuine causal relationships among features, constructing a directed graph for feature importance ranking. This mechanism enhances feature selection by capturing both dynamic and static relationships among variables. An enhanced fuzzy C-means clustering algorithm with similarity constraint (SCFCM) is introduced, which incorporates cosine similarity and Euclidean distance to improve sample discriminability in high-dimensional spaces and enhance clustering accuracy. Bayesian optimization is employed to dynamically determine the kernel sizes and numbers of the convolutional neural network-Transformer prediction network, thereby improving feature extraction efficiency. The unified architecture integrates feature selection, clustering, and forecasting, achieving superior predictive performance. This comprehensive prediction model is referred to as ATC-SCFCM-dynamic kernel-determined CNN-Transformer (DKCNT). Experiments on six real-world datasets demonstrate that ATC-SCFCM-DKCNT consistently outperforms state-of-the-art methods in terms of prediction accuracy and computational efficiency, highlighting its strong generalization ability and robustness in handling complex, high-dimensional data.

In the era of artificial intelligence, the complexity and diversity of data have posed unprecedented challenges for prediction tasks. Fuzzy information granules (FIGs) have emerged as a powerful technique to simplify these tasks by reducing data dimensionality and extracting interpretable trend information. This survey provides a comprehensive overview of the current state of FIG-based neural network prediction models, highlighting their theoretical foundations, practical applications, and future research directions. The integration of FIGs with neural networks enhances prediction accuracy and interpretability, making them suitable for complex and high-dimensional data. The main contributions of this survey include a systematic review of the theoretical underpinnings of FIGs and neural networks, a detailed analysis of the strengths and weaknesses of various FIG-based models, and an exploration of their applications in critical domains such as transportation, energy, and healthcare. Future research directions include developing more advanced and interpretable models, exploring new applications, and fostering interdisciplinary collaborations. Emerging trends such as quantum computing, hybrid neural architectures, and edge AI are expected to further enhance the capabilities of FIG-based neural network models. This survey is of significant value as it provides a unified perspective on the advancements in FIG-based neural network prediction models and highlights the unique contributions of FIGs in enhancing model interpretability and performance.

Granular ball computing (GBC) constitutes a geometrically interpretable paradigm for characterizing intricate data distributions and supporting supervised classification. However, prevailing granular ball generation (GBG) techniques predominantly adhere to top-down splitting or bottom-up merging strategies initiated from the finest granularity, thereby frequently overlooking subtle local structures and exhibiting substantial sensitivity to initial center configurations. These shortcomings typically induce redundant granular balls (GBs) or unstable partitions, ultimately undermining predictive accuracy. To remedy these limitations, this paper presents a boundary-driven GBG and classification framework grounded in three-way decision (TWD) theory, designated TWD-BDGB. The proposed generation mechanism adopts a boundary-region-driven bottom-up expansion strategy operating at intermediate granularity levels. Within this architecture, radii are adaptively constrained by heterogeneous blocking boundaries, whereas geometric distances induce fuzzy membership degrees without recourse to manual parameters. Adaptive thresholds segregate internal samples into positive and boundary regions, where high-uncertainty boundary instances serve as candidate seeds for recursive local GB construction. This design enables explicit modeling of interclass boundaries while preserving complete sample coverage. Moreover, homogeneous GB merging coupled with heterogeneous overlap resolution is performed to attenuate intra-class structural redundancy. For classification, a cooperative decision rule establishes interaction scopes via nearest-center distances and consolidates weighted contributions from multiple GBs aggregated at the class level. Notably, single-point GBs are retained as discriminative evidence, fostering stable and parameter-free inference. Extensive empirical assessments confirm that the TWD-BDGB framework delivers competitive classification accuracy together with exceptional robustness. The related experimental code has been released at (https://github.com/sw380957-create/TWD-BDGB).

Accurate and reliable interval prediction is essential for dispatch, resource planning, and risk management in energy and power systems. However, prevailing approaches often suffer from feature redundancy, inadequate treatment of temporal dependencies, and poorly calibrated prediction intervals. To address these limitations, this paper proposes DFS-FDP-FQAR, an interval prediction framework that integrates dynamic feature selection (DFS), frequency-domain prediction (FDP), and fuzzy quantile association rules (FQARs). The framework dynamically selects informative features to mitigate redundancy, leverages time-frequency transforms to capture complex temporal regularities, and constructs adaptive, better-calibrated intervals via fuzzy association rules. In the point-forecasting stage, the FDP module couples a long short-term memory (LSTM) backbone with a sparse-attention mechanism: the LSTM models periodic components in the real part, while sparse attention accentuates abrupt signals in the imaginary part, thereby enhancing expressiveness. In the interval-forecasting stage, an FQAR procedure based on residuals and quantile-level fuzzy memberships produces data-adaptive, well-calibrated prediction intervals. Extensive experiments on multiple real-world power-energy datasets demonstrate superior point accuracy and interval reliability relative to state-of-the-art baselines. Specifically, the proposed model achieves a prediction interval coverage probability (PICP) from 95.84% to 96.96%, while maintaining a prediction interval normalized average width (PINAW) between 0.0800 and 0.3992. These results highlight the robustness and practicality of the model in engineering applications, outperforming existing benchmark models in terms of both coverage probability and interval width, and validating the effectiveness of the theoretical innovations.