Feature selection in partially labeled data is critical for knowledge acquisition in large-scale applications, yet it remains challenging due to label scarcity. To address this, we propose a novel semi-supervised method for partially labeled generalized multi-scale multiset-valued decision systems (p-GMMDSs). Our approach first introduces three Hellinger distance-based measures to compute object distances, construct k-nearest neighbor classes, and derive maximum distribution decisions for label prediction. Using these decisions, we transform the p-GMMDS into three fully labeled GMMDSs. We then define positive region optimal scales and their corresponding reducts for each GMMDS, ensuring minimal feature subsets that preserve classification consistency. Finally, we design efficient heuristic algorithms to identify optimal scale reducts. The experiments on 12 UCI benchmark datasets validate the effectiveness of our method.

Optimal scale combination selection is a crucial issue in research on knowledge acquisition from multi-scale data. In a dynamic environment, the original optimal scale combinations may become invalid with the addition of new samples. In this paper, dynamic updates of optimal scale combinations based on the Dempster-Shafer theory of evidence in incomplete generalized multi-scale hybrid decision tables (IGMHDTs) composed of numerical and categorical conditional attributes are investigated. Fuzzy relations and similarity relations in an IGMHDT are first defined based on membership degrees, and information granules are then constructed through the cut sets of fuzzy classes generated by each fuzzy relation. Approximation operators, belief measures, and plausibility measures of an object set under different scale combinations are presented within the IGMHDT. To select suitable subsystems from IGMHDTs for subsequent knowledge discovery, concepts of belief optimal scale combinations (BOSCs) and plausibility optimal scale combinations (POSCs) are further introduced. Finally, BOSC and POSC update methods for incremental dynamic IGMHDTs are developed. Based on a BOSC in an original IGMHDT, a dynamic algorithm for the selection of a BOSC in the updated IGMHDT is implemented. Experiments are performed on 16 datasets and the dynamic BOSC selection algorithm is shown to be fast and effective.

Optimal scale selection represents a pivotal challenge in knowledge acquisition within multi-scale decision tables. In practical applications, most information tables rely on dominance relations with unknown or missing attribute values, rather than equivalence relations. This paper addresses optimal scale selection in incomplete multi-scale ordered data using the Dempster-Shafer theory of evidence (DSTE). We first formalize incomplete multi-scale ordered information tables (IMOITs) and incomplete multi-scale ordered decision tables (IMODTs). Subsequently, we construct dominance relations and their resultant dominance classes across scales in IMOITs. We further define upper and lower approximations of upward union of decision classes under decision dominance relations at different scales in IMODTs, and we also present fundamental relationships between these approximations. With reference to plausibility and belief functions in the DSTE, we then define the notions of ≥ -plausibility/belief optimal scale in IMOITs, and ≥ -relative plausibility/belief optimal scale in IMODTs. We clarify relationships between these new concepts of optimal scales and existing ones. We demonstrate that, in an IMOIT, a scale is ≥ -belief optimal if and only if (iff) it is ≥ -optimal. In an IMODT, a scale is Upp^≥ (respectively, Low^≥ ) optimal scale iff it is ≥ -relative plausibility (respectively, belief) one. Furthermore, in a consistent IMODT, the notions of ≥ -optimal and ≥ -relative belief optimal are equivalent, while they are indeed different notions in an inconsistent IMODT. Finally, there is no fixed relationship between the concepts of ≥ -belief optimal scale (respectively, ≥ -relative belief optimal scale) and ≥ -plausibility optimal scale (respectively, ≥ -relative plausibility optimal scale) in IMOITs (respectively, IMODTs).

In the digital era, data streams in practical applications are growing explosively and exhibiting high-dimensional dynamics and real-time evolution. Moreover, multi-scale data have gained significant attention due to their rich knowledge representational capacity. Online streaming feature selection methods have attracted widespread at tention for their efficient feature selection performance in dynamic data environments. Nevertheless, existing online streaming feature selection methods primarily focus on single-scale data and struggle to handle streaming multi-scale data, where feature scales arrive over time. To address the aforementioned issues, this paper fo cuses on two streaming scale states and proposes two novel online streaming scale and feature selection methods with multi-scale k-distance neighborhood granulation, respectively. First, a novel multi-scale k-distance neigh borhood granulation method is developed based on the k-nearest neighbor idea and a corresponding multi-scale k-distance neighborhood rough set is constructed. Second, considering the differences in streaming multi-scale data under different streaming scale scenarios in the real world, two states of streaming scale are formalized, and a streaming scale selection model based on a multi-scale k-distance neighborhood rough set is constructed. Building upon this model, two online streaming scale selection algorithms are designed. Subsequently, a forward feature selection algorithm based on the obtained optimal scale combination is proposed to reduce redundant features. Furthermore, by integrating these theories and algorithms, two online streaming scale and feature selec tion algorithms are developed. Finally, experimental results indicate that the proposed methods can effectively handle streaming multi-scale data, and compared with seven other advanced methods, the proposed methods demonstrate significantly superior performance.

Rough set theory represents a crucial methodology in the field of soft computation. Its boundary operator’s axiomatic properties mainly rely on the axiomatic framework of the approximation operator. However, the axiom system for the boundary operator has yet to be directly established. To explicitly characterize the axiomatic properties of boundary operators and further explore the effectiveness of boundary methods in feature selection, we first conduct a systematic comparison of relevant rough set models through the boundary region. The axiomatic system for boundary operators is presented directly. Secondly, we establish the equivalence between two rough set models based on binary relations and two models grounded in coverings. The approximation operators corresponding to B1 and B2-types are equivalent to those generated by a tolerance and preorder relation, respectively. Thirdly, to evaluate the effectiveness of the proposed boundary method, we designed forward and backward feature selection algorithms based on this approach. Finally, we compared the performance of various boundary operators, including fuzzy rough sets and whale optimization algorithms. Numerical experiments indicate that among the algorithms above, the B2-type boundary rough set model demonstrates significant advantages in terms of computational speed while maintaining a certain level of classification accuracy.

Multi-label feature selection (MFS) aims to select effective features that can be associated with multiple class labels. However, existing MFS methods usually constrain the feature selection matrix through regularization parameters, which does not explicitly determine the number of features to be retained. Moreover, conventional MFS methods only consider local pairwise structures and ignore the high-order structural information of the multi-label data. To address the abovementioned problems, we present a novel MFS method, named learning high-order structure information for efficient multi-label feature selection. Specifically, we first design a regression model based on & ell;(2,0 )norm constraint, which can effectively avoid the search for regularization parameter. Second, adaptive diffusion graph are introduced to learn high-order structural information, which can be fully exploited in global multi-label data. Finally, the well-defined objective function with an efficient optimization solution is constructed to perform the MFS based on the above two-step instructions. Experiments on real datasets and comparisons with state-of-the-art methods clearly validate the effectiveness of the proposed method

Multi-label learning plays a crucial role in numerous real-world applications, where each instance may be associated with multiple semantic labels. However, in practical scenarios, label noise is widespread and poses a significant challenge, as it can simultaneously distort multiple labels due to ambiguous annotations, human fatigue, or automated labeling inaccuracies. While considerable progress has been made in developing noise-robust methods for single-label learning, addressing noise in multi-label settings remains substantially more challenging due to the intricate interplay among multiple potentially corrupted labels. This underscores the pressing need for effective label correction strategies tailored to noisy multi-label learning. To address this gap, we propose a latent contrastive embedding framework designed for noisy multi-label scenarios. The approach not only learns robust feature representations through supervised contrastive learning but also dynamically identifies clean labels via a small-loss guided sample selection strategy. Moreover, the embedding and label correction processes are jointly optimized, allowing the model to capture the semantic structure of both features and labels under noisy conditions. Specifically, we adopt a small-loss criterion to distinguish clean from noisy samples during the early training phase. In addition, a balanced loss is introduced to mitigate the effects of label imbalance and sample difficulty. Finally, comprehensive experiments conducted under various patterns and levels of label noise demonstrate the superior robustness and generalization ability of the proposed method in noisy multi-label classification tasks.

Existing methods for analyzing multi-scale interval-valued ordered data typically rely on fixed-startpoint, full-path traversal to identify optimal scale combinations (OSCs). This necessitates restarting the entire search process upon sample updates, incurring significant computational redundancy. To address this limitation, we establish a knowledge acquisition framework for generalized multi-scale interval-valued ordered decision systems (GMIvODSs). First, we construct dominance relations using interval dominance degrees and overlap measures. A threshold-adaptive update mechanism ensures monotonicity of these relations across scales. We then introduce interval-valued dominance conditional entropy (IvDCE) invariance as the criterion for OSC selection, with attribute importance guiding scale screening order. Second, we design an incremental mechanism that updates the dominance relation matrix locally, preserving prior results. Theoretically, we prove the partial order inheritance of OSCs under sample increments. Leveraging this property, our proposed algorithm initiates directed searches from the previous IvDCE-optimal scale combination (IvDCE-OSC), avoiding redundant computation. Experiments demonstrate that the IvDCE-OSC achieves an average classification accuracy 0.91% higher than other scale combinations. In incremental scenarios, our dynamic algorithm reduces runtime by 67.6% on average compared to static recomputation approaches.

Granular-ball computing has emerged as a powerful framework for managing uncertainty, offering a more adaptive and interpretable approach to data analysis. In contrast, traditional fuzzy rough sets, which rely on fuzzy relations between individual data points, often suffer from limited granularity control, sensitivity to noise, and difficulties in handling large-scale or complex datasets. Moreover, the point-wise nature of fuzzy relations restricts the ability to capture group-based structural information inherent in real-world data. To address these limitations, we propose the granular-ball fuzzy rough set model, which integrates fuzzy rough set theory with the granular-ball computing paradigm. This novel model represents data in the form of fuzzy granular-balls, each encompassing a group of similar instances, thereby enhancing granularity management and improving robustness against noise and data sparsity. The lower and upper approximations in this model are redefined using these fuzzy granular-balls rather than individual objects, with the purity of each granular-ball directly influencing the certainty and precision of classification boundaries. This approach facilitates smoother and more stable delineations of positive, negative, and boundary regions in uncertain classification tasks. Additionally, the model introduces monotonous fuzzy granular-ball partitions that evolve with expanding attribute sets, providing a practical mechanism for evaluating attribute significance in feature selection. Overall, the proposed model retains the mathematical rigor of traditional fuzzy rough set theory while offering enhanced flexibility, interpretability, and effectiveness in handling real-world uncertain data.

Multilabel Class-Incremental Learning (MLCIL) refers to a variant of class-incremental learning and multilabel learning where models are required to learn from images or data associated with multiple labels, and new sets of classes are introduced incrementally. However, most existing MLCIL methods tend to rely heavily on limited single-view features, which makes it challenging for them to effectively capture class-specific characteristics and the correlations between different labels. Furthermore, MLCIL faces difficulties related to both intra-class and inter-class imbalances, which arise from the varying frequencies of class occurrences during each incremental session. To address these issues, we propose a novel MLCIL model called the Multi-View Fusion Graph Attention Network (MVGAT). First, the MVGAT architecture includes a multi-view feature extraction module that fuses class node features from three different perspectives of images, effectively capturing both local and global class-specific information. Second, MVGAT introduces a multi-view attention fusion module that combines the multi-view class node features based on label correlations. Importantly, the attention fusion modules trained in previous learning sessions are preserved, helping to mitigate catastrophic forgetting by providing independent probability predictions for their respective learned classes. Additionally, MVGAT is equipped with a pseudo-label correction module to enhance the accuracy of pseudo-labels by integrating predictions from the current session with those from historical frozen attention fusion modules. Moreover, an asymmetric loss function has been developed to balance intra-class and inter-class performance by dynamically adjusting negative focus parameters based on class occurrence frequency. Finally, experimental results on benchmark datasets demonstrate that MVGAT outperforms existing state-of-the-art methods.

The integration of three-way decision (3WD) into multiple attribute decision-making (MADM) problems has emerged as a pivotal research area. 3WD can effectively manage the inherent uncertainty within the decision-making process. Additionally, it offers a semantic interpretation of the outcomes. In this paper, we introduce two innovative 3WD-MADM approaches, with a focus on granule selection and the handling of multi-type information in the framework of three-way decisions. Firstly, we construct maximal consistent blocks (MCBs)-based pessimistic and optimistic probabilistic rough fuzzy set (RFS) models and investigate their properties to ascertain their efficacy and reliability in decision-making contexts. Then, we define relative loss functions associated with "good state" and "bad state" scenarios. Building on this, we introduce four types of 3WDs based on our newly proposed optimistic and pessimistic probabilistic RFSs. Furthermore, we integrate the 3WDs information from both scenarios to formulate optimistic and pessimistic 3WD-MADM approaches, handling both single-valued fuzzy and intuitionistic fuzzy information. Finally, we contrast our proposed methodologies with the current MADM methods, and demonstrate their validity, significance and generalization ability.

Multi-instance learning (MIL) is a potent framework for solving weakly supervised problems, with bags containing multiple instances. Various embedding methods convert each bag into a vector in the new feature space based on a representative bag or instance, aiming to extract useful information from the bag. However, since the distribution of instances is related to labels, these methods rely solely on the overall perspective embedding without considering the different distribution characteristics, which will conflate the varied distributions of instances and thus lead to poor classification performance. In this paper, we propose the dual-perspective multi-instance embedding learning with adaptive density distribution mining (DPMIL) algorithm with three new techniques. First, the mutual instance selection technique consists of adaptive density distribution mining and discriminative evaluation. The distribution characteristics of negative instances and heterogeneous instance dissimilarity are effectively exploited to obtain instances with strong representativeness. Second, the embedding technique mines two crucial information of the bag simultaneously. Bags are converted into sequence invariant vectors according to the dual-perspective such that the distinguishability is maintained. Finally, the ensemble technique trains a batch of classifiers. The final model is obtained by weighted voting with the contribution of the dual-perspective embedding information. The experimental results demonstrate that the DPMIL algorithm has higher average accuracy than other compared algorithms, especially on web datasets.

As a computing paradigm inspired by human cognition, granular computing has demonstrated remarkable effectiveness in processing large data sets. Multi-scale rough set analysis, a prominent framework within multi-granular computing, requires optimal scale selection as a critical prerequisite for knowledge extraction from multi-scale data. This study investigates optimal scale selection in generalized multi-scale set-valued ordered information systems (GMSOISs) using Dempster-Shafer evidence theory and information quantification. We first formalize GMSOISs by defining granular information transformations based on inclusion criteria. We then establish dominance relations over object sets induced by attribute subsets under different scale combinations, along with their associated information granules. Building on these constructs, we further derive lower/upper approximations and quantify belief/plausibility degrees of decision dominance classes in generalized multi-scale set-valued ordered decision systems (GMSODSs). Finally, six types of optimal scale combinations are rigorously defined for GMSOISs, consistent GMSODSs, and inconsistent GMSODSs, and their relationships are systematically elucidated. Case studies also validate the proposed theoretical framework with concrete examples.

When processing multi-scale hybrid data, the existing methods are insufficient to directly select the optimal scale for different types of data. To deal with this issue, the concept of generalized multi-scale hybrid decision systems (GMHDSs) consisting of numerical, nominal and set-valued values is first introduced. Then, under a scale combination, the information granules of different types of attributes in a GMHDS are constructed and they further fused as the granules of the system. Based on these granules of a given scale combination, positive region and conditional entropy are specified in a GMHDS. To select appropriate single scale systems to keep the positive region and the conditional entropy unchanged for final decision, concepts of positive region optimal scale combinations (POSCs) and conditional entropy optimal scale combinations (CEOSCs) in GMHDSs are defined, respectively. Furthermore, algorithms for calculating a POSC and a CEOSC in a GMHDS are also formulated. Finally, a comparative study of our methods with these based on original data under KNN and NB classifiers is conducted on twelve UCI datasets for the assessment of their classification performance. The experimental results indicate that the proposed methods are of better classification performance than the original data based methods in most cases.

Partial multilabel learning is a pivotal area in machine learning that tackles scenarios where training instances are annotated with a set of candidate labels, only a subset of which is relevant. Existing approaches typically rely on global-level feature learning or noise disambiguation; however, they often struggle to effectively capture the multigranularity relationships inherent in feature and label spaces, and tend to overlook critical intrafeature information essential for accurate label discrimination. To address these limitations, we propose a novel partial multilabel learning framework based on a dynamic coarse-to-fine granularity feature aggregation strategy, which hierarchically extracts feature representations across multiple levels of granularity and dynamically emphasizes label-relevant feature components. Specifically, the dynamic fine-granularity graph captures label-specific local information by modeling the fuzzy aggregations among fine-granularity feature components, while the dynamic coarse-granularity graph learns adaptive label representations by identifying feature-aware correlations of labels and suppressing noise. By jointly leveraging these two complementary granularity levels, the model effectively integrates multilevel semantic relationships and enhances the overall discriminative capacity of the learned features. Extensive experiments conducted on benchmark datasets under varying noise conditions demonstrate that the proposed method consistently outperforms state-of-the-art approaches in partial multilabel classification.

By offering a robust framework, granular computing empowers the field to effectively navigate and manage such challenging information, thereby facilitating human-like reasoning and decision-making capabilities. Within this context, a multi-scale information system (MSIS) serves as a complex big data system with inherent fuzziness. It allows for the comprehensive description of problems at different granularities and levels, presenting an opportunity to extract valuable knowledge for decision-making research. However, achieving effective collaboration between humans and machines during the decision-making process remains a significant task that warrants attention. Consequently, the paper introduces a novel method known as PT-IF-G3WD, which is based on prospect theory and utilizes intuitionistic fuzzy numbers (IFNs). By focusing on the challenges of decision risks and bounded rationality in uncertain multi-scale decision information systems (MSDISs), the primary objective of this method is to address the needs of MSDISs within a generalized three-way decision (G3WD) framework. Lastly, novel rules for three-way classification and ranking are developed, taking into account the perspective of IFNs. The experimental results on real-world datasets demonstrate the effectiveness and stability of the PT-IF-G3WD method.

Partial multi-label (PML) learning refers to the modeling of prediction patterns from data annotated with partially correct labels. Label embedding that finds a compact representation between the input and output spaces begets a family of efficient multi-label classification algorithms. Nevertheless, most existing label embedding methods fail to capture an accurate subspace when a large portion of data points are completely unlabeled, which can always lead to performance degradation. There are three specific problems to be addressed with semi-supervised embedding methods for multi-label (ML) learning: (1) The spaces of features and labels need to be linked together for co-training; (2) The shared latent patterns underlying in the two spaces need to be explored; (3) The embedded subspace should be capability of handling the erroneously labeled data points and absolutely unlabeled data points simultaneously. To this end, we formulate a PML learning framework via a compact and shared label embedding in semi-supervised setting. In particular, the tagging information and the input discriminative information are linked together into a shared label basis subspace by minimizing the reconfiguration loss from the shared subspace to the label space and simultaneously maximizing the dependence of the shared subspace and the feature space. Moreover, the feature and label manifolds provide auxiliaries for the framework construction. Theoretical and applied study demonstrate that the proposed approach is effectiveness.

Matrix factorization is one of the fundamental approaches of recommender systems. With the popular L2 loss, learning models tend to overfit significantly deviated predictions. However, predicting the actual rating of 5 as 1 or 2 makes no essential difference in the application. In this paper, we design a sigmoid-like function to control the loss of each individual prediction, which has two advantages. First, it reduces the loss corresponding to significantly deviated predictions. Therefore, the impact of these predictions, some of which may be caused by outliers, is also reduced. Second, it is independent of two classical over-fitting control techniques using regular terms and validation data, respectively. Hence, it can be combined with them to form a more powerful method. Experiments are undertaken on six benchmark datasets in comparison with different losses. Results show that the proposed loss function has good performance in terms of MAE, RMSE, and NDCG, however not so good in terms of HR and MAP.

One of the current research gaps in multi-scale data analysis is studying information systems characterized by attributes with interval sets as attribute values and multiple scales. To address this gap, we first introduce the concepts of a multi-scale interval-set information system (MISIS) and a multi-scale interval-set decision table (MISDT). We then define the similarity relation between objects in an MISIS and the corresponding rough approximations. We further propose the positive region optimal scale, the modified conditional entropy optimal scale, and the positive complementary conditional entropy optimal scale in an MISDT. We examine the relationships among these optimal scales in consistent and inconsistent MISDTs and show that the positive region optimal scale and the modified conditional entropy optimal scale are equivalent in a consistent MISDT, while in an inconsistent MISDT, the positive region optimal scale is the same as the positive complementary conditional entropy optimal scale, and the modified conditional entropy optimal scale is not greater than the positive complementary conditional entropy optimal scale. Based on the optimal scale, we also develop attribute reduction approaches in MISDTs. Finally, through experimental analysis of data on the UCI dataset, we verify the effectiveness and reasonableness of our proposed methods.

Mining association rules are a major area of research in data mining, as there are typically a large number of rules in each data set. And extracting necessary rules from each data set requires efficiency and careful consideration. In this paper, we propose a novel mining algorithm for efficiently acquiring positive and negative quantitative association rules (positive and negative QA-rules) in a fuzzy or multi-valued ordered context based on a three-way concept lattice (3CL). To this end, a new 3CL, called a one-sided fuzzy three-way concept lattice (OF3WC-lattice), is constructed based on a fuzzy formal context (FFcontext). The designed OF3WC-lattice describes the dependencies between objects and attributes, whether in the original FFcontext or its complement context. And the OF3WC-lattice is based on two kinds of two-way operators to make it consistent with practical linguistics. In addition, we propose an algorithm for constructing an OF3WC-lattice through analyzing relationships between the novel concept lattice and traditional one-sided fuzzy concept lattices. Experimental results demonstrate that our method effectively mines positive and negative QA-rules.