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.

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.

The integration of granular computing within human-inspired computational intelligence is crucial for addressing the complexities and uncertainties inherent in information. 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. Additionally, granular computing promotes a holistic and interdisciplinary approach to the development of intelligent systems. 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. In particular, this paper introduces a matrix theory-based$q$-consistent sub-system extraction mechanism as the initial design, which enables rapid attainment of optimal information acquisition. Second, the data information from multiple optimal sub-systems is fused using a group decision-making (GDM) perspective, incorporating binary relationships among the objects to accomplish the global evaluation of the objects. 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.

A granular structure of intuitionistic fuzzy (IF) information presents simultaneously the similarity and diversity of samples. However, this structural representation has rarely displayed its technical capability in data mining and information processing due to the lack of suitable constructive methods and semantic interpretation for IF information with regard to real data. To pursue better performance of the IF-based technique in real-world data mining, in this article, we examine information granularity, information entropy of IF granular structures, and their applications to data reduction of IF information systems. First, several types of partial-order relations at different hierarchical levels are defined to reveal the granularity of IF granular structures. Second, the granularity invariance between different IF granular structures is characterized by using relational mappings. Third, Shannon's entropies are generalized to IF entropies and their relationships with the partial-order relations are addressed. Based on the theoretical analysis above, the significance of intuitionistic attributes using the information measures is then introduced and the information-preserving algorithm for data reduction of IF information systems is constructed. Finally, by inducing substantial IF relations from public datasets that take both the similarity/diversity between the samples from the same/different classes into account, a collection of numerical experiments is conducted to confirm the performance of the proposed technique.

In this article, a novel fuzzy α-neighborhood operator with reflexivity is constructed and a new fuzzy rough set model based on the fuzzy α-neighborhood operator is proposed. Aiming at decision-making in information systems with real-valued information systems (RVISs), we first utilize data normalization method to effectively transform RVISs into information systems with fuzzy-valued information systems (FVISs). Then, we use the fuzzy α-neighborhood-based fuzzy rough set model to convert FVISs into information systems with intuitionistic fuzzy-valued information systems (IFVISs). By adopting the idea of the PROMETHEE II method, we develop three different sorting decision-making schemes on IFVISs, which consist of the subtraction of intuitionistic fuzzy numbers, sorting functions, and intimacy coefficients. Finally, numerical experiments demonstrate the effectiveness of our method. Comparative studies and Spearman rank correlation analyses explain the superiority of our schemes. Experimental results verify the stability of the performance of our strategy.

Attribute subset selection is an important issue in data mining and information processing. However, most automatic methodologies consider only the relevance factor between samples while ignoring the diversity factor. This may not allow the utilization value of hidden information to be exploited. For this reason, we propose a hybrid model named intuitionistic fuzzy (IF) rough set to overcome this limitation. The model combines the technical advantages of rough set and IF set and can effectively consider the above-mentioned statistical factors. First, fuzzy information granules based on IF relations are defined and used to characterize the hierarchical structures of the lower and upper approximations of IF rough set within the framework of granular computing. Then, the computation of IF rough approximations and knowledge reduction in IF information systems are investigated. Third, based on the approximations of IF rough set, significance measures are developed to evaluate the approximation quality and classification ability of IF relations. Furthermore, a forward heuristic algorithm for finding one optimal reduct of IF information systems is developed using these measures. Finally, numerical experiments are conducted on public datasets to examine the effectiveness and efficiency of the proposed algorithm in terms of the number of selected attributes, computational time, and classification accuracy.

Attribute reduction is one of the biggest challenges encountered in computational intelligence, data mining, pattern recognition, and machine learning. Effective in feature selection as the rough set theory is, it can only handle symbolic attributes. In order to overcome this drawback, the fuzzy rough set model is proposed, which is an extended model of rough sets and is able to deal with imprecision and uncertainty in both symbolic and numerical attributes. The existing attribute selection algorithms based on the fuzzy rough set model mainly take the angle of “attribute set,” which means they define the object function representing the predictive ability for an attribute subset with regard to the domain of discourse, rather than following the view of an “object pair.” Algorithms from the viewpoint of the object pair can ignore the object pairs that are already discerned by the selected attribute subsets and, thus, need only to deal with part of object pairs instead of the whole object pairs from the discourse, which makes such algorithms more efficient in attribute selection. In this paper, we propose the concept of reduced maximal discernibility pairs, which directly adopts the perspective of the object pair in the framework of the fuzzy rough set model. Then, we develop two attribute selection algorithms, named as reduced maximal discernibility pairs selection and weighted reduced maximal discernibility pair selection, based on the reduced maximal discernibility pairs. Experiment results show that the proposed algorithms are effective and efficient in attribute selection.

Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based fuzzy rough approximation operators determined by a fuzzy implication operator ℐ are i

The classical rough set theory is based on the conventional indiscernibility relation. It is not very good for analyzing incomplete information. Some successful extended rough set models based on different non-equivalence relations have been proposed

Abstract The notion of information systems provides a convenient tool for knowledge representation of objects in terms of their attribute values, while partial ordering is usually used to research the rough monotonicity of an uncertainty measure in information systems. In this paper, we first reveal the limitations of existing partial orderings to describe information granulations in information systems with several illustrative examples. Then, a generalized partial ordering with a set‐size nature is proposed to overcome their shortcoming and some of its important properties are derived. Finally, we prove that several existing information granulations all satisfy the granulation monotonicity induced by the proposed partial ordering. The presented partial ordering appears to be well suited to characterize the nature of information granulations in an information system. These results will be very helpful for studying granular computing and uncertainty in information systems.

This paper proposes an approach to attribute reduction in formal contexts via a covering rough set theory. The notions of reducible attributes and irreducible attributes of a formal context are first introduced and their properties are examined. Judg

Zadeh’s seminal work in theory of fuzzy-information granulation in human reasoning is inspired by the ways in which humans granulate information and reason with it. This has led to an interesting research topic: granular computing (GrC). Although many excellent research contributions have been made, there remains an important issue to be addressed: What is the essence of measuring a fuzzy-information granularity of a fuzzy-granular structure? What is needed to answer this question is an axiomatic constraint with a partial-order relation that is defined in terms of the size of each fuzzy-information granule from a fuzzy-binary granular structure. This viewpoint is demonstrated for fuzzy-binary granular structure, which is called the binary GrC model by Lin. We study this viewpoint from from five aspects in this study, which are fuzzy BINARY-granular-structure operators, partial-order relations, measures for fuzzy-information granularity, an axiomatic approach to fuzzy-information granularity, and fuzzy-information entropies.

Determined by a fuzzy implication operator, a general type of fuzzy belief structure and its induced dual pair of fuzzy belief and plausibility functions in infinite universes of discourse are first defined. Relationship between the belief-structure-based and the belief-space-based fuzzy Dempster–Shafer models is then established. It is shown that the lower and upper fuzzy probabilities induced by the fuzzy belief space yield a dual pair of fuzzy belief and plausibility functions. For any fuzzy belief structure, there must exist a fuzzy belief space such that the fuzzy belief and plausibility functions defined by the given fuzzy belief structure are just the lower and upper fuzzy probabilities induced by the fuzzy belief space, respectively. Essential properties of the fuzzy belief and plausibility functions are also examined. The fuzzy belief and plausibility functions are, respectively, a fuzzy monotone Choquet capacity and a fuzzy alternating Choquet capacity of infinite order.

Granular computing and knowledge reduction are two basic issues in knowledge representation and data mining. Granular structure of concept lattices with application in knowledge reduction in formal concept analysis is examined in this paper. Information granules and their properties in a formal context are first discussed. Concepts of a granular consistent set and a granular reduct in the formal context are then introduced. Discernibility matrices and Boolean functions are, respectively, employed to determine granular consistent sets and calculate granular reducts in formal contexts. Methods of knowledge reduction in a consistent formal decision context are also explored. Finally, knowledge hidden in such a context is unraveled in the form of compact implication rules.

This paper proposes a novel rough set approach to discover classification rules in real‐valued spatial data in general and remotely sensed data in particular. A knowledge induction process is formulated to select optimal decision rules with a minimal set of features necessary and sufficient for a remote sensing classification task. The approach first converts a real‐valued or integer‐valued decision system into an interval‐valued information system. A knowledge induction procedure is then formulated to discover all classification rules hidden in the information system. Two real‐life applications are made to verify and substantiate the conceptual arguments. It demonstrates that the proposed approach can effectively discover in remotely sensed data the optimal spectral bands and optimal rule set for a classification task. It is also capable of unraveling critical spectral band(s) discerning certain classes. The framework paves the road for data mining in mixed spatial databases consisting of qualitative and quantitative data.

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.

This article deals with approaches to knowledge reductions in inconsistent information systems (ISs). The main objective of this work was to introduce a new kind of knowledge reduction called a maximum distribution reduct, which preserves all maximum decision classes. This type of reduction eliminates the harsh requirements of the distribution reduct and overcomes the drawback of the possible reduct that the derived decision rules may be incompatible with the ones derived from the original system. Then, the relationships among the maximum distribution reduct, the distribution reduct, and the possible reduct were discussed. The judgement theorems and discernibility matrices associated with the three reductions were examined, from which we can obtain approaches to knowledge reductions in rough set theory (RST). © 2003 Wiley Periodicals, Inc.