Fuzzy rough set theory has made significant strides in the field of feature selection. However, it still faces challenges when dealing with noisy data. Most traditional models fail to incorporate sample weight information in the evaluation of sample similarity, leaving them prone to interference from noisy samples. To address this issue, this paper introduces a novel Weighted Fuzzy Rough Set (WFRS) model, designed to more accurately capture the uncertainty inherent in data. This model combines class distribution with the concept of neighborhood weights for samples, and proposes a directed weighted fuzzy binary relation to evaluate both the similarity and differences between samples. By doing so, it avoids the overfitting issues typically caused by over-reliance on distribution information from local noisy samples. Drawing on sample weighting, traditional fuzzy approximation operators are reinterpreted and redefined, leading to the construction of the WFRS model. Key uncertainty metrics, such as decision approximation and the positive region, are analyzed in depth, providing a solid theoretical foundation for subsequent feature selection and decision analysis. Based on this model, a forward heuristic feature selection algorithm is developed and compared with various state-of-the-art algorithms. Experimental results demonstrate that the proposed method performs exceptionally well across multiple evaluation metrics, fully validating the efficiency and robustness of the WFRS model.

Fuzzy rough sets have made considerable strides within the domain of machine learning and data mining and served as a valuable tool for feature selection. However, traditional models face challenges in computing fuzzy similarity relations. They oversimplify the treatment of diverse samples by assuming that they exist in the same class space, ignoring their labels and distribution information. Consequently, difficulties arise when dealing with data that exhibit considerable distribution variations across classes. To address this issue, this study proposes a directed fuzzy rough set model that better captures the inherent uncertainty in sample distribution compared with traditional models. In this model, class-subspace distribution information is seamlessly integrated into directed fuzzy binary relations. Furthermore, fuzzy rough approximation operators are redefined to accurately capture the uncertainty associated with class distribution, facilitating a comprehensive analysis of relevant properties concerning decision approximations for samples. Building on this background, a heuristic algorithm for feature selection and a K-nearest neighbor reduction classifier are developed. Comparative experiments with top-tier algorithms showcase the outstanding performance of our proposed model. This study provides a robust framework for addressing intricate machine learning and pattern recognition tasks.

Fuzzy rough set theory is an important approach for analyzing data uncertainty. However, the model lacks adaptive learning capabilities and cannot fit labeled data effectively in classification tasks. This study aims to introduce an adaptive learning mechanism into fuzzy rough set theory to enhance its data-fitting capability. To this end, this study seamlessly integrates fuzzy rough set theory with neural networks and proposes a novel fuzzy rough neural network model. This model adaptively learns fuzzy similarity relations in rough set models using the backpropagation algorithm. The proposed network model comprises five layers: the input, membership, fuzzy lower approximation, fully connected, and output layers. The fuzzy similarity relations between the input samples and training samples are computed in the membership layer. These relations are utilized in the fuzzy lower approximation layer to describe the degree to which the samples belong to different classes. The fuzzy rough lower approximations of the input samples are finally fused in the fully connected layer using feature weight coefficients. In the backpropagation stage, the gradient of the objective function is used to correct the fuzzy similarity relations and feature weight coefficients. This study theoretically proved that the proposed fuzzy rough network has a generalized function approximation property and can approximate any decision function. Experimental analysis showed that the proposed method is effective and performs better than most of the existing state-of-the-art algorithms.

This article studies the stability problem of discrete-time switched positive linear systems (SPLSs) with marginally stable subsystems. Based on the weak common linear copositive Lyapunov function (weak CLCLF) approach, the switching property and the state component property are combined to ensure the asymptotic stability of SPLSs under three types of switching signals. First, considering the transfer-restricted switching signal described by the switching digraph, novel cycle-dependent joint path conditions are proposed in combination with state component digraphs. Second, under the time interval sequence, two types of path conditions are constructed for designing switching schemes. Third, necessary and sufficient conditions for the asymptotic stability of SPLSs under arbitrary switching are established. Finally, three examples are provided to illustrate the effectiveness of the proposed method.

Fuzzy rough set (FRS) theory is generally used to measure the uncertainty of data. However, this theory cannot work well when the class density of a data distribution differs greatly. In this work, a relative distance measure is first proposed to fit the mentioned data distribution. Based on the measure, a relative FRS model is introduced to remedy the mentioned imperfection of classical FRSs. Then, the positive region, negative region, and boundary region are defined to measure the uncertainty of data with the relative FRSs. Besides, a relative fuzzy dependency is defined to evaluate the importance of features to decision. With the proposed feature evaluation, we propose a feature selection algorithm and design a classifier based on the maximal positive region. The classification principle is that an unlabeled sample will be classified into the class corresponding to the maximal degree of the positive region. Experimental results show the relative fuzzy dependency is an effective and efficient measure for evaluating features, and the proposed feature selection algorithm presents better performance than some classical algorithms. Besides, it also shows the proposed classifier can achieve slightly better performance than the KNN classifier, which demonstrates that the maximal positive region-based classifier is effective and feasible.

Fuzzy rough sets (FRSs) are considered to be a powerful model for analyzing uncertainty in data. This model encapsulates two types of uncertainty: 1) fuzziness coming from the vagueness in human concept formation and 2) roughness rooted in the granulation coming with human cognition. The rough set theory has been widely applied to feature selection, attribute reduction, and classification. However, it is reported that the classical FRS model is sensitive to noisy information. To address this problem, several robust models have been developed in recent years. Nevertheless, these models do not consider a statistical distribution of data, which is an important type of uncertainty. Data distribution serves as crucial information for designing an optimal classification or regression model. Thus, we propose a data-distribution-aware FRS model that considers distribution information and incorporates it in computing lower and upper fuzzy approximations. The proposed model considers not only the similarity between samples, but also the probability density of classes. In order to demonstrate the effectiveness of the proposed model, we design a new sample evaluation index for prototype-based classification based on the model, and a prototype selection algorithm is developed using this index. Furthermore, a robust classification algorithm is constructed with prototype covering and nearest neighbor classification. Experimental results confirm the robustness and effectiveness of the proposed model.

How to evaluate features and select nodes is one of the key issues in constructing decision trees. In this work fuzzy rough set theory is employed to design an index for evaluating the quality of fuzzy features or numerical attributes. A fuzzy rough

The theory of fuzzy rough sets is claimed to be a powerful mathematical tool for dealing with uncertainty in data analysis. Unluckily, the classical model of fuzzy rough sets is sensitive to noisy information. This disadvantage limits the applicabili

Rough sets, especially fuzzy rough sets, are supposedly a powerful mathematical tool to deal with uncertainty in data analysis. This theory has been applied to feature selection, dimensionality reduction, and rule learning. However, it is pointed out that the classical model of fuzzy rough sets is sensitive to noisy information, which is considered as a main source of uncertainty in applications. This disadvantage limits the applicability of fuzzy rough sets. In this paper, we reveal why the classical fuzzy rough set model is sensitive to noise and how noisy samples impose influence on fuzzy rough computation. Based on this discussion, we study the properties of some current fuzzy rough models in dealing with noisy data and introduce several new robust models. The properties of the proposed models are also discussed. Finally, a robust classification algorithm is designed based on fuzzy lower approximations. Some numerical experiments are given to illustrate the effectiveness of the models. The classifiers that are developed with the proposed models achieve good generalization performance.