Rough Set Model Research Articles

Multi-label feature selection using self-information in divergence-based fuzzy neighborhood rough sets

Multi-label feature selection corresponds to pattern recognition and knowledge mining, and its application has been expanded to different scenarios. As an excellent processing platform for uncertain and ambiguous information, divergence-based fuzzy rough sets (Div-FRSs) have been proposed and applied to feature selection. However, there are three critical problems to be solved when applying Div-FRSs to multi-label learning. The first is how to effectively dispose the noise produced by features in multi-label data. The second is how to synthetically consider the relevance among all labels. The last is how to thoroughly mine the uncertainty brought by upper approximations neglected in Div-FRSs existing researches. To address these issues, this study presents a new divergence-based fuzzy neighborhood rough set model (Div-FNRSs) for multi-label learning using self-information. First, the divergence-based fuzzy neighborhood relation and class are gradually raised to manage the noise in multi-label data, and fuzzy decision is introduced to dispose all labels as a whole. Combining them together, a new model Div-FNRSs is constructed. Then, divergence-based fuzzy neighborhood self-information containing upper approximations and lower approximations is designed to depict distinguishing ability of features through three-level uncertainty measure establishment and granulation property exploration. Furthermore, feature significance for choosing the optimal features is given and it motivates a heuristic feature-selection algorithm DivFNSI-FS. Finally, data experiments are completed to validate DivFNSI-FS effectiveness with six state-of-the-art multi-label feature selection approaches on fourteen multi-label datasets. A conclusion can be drawn that DivFNSI-FS outperforms existing algorithms to obtain better performance on eight commonly-used evaluation indexes.

On C̆ech L-fuzzy Rough Proximity Spaces

The aim of this paper is to study the relationship between the category of C̆ech [Formula: see text]-fuzzy rough proximity spaces and the category of C̆ech [Formula: see text]-fuzzy interior spaces which based on rough set models. In particular, we obtain some interesting adjunctions between the considered categories. Also, we give some examples. Moreover, we introduce [Formula: see text]-fuzzy rough grills and discuss some of their properties.

Covering-Based Intuitionistic Hesitant Fuzzy Rough Set Models and Their Application to Decision-Making Problems

In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy β-neighborhoods (IHF β-neighborhoods) and intuitionistic hesitant fuzzy complementary β-neighborhoods (IHFC β-neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF β-neighborhoods and IHFC β-neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated.

𝕃-valued variable precision rough sets

In this study, we focus on exploring a novel rough sets model, L -valued variable precision rough sets, employing a complete residuated lattice within the context of residuated lattices to offer an expansive perspective on lattice truth values. This model comprises three main elements: L -fuzzy set H representing the universal set, an L -valued relation on H , and an L -fuzzy subset of H . Also, the classical L -fuzzy rough set, L -valued fuzzy rough set, and L -fuzzy variable precision rough sets can be regarded as special cases of this model. Moreover, through constructive approaches, this paper comprehensively characterizes L -valued variable precision rough sets. Finally, we examine the connection between an L -quasi-topology and L -valued variable precision rough sets on the L -set H .

Fusing multiple interval-valued fuzzy monotonic decision trees

As a powerful knowledge mining technique for ordinal classification tasks, dominance-based rough set theory has many advantages but also some issues. Sensitivity to noisy information means that even a single mislabeled sample can lead to substantial fluctuations in the approximation calculations. Another issue is that most monotonic classifiers can only handle real-valued data and cannot directly deal with interval-valued data, which is common in practical applications. To address these issues, a tree-based fusion learning method for monotonic classification of interval-valued attributes, named FM-IFMDT, has been proposed. Its functional structure comprises three components: (i) The proposed robust β-precision interval-valued fuzzy dominance neighborhood rough set model (β-IFDNRS) can adaptively identify and filter noise samples. (ii) The interval dominance discernibility matrix based on β-IFDNRS is developed for feature selection and can generate a set of complete and diverse feature subsets. (iii) The novel interval-valued fuzzy monotonic decision tree (IFMDT) based on the probability distribution is trained on each feature subset and is used as the base classifier of the weighted voting fusion model. Extensive experiments show the proposed fusion learning method has significant advantages.

Multigranulation variable-scale fuzzy neighborhood measures and corresponding Choquet-like integrals for feature selection

Choquet-like integrals, a nonlinear fuzzy aggregation function, are diffusely applied in several real problems. However, the corresponding fuzzy measures in them are provided by human intervention and not by data-driven methods. As an effective knowledge representation tool, rough set models in different approximation spaces are established for data processing. Particularly, the multigranulation fuzzy β-covering approximation space has been concerned with only a single scale β∈(0,1]. However, different granulation structures should have different scales. Therefore, establishing a multigranulation approximation space with a variable scale by inducing fuzzy measures through data-driven methods and using corresponding Choquet-like integrals in practical problems is a significant challenge. To address this challenge, the notion of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented here, as well as multigranulation variable-scale fuzzy neighborhood measures in it. Furthermore, Choquet-like integrals with the presented measures are constructed to solve the issue of feature selection (i.e., attribute reduction) under the new approximation spaces. Firstly, the concept of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented, where different fuzzy β-coverings have different scales β∈Θ. Moreover, multigranulation variable-scale fuzzy neighborhood measures in it, as fuzzy measures, are presented. Subsequently, Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures are constructed. A novel attribute reduction method under Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures is proposed for any decision information table. Finally, the presented method is selected for solving problems of classification and diagnosis of rolling bearing faults. Several public data sets are used to demonstrate the effectiveness and feasibility of the presented methods mentioned above.

Double-quantitative multi-granularity kernel fuzzy rough sets model and its application in rheumatoid arthritis risk assessment

Double-quantitative multi-granularity kernel fuzzy rough sets model and its application in rheumatoid arthritis risk assessment

Attribute reduction for heterogeneous data based on monotonic relative neighborhood granularity

The neighborhood rough set model serves as an important tool for handling attribute reduction tasks involving heterogeneous attributes. However, measuring the relationship between conditional attributes and decision in the neighborhood rough set model is a crucial issue. Most studies have utilized neighborhood information entropy to measure the relationship between attributes. When using neighborhood conditional information entropy to measure the relationships between the decision and conditional attributes, it lacks monotonicity, consequently affecting the rationality of the final attribute reduction subset. In this paper, we introduce the concept of neighborhood granularity and propose a new form of relative neighborhood granularity to measure the relationship between the decision and conditional attributes, which exhibits monotonicity. Moreover, our approach for measuring neighborhood granularity avoids the logarithmic function computation involved in neighborhood information entropy. Finally, we conduct comparative experiments on 12 datasets using two classifiers to compare the results of attribute reduction with six other attribute reduction algorithms. The comparison demonstrates the advantages of our measurement approach.

Optimizing Attribute Reduction in Multi-Granularity Data through a Hybrid Supervised–Unsupervised Model

Attribute reduction is a core technique in the rough set domain and an important step in data preprocessing. Researchers have proposed numerous innovative methods to enhance the capability of attribute reduction, such as the emergence of multi-granularity rough set models, which can effectively process distributed and multi-granularity data. However, these innovative methods still have numerous shortcomings, such as addressing complex constraints and conducting multi-angle effectiveness evaluations. Based on the multi-granularity model, this study proposes a new method of attribute reduction, namely using multi-granularity neighborhood information gain ratio as the measurement criterion. This method combines both supervised and unsupervised perspectives, and by integrating multi-granularity technology with neighborhood rough set theory, constructs a model that can adapt to multi-level data features. This novel method stands out by addressing complex constraints and facilitating multi-perspective effectiveness evaluations. It has several advantages: (1) it combines supervised and unsupervised learning methods, allowing for nuanced data interpretation and enhanced attribute selection; (2) by incorporating multi-granularity structures, the algorithm can analyze data at various levels of granularity. This allows for a more detailed understanding of data characteristics at each level, which can be crucial for complex datasets; and (3) by using neighborhood relations instead of indiscernibility relations, the method effectively handles uncertain and fuzzy data, making it suitable for real-world datasets that often contain imprecise or incomplete information. It not only selects the optimal granularity level or attribute set based on specific requirements, but also demonstrates its versatility and robustness through extensive experiments on 15 UCI datasets. Comparative analyses against six established attribute reduction algorithms confirms the superior reliability and consistency of our proposed method. This research not only enhances the understanding of attribute reduction mechanisms, but also sets a new benchmark for future explorations in the field.

Teaching Quality Analysis of Health Management Professionals in Colleges and Universities Based on Big Data Decision Tree Algorithm

In this study, we investigate whether the big data decision tree approach can be utilised to evaluate the effectiveness of teaching in higher education by health management professors. In light of the expanding need for high-quality healthcare education by the professionals, it is absolutely necessary to evaluate and enhance the teaching efficacy of healthcare management specialists. The application of big data analytics towards the creation of a method for the evaluation of instructors that is both objective and precise is the focus of this study. Every educational system may be broken down into its two primary components: teachers and pupils. The students are not only passive recipients of the instruction that their teachers provide. All of the desired instructional achievements must be driven by the effort of the students in order to fall within the category of "subjective initiative." Therefore, the first step in any educational activity should be encouraging pupils to build their own sense of initiative and intrinsic motivation to learn. This should be the case in any educational endeavour. If teachers have access to and make use of reliable employment data for statistical analysis, they will be able to have a more significant impact on the kids they teach. Based on a preliminary set of actual university employment data from 2012, this study compares the results of employing the C4.5 approach with a decision tree generating technique for the assessment of the teaching quality by the professionals. Both approaches were used to analyse the data. The findings demonstrate that a straightforward decision tree structure may be obtained using the decision tree approach that makes use of the multiscale rough set model. In addition, our approaches don't need to use overlapping data sets, and they're quite efficient from a computing standpoint. The relevance of this study lies in the fact that it sheds light on how the expertise and motives of teachers who are healthcare professionals to be precise, reflect on the learning of their students and their relevant field skills.

Label disambiguation-based feature selection for partial label learning via fuzzy dependency and feature discernibility

Partial label learning is a multi-class classification issue in which each training instance is associated with a set of candidate labels. Feature selection is an effective method to improve the performance of the learning model, and at the same time, feature selection being a challenging problem in partial label learning due to the label ambiguity of partial labels. To tackle this challenge, this paper proposes a label disambiguation-based feature selection for partial label learning via fuzzy dependency and feature discernibility. Specifically, considering the high sensitivity of the fuzzy rough sets model to pseudo labels, a instance distribution-based label disambiguation method is presented to reduce the noise from the candidate labels. Based on this, a weighted fuzzy rough sets model is constructed in accordance with the distribution information of labels, and the function of fuzzy dependency is redefined. Then, the evaluation function of feature significance is obtained by fusing fuzzy dependency and feature discernibility for identifying the critical features. Finally, extensive experiments have confirmed the feasibility and effectiveness of the proposed method. Compared to other feature selection algorithms, the proposed method exhibits superior performance and enhances the generalization of partial label learning models. Furthermore, the feasibility of the proposed label disambiguation method is demonstrated through comparison with state-of-the-art label disambiguation methods.

A novel intuitionistic fuzzy rough instance selection and attribute reduction with kernelized intuitionistic fuzzy C-means clustering to handle imbalanced datasets

Due to advancement of internet and lab based technologies, large volume of high dimensional data are generated every day. These data usually consisted of several issues such as class imbalance, noise, later uncertainty, irrelevant and/or redundant features, and redundancy in size. These issues degrade the overall performance measures of the various machine learning algorithms. An efficient method to cope with such issues for a large sized datasets is to apply efficient data reduction techniques. In the recent years, numerous data reduction techniques have been presented based on fuzzy rough set theory to tackle these obstacles. However, building such a method that can handle all the above mentioned issues simultaneously is still a challenging task. In this study, we handle all these obstacles simultaneously by introducing a novel approach to obtain the reduced dataset by combining kernelized intuitionistic fuzzy C-means with intuitionistic fuzzy rough set model. Intuitionistic fuzzy rough set handles the vagueness and uncertainty in a better way than fuzzy set aided models as it takes use of membership, non-membership as well as hesitancy to capture the uncertainty of real-valued datasets. To generate the membership and non-membership grades, kernelized intuitionistic fuzzy C- means based notion is introduced. Further, an intuitionistic fuzzy rough set model is established by addressing lower and upper approximations based on a novel similarity relation. Moreover, all the necessary conditions are justified with the relevant mathematical theorems. Next, this model is employed for dimensionality reduction based on the concept of discernibility matrix by using the idea of different classes’ ratios to avoid the noise. Thereafter, positive region is defined with the help of lower approximation. The positive region information is applied to tackle problematic instances available in both minority and majority class for the imbalanced dataset after generation of artificial samples by synthetic minority oversampling technique (SMOTE). A comprehensive experimental study is added to show the effectiveness of the proposed technique. Finally, a framework is established to improve the prediction of animal toxin peptides.

Distance metric learning-based multi-granularity neighborhood rough sets for attribute reduction

Attribute reduction is a hot research topic in data mining, in which rough set theory-based attribute reduction methods have been widely focused. The neighborhood rough set (NRS) model has good generalization performance and practicality in uncertainty reasoning, so it is often used for attribute reduction in recent years. Calculating the distance between samples in different attribute spaces is a key step in the NRS-based attribute reduction methods, which directly affects the performance of the reduction algorithm. However, the NRS model uses a fixed computational paradigm in calculating the distance between samples and does not consider the influence of labels in the attribute spaces on the distance calculation, which is not conducive to improving the performance of the reduction algorithm. Distance metric learning takes full account of the labels information in the multi-dimensional attribute space, and it can learn the distance between samples by taking into account the integrated principle that samples with the same label are closer and samples with different labels are further away, which helps to reduce the classification uncertainty. Inspired by this, this paper firstly incorporates distance metric learning into the NRS model from the perspective of multi-dimensional attribute space and proposes a distance metric learning-based multi-granularity neighborhood rough set (DmlMNRS) model. The related properties of the DmlMNRS model are also introduced and proved. Then, the DmlMNRS-based attribute reduction criterion and the significance of the attributes are defined. A DmlMNRS-based heuristic attribute reduction (DMNHAR) algorithm is designed based on this. Finally, experiments are performed on fifteen publicly datasets, and the experimental results show that the proposed algorithm has better robustness and classification performance.

Three-way decision method based on triangular norms in incomplete information systems and its applications in medical diagnosis

Three-way decision, as an extension of traditional two-way decision, was proposed by Yao in 2009, which can effectively avoid unnecessary losses caused by incorrect decisions in the decision-making process. Meanwhile, incomplete hybrid information systems represent the database of the relationship between objects and attributes, which refers to a system with multiple data and missing data. In this paper, based on the fact that many existing literatures involving incomplete hybrid information systems did not fully consider the impact of different conditional attributes on decision attributes and lacked effective aggregation methods to integrate weights and distances, we propose a new three-way decision method to deal with incomplete hybrid information systems with the help of triangular norms. First, in incomplete hybrid information systems, we redefine the distance between two objects based on conditional attributes and give the calculation formula of different data attributes in conditional attributes. At the same time, we define a new weight calculation method based on the relationship between conditional attributes and decision attributes. And then, by the distance between different conditional attributes and their corresponding weights, the hybrid distance is obtained using triangular norms. Furthermore, we use the hybrid distance to get the tolerance relation on the target set of an incomplete hybrid information system, thereby, using this tolerance relation, we get a new decision theoretic rough set model and the corresponding decision rules. Finally, by two experiments involving medical diagnosis, we demonstrate that our model has better classification ability, lower misclassification rate, and better stability compared to other corresponding models, thereby confirming that the proposed model provides a new and effective method for handling incomplete hybrid information systems in practical applications.

Rough set model of incomplete interval rough number decision systems

The rough set model has been extended to interval rough number decision systems, but the existing studies do not consider interval rough number decision systems with missing values. To this end, a rough set model of incomplete interval rough number decision systems (IIRNDSs) is proposed, and its uncertainty measures are investigated. Firstly, the similarity of two incomplete interval rough numbers (IIRNs) are defined by calculating their optimistic and pessimistic distances of the lower and upper approximation intervals of IIRNs. Then, the rough sets in IIRNDSs are constructed by the induced similarity relation. Next, four uncertainty measures, including approximation accuracy, approximation roughness, conditional entropy, and decision rough entropy are given, which exhibit a monotonic variation with changes in the size of attribute sets, α, and θ. Finally, the experimental results demonstrate the proposed rough set model of IIRNDSs is feasible and effective.

A three-way decision method on multi-scale single-valued neutrosophic decision systems

In this paper, we propose a three-way decision (TWD) method on multi-scale single-valued neutrosophic decision systems (MS-SVNDSs). First, to explore the application of single-valued neutrosophic sets (SVNSs) in multi-scale environment, we establish a rough set model of MS-SVNDSs. Then, aiming at the problem of knowledge acquisition in MS-SVNDSs, we present the corresponding optimal scale selection and reduction methods by using evidence theory, a more direct and simpler algorithm is also discussed. For obtaining decision results that are more in line with human cognition, we further provide a novel three-way decision method. Comparative experiments are subsequently conducted to demonstrate the effectiveness of our approach. The experimental results show that our method not only improves the classification accuracy but also raises decision efficiency.

Adaptive neighborhood rough set model for hybrid data processing: a case study on Parkinson’s disease behavioral analysis

Extracting knowledge from hybrid data, comprising both categorical and numerical data, poses significant challenges due to the inherent difficulty in preserving information and practical meanings during the conversion process. To address this challenge, hybrid data processing methods, combining complementary rough sets, have emerged as a promising approach for handling uncertainty. However, selecting an appropriate model and effectively utilizing it in data mining requires a thorough qualitative and quantitative comparison of existing hybrid data processing models. This research aims to contribute to the analysis of hybrid data processing models based on neighborhood rough sets by investigating the inherent relationships among these models. We propose a generic neighborhood rough set-based hybrid model specifically designed for processing hybrid data, thereby enhancing the efficacy of the data mining process without resorting to discretization and avoiding information loss or practical meaning degradation in datasets. The proposed scheme dynamically adapts the threshold value for the neighborhood approximation space according to the characteristics of the given datasets, ensuring optimal performance without sacrificing accuracy. To evaluate the effectiveness of the proposed scheme, we develop a testbed tailored for Parkinson’s patients, a domain where hybrid data processing is particularly relevant. The experimental results demonstrate that the proposed scheme consistently outperforms existing schemes in adaptively handling both numerical and categorical data, achieving an impressive accuracy of 95% on the Parkinson’s dataset. Overall, this research contributes to advancing hybrid data processing techniques by providing a robust and adaptive solution that addresses the challenges associated with handling hybrid data, particularly in the context of Parkinson’s disease analysis.

Online group streaming feature selection based on fuzzy neighborhood granular ball rough sets

Online group streaming feature selection holds significant research value in large-scale streaming data processing scenarios, and the related work based on rough set theory has attracted academic interest. Nevertheless, most relevant algorithms come with parameters, and performing a grid search for the optimal parameters reduces the efficiency. Moreover, the existing online group streaming feature selection frameworks cannot effectively fit the situation in practice. Focusing on these issues, this paper investigates an online group streaming feature selection method based on fuzzy neighborhood granular ball rough sets. First, Canopy clustering is introduced to granular ball computing, and the adaptive neighborhood of samples is generated based on the granular ball distribution. Second, we construct a fuzzy neighborhood granular ball rough set (FNGBRS) model and propose the integrated dependence degree to achieve maximal dependency and minimum classification error. Then, the purity of granular balls is considered as the weight of features, and some uncertainty measures based on FNGBRS are presented. Finally, we define a random factor to control the size of streaming groups and design an online group streaming feature selection algorithm. Comparative experimental results on sixteen public datasets demonstrate that the proposed algorithm exhibits superior and stable classification performance, coupled with increased efficiency from its parameter-free design.

Quasi-atomic relations based rough set model and convex geometry

Quasi-atomic relations based rough set model and convex geometry

Covering variable precision fuzzy rough sets based on overlap functions and the application to multi-label classification

Fuzzy rough sets (FRSs) play a significant role in the field of data analysis, and one of the common methods for constructing FRSs is the use of the fuzzy logic operators. To further extend FRSs theory to more diverse information backgrounds, this article proposes a covering variable precision fuzzy rough set model based on overlap functions and fuzzy β-neighbourhood operators (OCVPFRS). Some necessary properties of OCVPFRS have also been studied in this work. Furthermore, multi-label classification is a prevalent task in the realm of machine learning. Each object (sample or instance) in multi-label data is associated with various labels (classes), and there are numerous features or attributes that need to be taken into account within the attribute space. To enhance various performance metrics in the multi-label classification task, attribute reduction is an essential pre-processing step. Therefore, according to overlap functions and fuzzy rough sets’ excellent work on applications: such as image processing and multi-criteria decision-making, we establish an attribute reduction method suitable for multi-label data based on OCVPFRS. Through a series of experiments and comparative analysis with existing multi-label attribute reduction methods, the effectiveness and superiority of the proposed method have been verified.