Search Results (26)

High-dimensional mixed data often lack a unified semantic representation for continuous and discrete attributes, which hinders mixed-attribute similarity modeling and can result in unstable reducts and overfitting in existing neighborhood rough set (NRS) methods. To address this issue, we propose IF-EMD-SPA, an attribute reduction method for NRS grounded in Information Flow theory. Unlike conventional NRS methods that rely on discretization or a single reduction criterion, IF-EMD-SPA first establishes a unified representation framework for heterogeneous attributes based on classifications and an Information Channel Core. It then integrates Earth Mover’s Distance (EMD) and Set Pair Analysis (SPA) to define a similarity metric for mixed attributes. In addition, a three-stage greedy reduction strategy is designed under the dual constraints of dependency preservation and structural error, consisting of dependency-driven forward selection, similarity-driven structure completion, and backward redundancy removal. Experiments on five UCI benchmark datasets and two high-dimensional gene expression datasets show that IF-EMD-SPA achieves average accuracies of 93.5% (k-Nearest Neighbors, KNN), 93.9% (Support Vector Machine, SVM), and 90.8% (Classification and Regression Trees, CART), with SVM achieving the best results on all seven datasets. Under CART, it reaches 100% accuracy on Wine and WPBC, improving performance by up to 37.5 percentage points over comparison methods. Full article

As a foundational analytical tool, the discernibility matrix plays a pivotal role in the systematic reduction of knowledge in rough set-based systems. Recent advancements in rough set theory have witnessed the proliferation of discernibility matrix-based knowledge reduction algorithms, with notable applications in classical, neighborhood, covering, and fuzzy rough set models. However, the quadratic growth of the discernibility matrix’s complexity (relative to domain size) imposes fundamental scalability limits, rendering it inefficient for real-world applications with massive datasets. To address this issue, we introduced a discernibility hashing strategy to limit the growth scale of the discernibility attributes and proposed a feature selection algorithm via discernibility hash based on rough set theory. First, on the premise of keeping the information of the original discernibility matrix unchanged, the method maps the discernibility attribute set of all objects to the storage unit through a hash function and records the number of collisions to construct a discernibility hash. By using this mapping, the two-dimensional matrix space can be reduced to a one-dimensional hash space, which greatly removes invalid and redundant elements. Secondly, based on the discernibility hash, an efficient knowledge reduction algorithm is proposed. The algorithm avoids invalid and redundant element attribute sets to participate in the knowledge reduction process and improves the efficiency of the algorithm. Finally, the experimental results show that the method is superior to the discernibility matrix method in terms of storage space and running time. Full article

A critical step for gene selection algorithms using rough set theory is the establishment of a gene evaluation function to assess the classification ability of candidate gene subsets. The concept of dependency in a classic neighborhood rough set model plays the role of this evaluation function. This criterion only notes the information provided by the lower approximation and omits the upper approximation, which may result in the loss of some important information. This paper proposes gene selection algorithms within a single-cell gene decision space by employing self-information, taking into account both lower and upper approximations. Initially, the distance between gene expression values within each subspace is defined to establish the tolerance relation on the cell set. Subsequently, self-information is introduced through the lens of tolerance classes. The relationship between these measures and their respective properties is then examined in detail. For gene expression data, the proposed self-information metric demonstrates superiority over other measures by accounting for both lower and upper approximations, thereby facilitating the selection of optimal gene subsets. Finally, gene selection algorithms within a single-cell gene decision space are developed based on the proposed self-information metric, and experiments conducted on 10 publicly available single-cell datasets indicate that the classification performance of the proposed algorithms can be enhanced through the selection of genes pertinent to classification. The results demonstrate that $Fi-SI$ achieves an average classification accuracy of 93.7% (KNN) while selecting 48.3% fewer genes than Fisher’s score. Full article

As an effective method for uncertain knowledge discovery and decision-making, the three-way decisions model has attracted extensive attention from scholars. However, in practice, the existing sequential three-way decision model often faces challenges due to factors such as missing data and unbalanced attribute granularity. To address these issues, we propose an intuitionistic fuzzy sequential three-way decision (IFSTWD) model, which introduces several significant contributions: (1) New intuitionistic fuzzy similarity relations. By integrating possibility theory, our model defines similarity and dissimilarity in incomplete information systems, establishing new intuitionistic fuzzy similarity relations and their cut relations. (2) Granulation method innovation. We propose a density neighborhood-based granulation method to partition decision attributes and introduce a novel criterion for evaluating attribute importance. (3) Enhanced decision process. By incorporating sequential three-way decision theory and developing a multi-level granularity structure, our model replaces the traditional equivalent relation in the decision-theoretic rough sets model, thus advancing the model’s applicability and effectiveness. The practical utility of our model is demonstrated through an example analysis of “Chinese + vocational skills” talent competency and validated through simulation experiments on the UCI dataset, showing superior performance compared to existing methods. Full article

Rough set theory is a methodology that defines the definite or probable membership of an element for exploring data with uncertainty and incompleteness. It classifies data sets using lower and upper approximations to model uncertainty and missing information. To contribute to this goal, this study presents a newer approach to the concept of rough sets by introducing a new type of neighborhood called j-transitive neighborhood or j-TN. Some of the basic properties of j-transitive neighborhoods are studied. Also, approximations are obtained through j-TN, and the relationships between them are investigated. It is proven that these approaches provide almost all the properties provided by the approaches given by Pawlak. This study also defines the concepts of lower and upper approximations from the topological view and compares them with some existing topological structures in the literature. In addition, the applicability of the j-TN framework is demonstrated in a medical scenario. The approach proposed here represents a new view in the design of rough set theory and its practical applications to develop the appropriate strategy to handle uncertainty while performing data analysis. Full article

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. Full article

Point cloud data generated by LiDAR sensors play a critical role in 3D sensing systems, with applications encompassing object classification, part segmentation, and point cloud recognition. Leveraging the global learning capacity of dot product attention, transformers have recently exhibited outstanding performance in point cloud learning tasks. Nevertheless, existing transformer models inadequately address the challenges posed by uncertainty features in point clouds, which can introduce errors in the dot product attention mechanism. In response to this, our study introduces a novel global guidance approach to tolerate uncertainty and provide a more reliable guidance. We redefine the granulation and lower-approximation operators based on neighborhood rough set theory. Furthermore, we introduce a rough set-based attention mechanism tailored for point cloud data and present the rough set transformer (RST) network. Our approach utilizes granulation concepts derived from token clusters, enabling us to explore relationships between concepts from an approximation perspective, rather than relying on specific dot product functions. Empirically, our work represents the pioneering fusion of rough set theory and transformer networks for point cloud learning. Our experimental results, including point cloud classification and segmentation tasks, demonstrate the superior performance of our method. Our method establishes concepts based on granulation generated from clusters of tokens. Subsequently, relationships between concepts can be explored from an approximation perspective, instead of relying on specific dot product or addition functions. Empirically, our work represents the pioneering fusion of rough set theory and transformer networks for point cloud learning. Our experimental results, including point cloud classification and segmentation tasks, demonstrate the superior performance of our method. Full article

Considering the nonlinear, time-varying, and multivariate coupling nature of the welding process, achieving excellent control of the welding process can be challenging. In addition, welding experience varies from person to person, making it difficult to establish a uniform standard. In this work, rough set theory is introduced and applied to arc welding process modeling and quality control to achieve effective online control of weld penetration during welding. A variable precision neighborhood rough-fuzzy method is proposed to enhance the efficiency and adaptability of rough set theory for information processing in the welding process. By designing welding experiments with different gaps and currents, descriptors such as the tail area coefficient and the length-width ratio of the melt pool have been proposed to characterize the melt pool. Rough set theory has been used to extract decision classification rules for welding percolation state information, and clustering analysis, fuzzy logic, and min-max fuzzy methods have been introduced for knowledge modeling. The proposed variable precision neighborhood rough-fuzzy control model is verified via three sets of experiments, and the results show that the model has excellent stability and effectiveness. Full article

Rough set theory is a mathematical approach that deals with the problems of uncertainty and ambiguity in knowledge. Neighborhood systems are the most effective instruments for researching rough set theory in general. Investigations on boundary regions and accuracy measures primarily rely on two approximations, namely lower and upper approximations, by using these systems. The concept of the ideal, which is one of the most successful and effective mathematical tools, is used to obtain a better accuracy measure and to decrease the boundary region. Recently, a generalization of Pawlak’s rough set concept has been represented by neighborhood systems of graphs based on rough sets. In this research article, we propose a new method by using the concepts of the ideal and different neighborhoods from graph vertices. We examine important aspects of these techniques and produce accuracy measures that exceed those previously = reported in the literature. Finally, we show that our method yields better results than previous techniques utilized in chemistry. Full article

In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhood systems inspired by the system of maximal neighborhood systems. We benefit from the symmetry between rough approximations (lower and upper) and topological operators (interior and closure) to structure the current generalized rough approximation spaces. First, we display two novel types of rough set models produced by maximal neighborhoods, namely, type 2 $m_{\xi }$-neighborhood and type 3 $m_{\xi }$-neighborhood rough models. We investigate their master properties and show the relationships between them as well as their relationship with some foregoing ones. Then, we apply the idea of adhesion neighborhoods to introduce three additional rough set models, namely, type 4 $m_{\xi }$-adhesion, type 5 $m_{\xi }$-adhesion and type 6 $m_{\xi }$-adhesion neighborhood rough models. We establish the fundamental characteristics of approximation operators inspired by these models and discuss how the properties of various relationships relate to one another. We prove that adhesion neighborhood rough models increase the value of the accuracy measure of subsets, which can improve decision making. Finally, we provide a comparison between Yao’s technique and current types of adhesion neighborhood rough models. Full article

With the intensification of population aging and the increasing awareness of public health protection in the post-epidemic era, the renewal of the old urban community neighborhood space is facing many new challenges and problems. Neighborhood Public Open Space (POS) is the main place for people to carry out various social activities in community life. The quality of the social interaction environment that a neighborhood POS can provide can have a vital impact on people’s well-being, as well as their physical and mental health. Therefore, the purpose of this research is to identify and clarify the key physical environmental design attributes/features of the old urban community neighborhood POS, and to explore the relationship between them from the perspective of creating a high-quality social environment. Through the investigation of relevant cases in Shenzhen and Guangzhou, China, the classification performance of each case on the key physical and environmental elements is used as the conditional attribute, and the quality of the social interaction environment in the current situation of each case is used as the decision making attribute to conduct a data mining analysis. Using rough set theory, this study screened out four important elements: greenbelt form planning (C₁); ped and bike system (C₂); space organization and zoning planning (C₆); Public facilities (C₈). Moreover, this study also presents a set of hierarchical decision rules to describe the classification status of the matching physical environmental design elements when the social interaction environment reaches a high quality in the neighborhood POS. This study provides local policy makers with key current situation assessment and diagnostic tools in urban-built environmental renewal projects. The results of this study can help designers draw up the renovation design plans of neighborhood POS on the basis of efficiently obtaining the practical experience of relevant cases, and then create a high-quality social interaction environment. Full article

Most elderly people choose to age in place, making neighborhood environments essential factors affecting their health status. The policies, economic status, and housing conditions of old neighborhoods have led many elderly people to live in skipped-generation households (SGHs), where they have gradually weakened physical functions and are responsible for raising grandchildren; this puts their health in a more fragile state than that of the average elderly person. Practical experience has shown that when faced with complex environmental renovation problems in old communities, many cases often adopt a one-step treatment strategy; however, many scholars have questioned the sustainability of such unsystematically evaluated renovation projects. Therefore, it is often valuable to explore the root causes of these old neighborhood problems and conduct targeted transformations and upgrades according to the interactive relationship between various influencing factors. This study attempted to establish a novel evaluation system to benefit the health of elderly families in old neighborhoods and develop an understanding of the impact relationship among the indicators, while avoiding any form of waste when collecting responses in regard to the future transformation of old neighborhoods. A questionnaire survey was conducted on the elderly in the Guangzhou Che Bei neighborhood in China, and by applying the rough set theory of the decision-making trial and evaluation laboratory model, we established a preliminary evaluation system, obtained key environmental factors affecting the health of elderly people living in SGHs, and clarified their mutual relationships. Finally, on this basis, we proposed corresponding neighborhood renewal suggestions. The results of this study provide a theoretical basis for future research, and our research model can be applied to similar aging research in the future. Full article

The grade-added rough set (GRS) approach is an extension of the rough set theory proposed by Pawlak to deal with numerical data. However, the GRS has problems with overtraining, unclassified and unnatural results. In this study, we propose a new approach called the directional neighborhood rough set (DNRS) approach to solve the problems of the GRS. The information granules in the DNRS are based on reflexive and antisymmetric relations. Following these relations, new lower and upper approximations are defined. Based on these definitions, we developed a classifier with a three-step algorithm, including DN-lower approximation classification, DN-upper approximation classification, and exceptional processing. Three experiments were conducted using the University of California Irvine (UCI)’s machine learning dataset to demonstrate the effect of each step in the DNRS model, overcoming the problems of the GRS, and achieving more accurate classifiers. The results showed that when the number of dimensions is reduced and both the lower and upper approximation algorithms are used, the DNRS model is more efficient than when the number of dimensions is large. Additionally, it was shown that the DNRS solves the problems of the GRS and the DNRS model is as accurate as existing classifiers. Full article

Intuitionistic Fuzzy Sets ($IF{S}_s$) and rough sets depending on covering are important theories for dealing with uncertainty and inexact problems. We think the neighborhood of an element is more realistic than any cluster in the processes of classification and approximation. So, we introduce intuitionistic fuzzy sets on the space of rough sets based on covering by using the concept of the neighborhood. Three models of intuitionistic fuzzy set approximation space based on covering are defined by using the concept of neighborhood. In the first and second model, we approximate IFS by rough set based on one covering (C) by defining membership and non-membership degree depending on the neighborhood. In the third mode, we approximate IFS by rough set based on family of covering ($C_i$) by defining membership and non-membership degree depending on the neighborhood. We employ the notion of the neighborhood to prove the definitions and the features of these models. Finlay, we give an illustrative example for the new covering rough $IF$ approximation structure. Full article

As one of the key topics in the development of neighborhood rough set, attribute reduction has attracted extensive attentions because of its practicability and interpretability for dimension reduction or feature selection. Although the random sampling strategy has been introduced in attribute reduction to avoid overfitting, uncontrollable sampling may still affect the efficiency of search reduct. By utilizing inherent characteristics of each label, Multi-label learning with Label specIfic FeaTures (Lift) algorithm can improve the performance of mathematical modeling. Therefore, here, it is attempted to use Lift algorithm to guide the sampling for reduce the uncontrollability of sampling. In this paper, an attribute reduction algorithm based on Lift and random sampling called ARLRS is proposed, which aims to improve the efficiency of searching reduct. Firstly, Lift algorithm is used to choose the samples from the dataset as the members of the first group, then the reduct of the first group is calculated. Secondly, random sampling strategy is used to divide the rest of samples into groups which have symmetry structure. Finally, the reducts are calculated group-by-group, which is guided by the maintenance of the reducts’ classification performance. Comparing with other 5 attribute reduction strategies based on rough set theory over 17 University of California Irvine (UCI) datasets, experimental results show that: (1) ARLRS algorithm can significantly reduce the time consumption of searching reduct; (2) the reduct derived from ARLRS algorithm can provide satisfying performance in classification tasks. Full article