Multigranulation Rough Set Research Articles

Attribute reduction using self-information uncertainty measures in optimistic neighborhood extreme-granulation rough set

The pessimistic and optimistic neighborhood multi-granulation rough sets (PNMRS and ONMRS) have been applied to attribute reduction. Nonetheless, the setting of the granulation space in both models is usually based on expert experience or continuous trials, which are poorly interpretable. Besides, the dependency, an important attribute evaluation function in PNMRS and ONMRS, only considers classification information in the lower approximation and ignores that of the upper approximation, affecting its evaluation effect. Thus, we firstly propose the pessimistic and optimistic neighborhood extreme-granulation rough sets (PNERS and ONERS) based on the minimum granulation space, avoiding the unobjective setting of the granulation space. However, PNERS describes knowledge with low accuracy, and therefore we construct two self-information uncertainty measures in ONERS and propose the joint self-information that is more suitable for attribute reduction as it takes full consideration of classification information in the lower and upper approximations. Then, an attribute reduction method using the joint self-information is designed, and Fisher Score is introduced into our method to decrease time cost when processing high dimensional data. Extensive experiments validate that our method is able to achieve superior reduction and classification results on different dimensional datasets.

Matrix-based incremental feature selection method using weight-partitioned multigranulation rough set

Incremental feature selection methods have gained increasing research attention as they improve the efficiency of feature selection for dynamic datasets. Multigranulation rough set, as an extension of rough set theory, allows for a comprehensive and rational analysis of problems from multiple hierarchical and granular perspectives. However, existing research on granularity partitioning relies on the decision maker's subjective experience, which lacks convincing power. In this paper, we propose a generalized multigranulation neighborhood rough set based on weight partition model, using a matrix form. We discuss several properties and define a new entropy measure to evaluate feature importance. A heuristic feature selection algorithm is developed based on this entropy to search for the optimal subset. Furthermore, we discuss dynamic updating mechanism and design two incremental feature selection algorithms. Finally, we conduct experiments on 12 public datasets to evaluate the performance of the proposed algorithms and validate their effectiveness and efficiency in feature selection for both static and dynamic datasets.

Uncertainty measures and feature selection based on composite entropy for generalized multigranulation fuzzy neighborhood rough set

With the continuous advancement of information technology, the information and data covered by various information systems become increasingly complex and diverse, it is essential to perform knowledge mining from multiple perspectives to extract valuable insights. Fuzzy neighborhood multigranulation rough set, as an excellent feature selection model, is capable of handling heterogeneous datasets more effectively, significantly improving learning efficiency. In this study, we investigate a feature selection method based on a generalized multigranulation fuzzy rough set (GMFNRS) in fuzzy decision systems. First, the concepts of fuzzy neighborhood rough sets and generalized multigranulation rough sets are introduced. Subsequently, the GMFNRS model is established to enable data mining and rule extraction from various perspectives. Secondly, from an informational perspective, the study investigates uncertainty measurement methods through fuzzy neighborhood joint entropy. Furthermore, a novel fuzzy neighborhood generalized composite entropy is proposed by integrating the GMFNRS model with uncertainty measures. Finally, a forward greedy feature selection algorithm is considered to extract essential information from complex datasets. Experimental results on 15 public datasets demonstrate that the proposed model effectively selects important features in fuzzy systems and exhibits excellent classification performance.

Feature selection for multi-label learning based on variable-degree multi-granulation decision-theoretic rough sets

Multi-label learning (MLL) suffers from the high-dimensional feature space teeming with irrelevant and redundant features. To tackle this, several multi-label feature selection (MLFS) algorithms have emerged as vital preprocessing steps. Nonetheless, existing MLFS methods have their shortcomings. Primarily, while they excel at harnessing label-feature relationships, they often struggle to leverage inter-feature information effectively. Secondly, numerous MLFS approaches overlook the uncertainty in the boundary domain, despite its critical role in identifying high-quality features. To address these issues, this paper introduces a novel MLFS algorithm, named VMFS. It innovatively integrates multi-granulation rough sets with three-way decision, leveraging multi-granularity decision-theoretic rough sets (MGDRS) with variable degrees for optimal performance. Initially, we construct coarse decision (RDC), fine decision (RDF), and uncertainty decision (RDU) functions for each object based on MGDRS with variable degrees. These decision functions then quantify the dependence of attribute subsets, considering both deterministic and uncertain aspects. Finally, we employ the dependency to assess attribute importance and rank them accordingly. Our proposed method has undergone rigorous evaluation on various standard multi-label datasets, demonstrating its superiority. Experimental results consistently show that VMFS significantly outperforms other algorithms on most datasets, underscoring its effectiveness and reliability in multi-label learning tasks.

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The rough set (RS) and multi-granulation rough set (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, bipolarity refers to the explicit handling of positive and negative aspects of data. In this paper, with the help of bipolar fuzzy preference relation (BFPR) and bipolar fuzzy preference δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}-covering (BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C), we put forward the idea of BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C based optimistic multi-granulation bipolar fuzzy rough set (BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C-OMG-BFRS) model and BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C based pessimistic multi-granulation bipolar fuzzy rough set (BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C-PMG-BFRS) model. We examine several significant structural properties of BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C-OMG-BFRS and BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C-PMG-BFRS models in detail. Moreover, we discuss the relationship between BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C-OMG-BFRS and BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C-PMG-BFRS models. Eventually, we apply the BFPδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}C-OMG-BFRS model for solving multi-criteria decision-making (MCDM). Furthermore, we demonstrate the effectiveness and feasibility of our designed approach by solving a numerical example. We further conduct a detailed comparison with certain existing methods. Last but not least, theoretical studies and practical examples reveals that our suggested approach dramatically enriches the MGRS theory and offers a novel strategy for knowledge discovery, which is practical in real-world circumstances.

On Multi-Granulation Rough Sets with Its Applications

On Multi-Granulation Rough Sets with Its Applications

Three-way decision-making methods with multi-intuitionistic β-neighborhood-based multiattribute group decision-making problems

Multiattribute group decision-making (MAGDM) is a decision analysis method used to address decision-making problems that have multiple attributes and multiple decision alternatives. It is generally believed that multigranulation rough sets (MGRSs) are a twofold scheme to solve MAGDM problems. Thus, in this paper, we aim to generalize MGRSs and decision-theoretic rough sets (DTRSs) to intuitionistic fuzzy β-covering (IFβC) information systems and propose a novel MAGDM method to handle decision-making problems, which not only deepens the cognition of the three-way decision (3WD) model but also expands its application in decision-making problems. The paper first introduces a novel conditional probability using the ideal positive degree of intuitionistic fuzzy numbers (IFNs) and then investigates its properties. Second, in the IFβC environment, we utilize the proposed conditional probabilities to construct two types of multigranulation decision-theoretic rough set (MGDTRS) models, an optimistic strategy and a pessimistic strategy, discuss their theoretical properties and explore the relationship between the two strategies. Third, a novel MAGDM method for multi-intuitionistic β-neighborhoods is established in accordance with the proposed MGDTRS model. We also establish an algorithm for the proposed MAGDM method. Fourth, we apply the proposed method to address several MAGDM problems. By conducting comparative analysis with existing methods, we demonstrate the effectiveness of the proposed method and discuss the advantages and limitations of the proposed method. Furthermore, we conduct extensive parameter experimentation analysis on the proposed method from different perspectives. The experimental results demonstrate the stability and effectiveness of our proposed method.

Neighborhood multigranulation rough sets for cost-sensitive feature selection on hybrid data

Feature selection is a vital preprocessing step in real applications of data mining and machine learning. With the prevalence of high-dimensional hybrid data sets in real-world scenarios, along with the presence of test costs and misclassification costs, the need for effective feature selection methods has become more prominent. However, existing feature selection approaches mainly focus on cost-sensitive data from a single granularity perspective, and they are primarily applicable to single-typed data sets. To address these limitations, this paper presents a novel feature selection approach specifically designed for hybrid data, considering variable test costs and misclassification costs. The proposed method is based on neighborhood multigranulation rough sets (NMRS), which provides more comprehensive and multi-angle data analysis for cost-sensitive hybrid data. First, a novel multigranulation model is developed to effectively process cost-sensitive hybrid data. Building upon this model, a cost-based multi-criteria measure is proposed to evaluate the significance of features. This measure takes into account the comprehensive information of candidate features, including their power in algebraic view, information view, and associated costs. Furthermore, a heuristic feature selection algorithm based on NMRS is proposed to handle hybrid data with the test costs and misclassification costs. This algorithm leverages the benefits of the proposed multigranulation model and cost-based measure to identify the most discriminative features efficiently. Finally, the experimental results on twelve different datasets show that the proposed heuristic algorithm outperforms other compared algorithms, especially in total cost and classification accuracy.

Covering based multi-granulation rough fuzzy sets with applications to feature selection

Feature selection acts as an important preprocessing method to reduce redundant information. In order to effectively evaluate the classification information hidden in a given attribute subset, a novel rough set model is put forth via integrating covering based rough fuzzy sets with multi-granulation rough sets. In view of this, fuzzy β-neighborhood is employed to describe the information representation and knowledge fusion of covering families, by which a pair of approximation operators are formulated and a new multi-granulation rough fuzzy set model is introduced. The generalized model gives a unified perspective for existing rough set models. We then investigate the axiomatic characterizations by view of optimism and pessimism. Finally, the data reduction is processed from the point of keeping the discrimination ability. The multi-granulation significance function of a candidate attribute in term of fuzzy decisions is defined, using which a greedy algorithm is developed for multi-granulation feature selection. Experiments on twelve different types of datasets show that our model is efficient and superior to three popular algorithms in terms of reduction rate and classification performance.

Multi-granulation rough approximations under normal distribution

Multi-granulation decision-theoretic rough set effectively combines Bayesian decision approaches with multi-granulation rough set theory, and provides an important theoretical framework for studying rough set. In this paper, we explore several extensional models of multi-granulation decision-theoretic rough sets under the normal distribution of the decision loss function. Using the 3σ rule of normal distribution, we transform the decision loss of the multi-granulation decision-theoretic rough set into a set of interval values. We construct the upper and lower approximations from the optimistic, weakly optimistic, pessimistic, weakly pessimistic, optimistic-pessimistic, weakly optimistic-pessimistic, pessimistic-optimistic, and weakly pessimistic-optimistic viewpoints, and provide the decision rules of the proposed rough set models. The work in this paper brings the decision behavior based on a multi-granulation decision-theoretic rough set closer to the actual situation.

A multigranulation rough set model based on variable precision neighborhood and its applications

A multigranulation rough set model based on variable precision neighborhood and its applications

Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis

Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis

Optimistic multigranulation roughness of fuzzy bipolar soft sets by soft binary relations and its applications

Two important mathematical methods for addressing uncertainty in data processing are multigranulation rough set (MGRS) and fuzzy bipolar soft set (FBSS). This paper describes a certain kind of multigranulation rough set in the context of multiple soft binary relations. We first define the multigranulation roughness of fuzzy bipolar soft sets in the two universes. Moreover, a detailed study of structural properties has been conducted in order to explore this concept. The key characteristics of the traditional MGRS model are completely preserved in this new approach. Following that, we suggest two decision-making algorithms with respect to aftersets and foresets of the soft binary relations over dual universes. This approach appears to be better suited and more adaptable than other available methods, making it a favorable option for addressing decision-making problems. Finally, we provide a practical application of the suggested approach to a real-world problem.

A Novel Diversified Attribute Group Decision-Making Method Over Multisource Heterogeneous Fuzzy Decision Systems With Its Application to Gout Diagnosis

Group decision-making (GDM) is a useful uncertain decision theory and tool. With the evolution of time, GDM problems become more and more complex. In reality, there are plenty of GDM problems with diversified attributes and heterogeneous information. In this paper, the diversified attributes describe the differences in attributes given by different decision-makers, and heterogeneous information refers to the differences in data types. Nonetheless, few existing GDM studies simultaneously focus on the above two characteristics of GDM problems. Moreover, the scenario of multiple decision preferences, and the attribute and expert weights based on heterogeneous information are also seldom discussed. Given this, by considering a kind of GDM problem with the characteristics of multi-source, heterogeneity, diversity, and multiple fuzzy decisions, this paper builds a novel GDM method from the perspective of multigranulation rough sets (MGRSs). Firstly, we construct a new weighted multigranulation generalized fuzzy rough set (WMGGFRS) over multi-source heterogeneous fuzzy decision systems. Subsequently, in response to heterogeneous information, the extended entropy weight methods are given to calculate the weight of each attribute and the weight of each expert. After that, we establish a GDM method using the WMGGFRS model to realize multi-source information fusion. Lastly, we apply the established method to the management decision-making problem of gout diagnosis. The results of comparative and sensitivity analyses demonstrate the feasibility, effectiveness, stability, and superiority of the method.

A Collaborative Multi-Granularity Architecture for Multi-Source IoT Sensor Data in Air Quality Evaluations

Air pollution (AP) is a significant environmental issue that poses a potential threat to human health. Its adverse effects on human health are diverse, ranging from sensory discomfort to acute physiological reactions. As such, air quality evaluation (AQE) serves as a crucial process that involves the collection of samples from the environment and their analysis to measure AP levels. With the proliferation of Internet of Things (IoT) devices and sensors, real-time and continuous measurement of air pollutants in urban environments has become possible. However, the data obtained from multiple sources of IoT sensors can be uncertain and inaccurate, posing challenges in effectively utilizing and fusing this data. Meanwhile, differences in opinions among decision-makers regarding AQE can affect the outcome of the final decision. To tackle these challenges, this paper systematically investigates a novel multi-attribute group decision-making (MAGDM) approach based on hesitant trapezoidal fuzzy (HTrF) information and discusses its application to AQE. First, by combining HTrF sets (HTrFSs) with multi-granulation rough sets (MGRSs), a new rough set model, named HTrF MGRSs, on a two-universe model is proposed. Second, the definition and property of the presented model are studied. Third, a decision-making approach based on the background of AQE is constructed via utilizing decision-making index sets (DMISs). Lastly, the validity and feasibility of the constructed approach are demonstrated via a case study conducted in the AQE setting using experimental and comparative analyses. The outcomes of the experiment demonstrate that the presented architecture owns the ability to handle multi-source IoT sensor data (MSIoTSD), providing a sensible conclusion for AQE. In summary, the MAGDM method presented in this article is a promising scheme for solving decision-making problems, where HTrFSs possess excellent information description capabilities and can adequately describe indecision and uncertainty information. Meanwhile, MGRSs serve as an outstanding information fusion tool that can improve the quality and level of decision-making. DMISs are better able to analyze and evaluate information and reduce the impact of disagreement on decision outcomes. The proposed architecture, therefore, provides a viable solution for MSIoTSD facing uncertainty or hesitancy in the AQE environment.

A novel multigranulation roughness of bipolar fuzzy set over dual universes and its applications

In the world, multigranulation rough sets and bipolar fuzzy sets are the practical tools for dealing with the uncertainty, vagueness, and imperfection that frequently arise in decision making problems. The goal of multigranulation rough sets is to characterize uncertain situations in various granularity spaces, whereas bipolar fuzzy sets (BFSs) have the capacity to handle uncertainty as well as informational bipolarity in a variety of contexts. This article examines the optimistic multigranulation rough approximation of a BFS in the light of multi-soft binary relations across two different universes. We investigate some algebraic properties of our newly constructed optimistic multigranulation rough set scheme. Measures of accuracy and roughness are also covered in this paper. Finally, two decision algorithms are designed with respect to aftersets and foresets that are applied to a decision making problem in disease diagnoses, and the applicability of the method is illustrated by a numerical example.

A dynamic framework for updating approximations with increasing or decreasing objects in multi-granulation rough sets

The data we need to deal with are getting bigger and bigger in recent years, and the same happens to multi-granulation rough sets, so updated schemes have been proposed with the variation of attributes or attribute values in multi-granulation rough sets. This paper puts forward a dynamic mechanism to update the approximations in multi-granulation rough sets when increasing or decreasing objects. Firstly, the relationships between the original approximations and updated approximations are explored when adding or deleting objects and the dynamic processes of updating the lower and upper approximations in optimistic and pessimistic approximations are proposed. Secondly, two corresponding dynamic algorithms and their time complexity are given. Finally, the experimental evaluations show the effectiveness of the proposed dynamic updating algorithms compared with the static algorithm.

Multigranular rough set model based on robust intuitionistic fuzzy covering with application to feature selection

Fuzzy and intuitionistic fuzzy β covering has attracted the interest of many researchers recently. However, some of the factors namely 1. the lack of inclusion relationship between lower and upper approximation, 2. Inability to fit real valued dataset i.e. misclassification, hinder its application in decision making. Also, majority of these approaches are affected by noise. All these factors have created the need for a robust model. This paper proposes a novel intutitionistic fuzzy β covering model which is robust, combining intuitionistic fuzzy set, β covering and multigranulation rough sets. A new intuitionistic fuzzy β covering based multigranulation model is proposed which satisfies inclusion relationship between two approximations. This robust model is used to formulate dependency degree, which is evaluated at various granularity levels and is thereby employed for feature subset selection. Series of experiments are conducted on real valued datasets to illustrate the robustness and effectiveness of the underlying model. Furthermore, a comparative analysis with state of art approaches followed by statistical test lays down the superiority of the proposed model.

Matrix Approaches for Covering-Based Multigranulation Fuzzy Rough Set Models

Multigranulation rough set theory is one of the most effective tools for data analysis and mining in multicriteria information systems. Six types of covering-based multigranulation fuzzy rough set (CMFRS) models have been constructed through fuzzy β -neighborhoods or multigranulation fuzzy measures. However, it is often time-consuming to compute these CMFRS models with a large fuzzy covering using set representation approaches. Hence, presenting novel methods to compute them quickly is our motivation for this paper. In this article, we study the matrix representations of CMFRS models to save time in data processing. Firstly, some new matrices and matrix operations are proposed. Then, matrix representations of optimistic CMFRSs are presented. Moreover, matrix approaches for computing pessimistic CMFRSs are also proposed. Finally, some experiments are proposed to illustrate the effectiveness of our approaches.

A novel pessimistic multigranulation roughness by soft relations over dual universe

<abstract><p>A multigranulation rough set over two universes delivers a unique perspective on the combination of multigranulation information. This paper presents the pessimistic multignualtion rough set over dual universes based on soft binary relations. Firstly, a new pessimistic multigranualtion rough set over dual universes based on two soft binary relations has been developed, and their properties are derived. Then we extend this idea and present pessimistic multigranulation roughness over dual universes based on the finite number of soft binary relations. Finally, we present an example to illustrate our proposed multigranualtion rough set model.</p></abstract>