Showing papers on "Rough set published in 2022"

Tri-level attribute reduction in rough set theory

Abstract: Attribute reduction serves as a pivotal topic of rough set theory for data analysis. The ideas of tri-level thinking from three-way decision can shed new light on three-level attribute reduction. Existing classification-specific and class-specific attribute reducts consider only macro-top and meso-middle levels. This paper introduces a micro-bottom level of object-specific reducts. The existing two types of reducts apply to the global classification with all objects and a local class with partial objects, respectively. The new type applies to an individual object. These three types of reducts constitute tri-level attribute reducts. Their development and hierarchy are worthy of systematical explorations. Firstly, object-specific reducts are defined by object consistency from dependency, and they improve both classification-specific and class-specific reducts. Secondly, tri-level reducts are unified by tri-level consistency. Hierarchical relationships between object-specific reducts and class-specific, classification-specific reducts are analyzed, and relevant connections of three-way classifications of attributes are given. Finally, tri-level reducts are systematically analyzed, and two approaches, i.e., the direct calculation and hierarchical transition, are suggested for constructing a specific reduct. We build a framework of tri-level thinking and analysis of attribute reduction to enrich three-way granular computing. Tri-level reducts lead to the sequential development and hierarchical deepening of attribute reduction, and their results profit intelligence processing and system reasoning.

Tri-level attribute reduction in rough set theory

Abstract: Attribute reduction serves as a pivotal topic of rough set theory for data analysis. The ideas of tri-level thinking from three-way decision can shed new light on three-level attribute reduction. Existing classification-specific and class-specific attribute reducts consider only macro-top and meso-middle levels. This paper introduces a micro-bottom level of object-specific reducts. The existing two types of reducts apply to the global classification with all objects and a local class with partial objects, respectively. The new type applies to an individual object. These three types of reducts constitute tri-level attribute reducts. Their development and hierarchy are worthy of systematical explorations. Firstly, object-specific reducts are defined by object consistency from dependency, and they improve both classification-specific and class-specific reducts. Secondly, tri-level reducts are unified by tri-level consistency. Hierarchical relationships between object-specific reducts and class-specific, classification-specific reducts are analyzed, and relevant connections of three-way classifications of attributes are given. Finally, tri-level reducts are systematically analyzed, and two approaches, i.e., the direct calculation and hierarchical transition, are suggested for constructing a specific reduct. We build a framework of tri-level thinking and analysis of attribute reduction to enrich three-way granular computing. Tri-level reducts lead to the sequential development and hierarchical deepening of attribute reduction, and their results profit intelligence processing and system reasoning.

Incremental Feature Selection Using a Conditional Entropy Based on Fuzzy Dominance Neighborhood Rough Sets

Abstract: Incremental feature selection approaches can improve the efficiency of feature selection used for dynamic datasets, which has attracted increasing research attention. Nevertheless, there is currently no work on incremental feature selection approaches for dynamic ordered data. Moreover, the monotonic classification effect of ordered data is easily affected by noise, so a robust feature evaluation metric is needed for feature selection algorithm. Motivated by these two issues, we investigate incremental feature selection approaches using a new conditional entropy with robustness for dynamic ordered data in this study. First, we propose a new rough set model, i.e., fuzzy dominance neighborhood rough sets (FDNRS). Second, a conditional entropy with robustness is defined based on FDNRS model, which is used as evaluation metric for features and combined with a heuristic feature selection algorithm. Finally, two incremental feature selection algorithms are designed on the basis of the above researches. Experiments are performed on ten public datasets to evaluate the robustness of the proposed metric and the performance of the incremental algorithms. Experimental results verify that the proposed metric is robust and our incremental algorithms are effective and efficient for updating reducts in dynamic ordered data.

Subset neighborhood rough sets

Abstract: We present a novel kind of neighborhood, named subset neighborhood and denoted as Sρ-neighborhood. It is defined under an arbitrary binary relation using the inclusion relations between Nρ-neighborhoods. We study its relationships with some kinds of neighborhood systems given in the literature. Then, we formulate the concepts of Sρ-lower and Sρ-upper approximations, and Sρ-accuracy and roughness measures based on Sρ-neighborhoods. We show in which cases the Sρ-accuracy measure is the highest among related approximations and investigate under which conditions the Sρ-accuracy and Sρ-roughness measures are monotonic. Moreover, we compare our approach with two existing ones and elucidate the advantages of our technique to obtain accuracy measures under some specific relations. To support the obtained results, we provide two medical examples.

Topological approach to generate new rough set models

Abstract: Abstract In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ N ρ -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ α -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work.

Fuzzy Measures and Choquet Integrals Based on Fuzzy Covering Rough Sets

Abstract: Fuzzy sets and fuzzy rough sets are widely applied in data analysis, data mining, and decision-making. So far, the common method is to use rough approximate operators to induce aggregation functions when fuzzy rough sets are used for multicriteria decision-making (MCDM). However, they are parametric linear and the corresponding weights are additive measures. In this article, we give a novel method for MCDM based on fuzzy covering rough sets by using the nonadditive measure [i.e., fuzzy measure (FM)] and the nonlinear integral [i.e., Choquet integral (ChI)]. First, two nonadditive measures are presented by fuzzy covering lower and upper approximation operators, respectively. Moreover, both of them are FMs which are called $\beta$ -neighborhood approximation measures. Second, two types of ChIs with respect to $\beta$ -neighborhood approximation measures are constructed. A novel method, which considers the association, is presented to solve the problem of MCDM under the fuzzy covering rough set model. Third, a new approach based on $\beta$ -neighborhood approximation measures is proposed for attribute reductions in a fuzzy $\beta$ -covering information table. This approach of attribute reductions is used in MCDM. Finally, both new methods above are compared with other methods through some numerical examples and UCI datasets, respectively.

Interval Dominance-Based Feature Selection for Interval-Valued Ordered Data.

Abstract: Dominance-based rough approximation discovers inconsistencies from ordered criteria and satisfies the requirement of the dominance principle between single-valued domains of condition attributes and decision classes. When the ordered decision system (ODS) is no longer single-valued, how to utilize the dominance principle to deal with multivalued ordered data is a promising research direction, and it is the most challenging step to design a feature selection algorithm in interval-valued ODS (IV-ODS). In this article, we first present novel thresholds of interval dominance degree (IDD) and interval overlap degree (IOD) between interval values to make the dominance principle applicable to an IV-ODS, and then, the interval-valued dominance relation in the IV-ODS is constructed by utilizing the above two developed parameters. Based on the proposed interval-valued dominance relation, the interval-valued dominance-based rough set approach (IV-DRSA) and their corresponding properties are investigated. Moreover, the interval dominance-based feature selection rules based on IV-DRSA are provided, and the relevant algorithms for deriving the interval-valued dominance relation and the feature selection methods are established in IV-ODS. To illustrate the effectiveness of the parameters variation on feature selection rules, experimental evaluation is performed using 12 datasets coming from the University of California-Irvine (UCI) repository.

Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications

Abstract: The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.

A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures

Abstract: Rough set theory provides a useful tool for data analysis, data mining and decision making. For multi-criteria decision making (MCDM), rough sets are used to obtain decision rules by reducing attributes and objects. However, different reduction methods correspond to different rules, which will influence the decision result. To solve this problem, we propose a novel method for MCDM based on rough sets and a fuzzy measure in this paper. Firstly, a type of non-additive measure of attributes is presented by the importance degree in rough sets, which is a fuzzy measure and called an attribute measure. Secondly, for a decision information system, the notion of the matching degree between two objects is presented under an attribute. Thirdly, based on the notions of the attribute measure and matching degree, a Choquet integral is constructed. Moreover, a novel MCDM method is presented by the Choquet integral. Finally, the presented method is compared with other methods through a numerical example, which is used to illustrate the feasibility and effectiveness of our method.

Multi-label feature selection based on fuzzy neighborhood rough sets

Abstract: Abstract Multi-label feature selection, a crucial preprocessing step for multi-label classification, has been widely applied to data mining, artificial intelligence and other fields. However, most of the existing multi-label feature selection methods for dealing with mixed data have the following problems: (1) These methods rarely consider the importance of features from multiple perspectives, which analyzes features not comprehensive enough. (2) These methods select feature subsets according to the positive region, while ignoring the uncertainty implied by the upper approximation. To address these problems, a multi-label feature selection method based on fuzzy neighborhood rough set is developed in this article. First, the fuzzy neighborhood approximation accuracy and fuzzy decision are defined in the fuzzy neighborhood rough set model, and a new multi-label fuzzy neighborhood conditional entropy is designed. Second, a mixed measure is proposed by combining the fuzzy neighborhood conditional entropy from information view with the approximate accuracy of fuzzy neighborhood from algebra view, to evaluate the importance of features from different views. Finally, a forward multi-label feature selection algorithm is proposed for removing redundant features and decrease the complexity of multi-label classification. The experimental results illustrate the validity and stability of the proposed algorithm in multi-label fuzzy neighborhood decision systems, when compared with related methods on ten multi-label datasets.

Maximal rough neighborhoods with a medical application

Abstract: In this paper, we focus on the main concepts of rough set theory induced from the idea of neighborhoods. First, we put forward new types of maximal neighborhoods (briefly, Mσ -neighborhoods) and explore master properties. We also reveal their relationships with foregoing neighborhoods and specify the sufficient conditions to obtain some equivalences. Then, we apply Mσ -neighborhoods to define Mσ -lower and Mσ -upper approximations and elucidate which one of Pawlak's properties are preserved (evaporated) by these approximations. Moreover, we research AMσ -accuracy measures and prove that they keep the monotonic property under any arbitrary relation. We provide some comparisons that illustrate the best approximations and accuracy measures are obtained when σ=⟨i⟩ . To show the importance of Mσ -neighborhoods, we present a medical application of them in classifying individuals of a specific facility in terms of their infection with COVID-19. Finally, we scrutinize the strengths and limitations of the followed technique in this manuscript compared with the previous ones.

A Decision-Making Framework Using q-Rung Orthopair Probabilistic Hesitant Fuzzy Rough Aggregation Information for the Drug Selection to Treat COVID-19

Abstract: In our current era, a new rapidly spreading pandemic disease called coronavirus disease (COVID-19), caused by a virus identified as a novel coronavirus (SARS-CoV-2), is becoming a crucial threat for the whole world. Currently, the number of patients infected by the virus is expanding exponentially, but there is no commercially available COVID-19 medication for this pandemic. However, numerous antiviral drugs are utilized for the treatment of the COVID-19 disease. Identification of the appropriate antivirus medicine to treat the infection of COVID-19 is still a complicated and uncertain decision. This study’s key objective is to develop a novel approach called q-rung orthopair probabilistic hesitant fuzzy rough set (q-ROPHFRS), which incorporates the q-rung orthopair fuzzy set, probabilistic hesitant fuzzy set, and rough set structures. New q-ROPHFR aggregation operators have been established: the q-ROPHFR Einstein weighted averaging (q-ROPHFREWA) operator and the q-ROPHFR Einstein weighted geometric (q-ROPHFREWG) operator. In this study, we explored some basic features of the developed operators. Afterward, to demonstrate the viability and feasibility of the established decision-making approach in real-world applications, a case study related to selecting drugs for COVID-19 pandemic is addressed. Furthermore, a comprehensive comparison with the q-rung orthopair probabilistic hesitant fuzzy rough TOPSIS technique is also presented to illustrate the benefits of the new framework. The obtained results confirm the reliability and effectiveness of the proposed approach for finding uncertainty in real-world decision-making.

A Novel Rough Numbers based Extended MACBETH Method Implementation in the Prioritization of the Connected Autonomous Vehicles

Abstract: Digital transformation can help to make better use of existing transportation networks that are congested. One solution to the road congestion problem is real-time traffic management, which focuses on enhancing traffic flow conditions. The advantages of real-time traffic management systems have developed significantly as a result of connected autonomous vehicle (CAV) innovations. CAVs can act as enforcers for managing the traffic. This study aims to propose a novel rough numbers-based extended Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH) method for prioritizing real-time traffic management systems. Furthermore, a new approach for defining rough numbers is proposed, based on an improved methodology for defining rough numbers' lower and upper limits. This allows consideration of mutual relations between a set of objects and flexible representation of rough boundary interval depending on the dynamic environmental conditions. In this study, three main alternatives are defined for real-time traffic management systems: real-time traffic management, real-time traffic management integrated with CAVs, and real-time traffic management by using CAVs. For these alternatives, 5 main criteria and 18 sub-criteria are defined and then prioritized using the fuzzy multi-criteria decision-making (MCDM) approach. The proposed method's performance is validated through scenario analysis. The findings demonstrate that the proposed method is effective and applicable to real-world conditions. According to the study's findings, real-time traffic management with CAVs is the most advantageous alternative, while real-time traffic management integrated with CAVs is the least advantageous

Feature Selection With Fuzzy-Rough Minimum Classification Error Criterion

Abstract: Classical fuzzy rough set often uses fuzzy rough dependency as an evaluation function of feature selection. However, this function only retains the maximum membership degree of a sample to one decision class, it cannot describe the classification error. Therefore, in this article, a novel criterion function for feature selection is proposed to overcome this weakness. To characterize the classification error rate, we first introduce a class of irreflexive and symmetric fuzzy binary relations to redefine the concepts of fuzzy rough approximations. Then, we propose a novel concept of dependency: inner product dependency to describe the classification error and construct a criterion function to evaluate the importance of candidate features. The proposed criterion function not only can maintain a maximum dependency function, but also guarantees the minimum classification error. The experimental analysis shows that the proposed criterion function is effective for datasets with a large overlap between different categories.