Covering Rough Set Research Articles

Hesitant fuzzy β-covering ( T , I ) rough set models: An application to multi-attribute decision-making

Covering rough sets have been successfully applied to decision analysis because of the strong representing capability for uncertain information. As a research hotspot in decision analysis, hesitant fuzzy multi-attribute decision-making (HFMADM) has received increasing attention. However, the existing covering rough sets cannot handle hesitant fuzzy information, which limits its application. To tackle this problem, we set forth hesitant fuzzy β-covering rough set models and discuss their application to HFMADM. Specifically, we first construct four types of hesitant fuzzy β-covering ( T , I ) rough set models via hesitant fuzzy logic operators and hesitant fuzzy β-neighborhoods, which can handle hesitant fuzzy information without requiring any prior knowledge other than the data sets. Then, some intriguing properties of these models and their relationships are also discussed. In addition, we design a new method to deal with HFMADM problems by combining the merits of the proposed models and the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method. In this method, we not only consider the risk preferences of decision-makers, but also present a new hesitant fuzzy similarity measure expressed by hesitant fuzzy elements to measure the degree of closeness between two alternatives. Finally, an enterprise project investment problem is applied to illustrate the feasibility of our proposed method. Meanwhile, the stability and effectiveness of our proposed method are also verified by sensitivity and comparative analyses.

A Novel Fuzzy Covering Rough Set Model Based on Generalized Overlap Functions and Its Application in MCDM

As nonassociative fuzzy logic connectives, it is important to study fuzzy rough set models using overlap functions that replace the role of t-norms. Overlap functions and t-norms are logical operators with symmetry. Recently, intuitionistic fuzzy rough set and multi-granulation fuzzy rough set models have been proposed based on overlap functions. However, some results (that contain five propositions, two definitions, six examples and a proof) must be improved. In this work, we improved the existing results. Moreover, to extend the existing fuzzy rough sets, a new fuzzy covering rough set model was constructed by using the generalized overlap function, and it was applied to the diagnosis of medical diseases. First, we improve some existing results. Then, in order to overcome the limitations of the fuzzy covering rough set model based on overlap functions, a fuzzy β-covering rough set model based on generalized overlap functions was established. Third, some properties of the fuzzy β-covering rough set model based on generalized overlap functions are discussed. Finally, a multi-criteria decision-making (MCDM) method of the fuzzy β-covering rough set based on generalized overlap functions was proposed. Taking medical disease diagnosis as an example, the comparison with other methods shows that the proposed method is feasible and effective.

Neighborhood rough set‐based route selection for mobile ad hoc networks

SummaryThe main aim of this paper is to address the problem of redundant broadcast packets using the extension of rough set concept. In general, a rough set is a mathematical tool for dealing with issues of uncertainty. In MANET, mobile nodes are moving from one place to another place in a simulation environment; hence, it creates uncertainty issues. Due to the fast mobility of mobile nodes, network metrics such as bandwidth and hop count vary. The findings were useful in identifying and improving the network's performance. The proposed NRS‐based route selection approach has been compared with conventional techniques such as rough set, covering rough set (CRS). The reduced control packets are obtained using pruning concept based on selection of one‐hop and two‐hop nodes. Eventually, the proposed approach proved that it attains a higher throughput (85%), reducing the route request packets (3406) and delay of data transmission (0.02274 s). Also, two well‐known ad hoc routing protocols were used such as Dynamic Source Routing (DSR) and Ad Hoc On‐Demand Distance Vector (AODV) protocols.

A Class of Stochastic Programming Model in Investment Portfolio Based on Covering Rough Set

In order to study the investment portfolio problem, this paper propose a class of stochastic programming model with rough feasible region, where randomness and roughness coexist. Based on the covering rough set, the concept of the discrete degree covering is defined to divide the rough feasible region. Furthermore, the discrete degree covering stochastic rough programming model (DDC-SRP) is constructed depending on a synthesis effect function that considers discrete degree and the expectation and variance for random objective function. Properties of the DDC-SRP model are discussed. In addition, the convexity of the DDC-SRP model is obtained in some certain conditions. Considering the random rough simulation, a genetic algorithm is introduced. Finally, a numerical example is given to show the validity of the DDC-SRP model.

A Further Study on L-Fuzzy Covering Rough Sets

For L L = ∗ → ( , , ) a complete residuated lattice, a type of L -fuzzy covering rough sets was defined by Li [8] in 2017. In this paper, a further study on rough sets was given. Precisely, a single axiomatic characterization of the L -fuzzy covering rough sets was presented, and the relationships between the -fuzzy covering rough sets and L -fuzzy relation rough sets were established.

Characteristic numbers and approximation operators in generalized rough approximation system

Covering rough set theory and binary relation based rough set theory are regarded as two important different generalizations of Z. Pawlak's classical rough set theory. In fact, when serial relations are considered, they are the same thing. If R is a serial relation from a universe U to another universe V, then {{R−1(y)}:y∈V} is a covering of U and {{R(x)}:x∈U} is a covering of V. In a covering approximation space (U,C), the relation R defined as R(x)={C∈C:x∈C} is just a serial relation from U to V=C. So U and V have the same status and (U,V,R) is indeed a whole, then (U,V,R) is called an Approximation System in order to take a comprehensive study from a new and higher perspective. By introducing nthl neighborhoods and kthr neighborhoods recursively, a new set of upper and lower approximation operators is established, and the Approximation System is further referred to as the Generalized Rough Approximation System (GRAS). In order to describe some stability of the Approximate System, characteristic numbers such as l-cycle number, r-cycle number, link number and connect number are also introduced. From there, partitions of GRAS can be constructed and sub-GRAS can be defined. This makes the whole of GRAS modularized, which is a big simplification when it comes to solving real problems. In addition, some applications of characteristic numbers and approximation operators are illustrated by examples, and the Boolean matrix calculation formulas of all approximations are proved. Finally, the important special GRAS (U,U,R) is studied in detail and an application example is given.

On Different Types of Single-Valued Neutrosophic Covering Rough Set with Application in Decision-Making

This paper aims to propose the notion of Type-1 single-valued neutrosophic complementary β -neighborhood (briefly, Type-1 SVN complementary β -neighborhood) and use it to introduce a novel class of 1-single-valued neutrosophic β -covering rough set (briefly, 1-SVN β -CRS). Then, we will merge the 1-SVN β -neighborhood and 1-SVN complementary β -neighborhood to create new two models of 1-SVN β -CRS. Furthermore, we will discuss the relationships between the present work and Wang and Zhang’s work. For further study on Type-2 Wang and Zhang’s models, we will define the 2-SVN complementary β -neighborhood and use it to present a novel class of 2-SVN β -CRS. Also, we combine the 2-SVN β -neighborhood and 2-SVN complementary β -neighborhood to investigate the new two models of 2-SVN β -CRS. Lately, we will demonstrate two illustrative examples as real problems to show the differences between two of our approaches and Wang and Zhang’s approach.

Fuzzy Measures and Choquet Integrals Based on Fuzzy Covering Rough Sets

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> -neighborhood approximation measures. Second, two types of ChIs with respect to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> -neighborhood approximation measures is proposed for attribute reductions in a fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> -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 neutrosophic covering rough sets based on neighborhoods

<abstract> Covering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make multi-attribute decision making problem more tractable. Interval neutrosophic covering rough sets can be viewed as the bridge connecting Interval neutrosophic sets and covering rough sets. Firstly, the paper introduces the definition of interval neutrosophic sets and covering rough sets, where the covering rough set is defined by neighborhood. Secondly, Some basic properties and operation rules of interval neutrosophic sets and covering rough sets are discussed. Thirdly, the definition of interval neutrosophic covering rough sets are proposed. Then, some theorems are put forward and their proofs of interval neutrosophic covering rough sets also be gived. Lastly, this paper gives a numerical example to apply the interval neutrosophic covering rough sets. </abstract>

A New Method of Translating Covering Rough Set into Classical Rough Set

Binary relational rough sets enrich the applicable scope of classic rough set, but they lose some excellent properties. Therefore, covering translates to partition has become one of the key points in the study of covering approximate spaces. However, the existing translation methods have some shortcomings, such as the inconsistency between the partitions translated by covering and covering reduction, the inconsistency between the monotonicity of the covering and the translated partition, and the limited application of the translation method, and so on. In view of this situation, the basic requirements for covering translate partition are put forward, and then the concepts of transposed and symmetric classes are defined. On this basis, the translation method is proposed which gets over the shortcomings of the existing methods, and the effectiveness of the way is proved theoretically. At the same time, in consideration of the situation that practical data cannot form a single coverage, the new method is extended to the multi-covering approximate space by the minimum description of multi-covering elements.

Route classification scheme based on covering rough set approach in mobile ad hoc network (CRS-MANET)

PurposeThe purpose of this paper is to obtain correctly classified routes based on their parameters.Design/methodology/approachIn this paper, a covering rough set (CRS) approach is proposed for route classification in wireless ad hoc networks. In a wireless network, mobile nodes are deployed randomly in a simulation region. This work addresses the problem of route classification.FindingsThe network parameters such as bandwidth, delay, packet byte rate and packet loss rate changes due to the frequent mobility of nodes lead to uncertainty in wireless networks. This type of uncertainty can be very well handled using a rough set concept. An ultimate aim of classification is to correctly predict the decision class for each instance in the data.Originality/valueThe traditional classification algorithms, named K-nearest neighbor, J48, general rough set theory, naive Bayes, JRIP and multilayer perceptron, are used in this work for comparison and for the proposed CRS based on route classification approach revealing better accuracy than traditional classification algorithms.

A New Type of Single Valued Neutrosophic Covering Rough Set Model

Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making

Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making

Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making

In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented. Firstly, the notion of SVN β -covering approximation space is proposed, and some concepts and properties in it are investigated. Secondly, based on SVN β -covering approximation spaces, two types of SVN covering rough set models are proposed. Then, some properties and the matrix representations of the newly defined SVN covering approximation operators are investigated. Finally, we propose a novel method to decision making (DM) problems based on one of the SVN covering rough set models. Moreover, the proposed DM method is compared with other methods in an example.

The structures and the connections on four types of covering rough sets

Covering rough set model is an important extension of Pawlak rough set model, and its structure is the foundation of covering rough set theory. This paper considers four covering approximations and studies the structures of the families of their covering upper (or lower) definable sets by means of lattice theory. We provide some conditions under which the families of covering upper (or lower) definable sets with respect to these covering approximations are lattices of sets, or distributive lattices, or geometric lattices, or Boolean lattices. Furthermore, based on these results, we give the relationship among the four covering approximations and establish the connection between matroids and covering rough sets from the viewpoint of lattice theory.

Operation properties and algebraic properties of multi-covering rough sets

The multi-covering rough sets (MCRSs) are a popular aspect of rough sets. It is easy to see that classical rough sets, covering rough sets (CRSs) and multi-granulation rough sets (MGRSs) are all the special cases of the MCRSs. Recently, the algebraic theory of these rough set models mentioned above have been researched in detail. However, the algebraic theory of MCRSs has not been studied until now. It is necessary for researchers to explore the algebraic theory of MCRSs. In this paper, we focus on the operation and algebraic theories of two types of MCRS models. First, the properties of the two types of multi-covering set approximations are discussed. Especially, the properties of multi-covering approximation operators based on the unary coverings are deeply researched. Second, the operation properties with respect to intersection and union of MCRSs are researched. Meanwhile, to compute the intersection and union of MCRSs, several algorithms are constructed. Finally, on the basis of the operation properties of MCRSs, many meaningful algebraic properties of MCRSs are deeply studied.

Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making

Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

The comparative study of covering rough sets and multi-granulation rough sets

The covering rough set (CRS) theory and the multi-granulation rough set (MGRS) theory are both the important generalizations of Pawlak rough set theory. Up to now, substantial contributions have been made to the development of CRS and MGRS. In this paper, in order to shed some light on the comparison and combination of CRS theory and MGRS theory, we investigate the relationship between CRS and MGRS based on different aspects. We firstly put forward an effective approach to describe the covering rough sets by means of the multi-granulation rough sets. Then, we, respectively, study the differences and relations of lower and upper operators, reduction, operation properties and algebraic properties between CRS and MGRS.

Attribute Reduction Based on Consistent Covering Rough Set and Its Application

As an important processing step for rough set theory, attribute reduction aims at eliminating data redundancy and drawing useful information. Covering rough set, as a generalization of classical rough set theory, has attracted wide attention on both theory and application. By using the covering rough set, the process of continuous attribute discretization can be avoided. Firstly, this paper focuses on consistent covering rough set and reviews some basic concepts in consistent covering rough set theory. Then, we establish the model of attribute reduction and elaborate the steps of attribute reduction based on consistent covering rough set. Finally, we apply the studied method to actual lagging data. It can be proved that our method is feasible and the reduction results are recognized by Least Squares Support Vector Machine (LS-SVM) and Relevance Vector Machine (RVM). Furthermore, the recognition results are consistent with the actual test results of a gas well, which verifies the effectiveness and efficiency of the presented method.

Covering rough set-based classification for cardiac arrhythmia

The objective of this work is to use data processing methods to unravel the biomedical difficulties of detecting a selection of arrhythmia conditions from patient's electrocardiograph (ECG) signals. ECG graphical signal record waveforms square portion analysed supported morphological variations between irregular waves and regular waves. The Pan-Tompkins (PT) method is applied for takeout P, R, Q, S and T morphological peaks and wavelet transform (WT) temporal features are tested on five categories of graphical record ECG signals. During this paper, we tend to propose the covering rough set (CRS)-based classification method for classification of heartbeats to sign interior cardiac arrhythmia in ECG signals. The proposed classification system is tested using ECG records in Physiobank databases and also the results were compared to those from many prior studies. Experimental results show that our proposed approach in truth diagnoses heart cardiac arrhythmia. The experimental results show that the proposed system outperforms other classifiers.