Matrix approaches for some issues about minimal and maximal descriptions in covering-based rough sets

Wang, Jingqian; Zhang, Xiao­hong

doi:10.1016/j.ijar.2018.10.021

Cited by 19 publications

(7 citation statements)

References 59 publications

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“…Covering-based rough sets [6][7][8][9] were proposed to deal with the type of covering data. In application, they have been applied to knowledge reduction [10,11], decision rule synthesis [12,13], and other fields [14,15]. In theory, covering-based rough set theory has been connected with matroid theory [16][17][18], lattice theory [19,20], and fuzzy set theory [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A New Type of Single Valued Neutrosophic Covering Rough Set Model

Wang

Zhang

2019

Symmetry

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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.

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Section: Introductionmentioning

confidence: 99%

A New Type of Single Valued Neutrosophic Covering Rough Set Model

Wang

Zhang

2019

Symmetry

Self Cite

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“…Covering-based rough sets [3][4][5] were proposed to deal with the type of covering data. In application, they have been applied to knowledge reduction [6,7], decision rule synthesis [8,9], and other fields [10][11][12]. In theory, covering-based rough set theory has been connected with matroid theory [13][14][15][16], lattice theory [17,18] and fuzzy set theory [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Zhang

2018

Symmetry

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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.

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“…These studies are mostly based on matrix product or other operations. Scholars often change a set into a binary matrix, and then design algorithms based on properties of binary matrix (see Jingqian Wang [45], Chengxiang Hu [46], Yanyong Huang [47] Yunge Jing [48], etc.). Although the time complexity of determining the relation between two sets via matrix approach is a constant, they often consider all the objects in the universe without filtering.…”

Section: Introductionmentioning

confidence: 99%

Matrix-Based Approaches for Updating Approximations in Multigranulation Rough Set While Adding and Deleting Attributes

Yu¹,

Li²,

Wang³

et al. 2019

IJCIS

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With advanced technology in medicine and biology, data sets containing information could be huge and complex that sometimes are difficult to handle. Dynamic computing is an efficient approach to solve some problems. Since multigranulation rough sets were proposed, many algorithms have been designed for updating approximations in multigranulation rough sets, but they are not efficient enough in terms of computational time. The purpose of this study is to further reduce the computational time of updating approximations in multigranulation rough sets. First, searching regions in data sets for updating approximations in multigranulation rough sets are shrunk. Second, matrix-based approaches for updating approximations in multigranulation rough set are proposed. The incremental algorithms for updating approximations in multigranulation rough sets are then designed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.

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Matrix approaches for some issues about minimal and maximal descriptions in covering-based rough sets

Cited by 19 publications

References 59 publications

A New Type of Single Valued Neutrosophic Covering Rough Set Model

A New Type of Single Valued Neutrosophic Covering Rough Set Model

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

Matrix-Based Approaches for Updating Approximations in Multigranulation Rough Set While Adding and Deleting Attributes

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