Covering rough set structures for a locally finite covering approximation space

2019 ◽  
Vol 480 ◽  
pp. 420-437 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Rough Set ◽  
Approximation Space ◽  
Finite Covering ◽  
Locally Finite ◽  
Covering Rough Set

scholarly journals A New Type of Single Valued Neutrosophic Covering Rough Set Model

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1074
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Inclusion Relation ◽  
Approximation Space ◽  
Matrix Representations ◽  
Model Based ◽  
Approximation Operators ◽  
New Type ◽  
Novel Method ◽  
Covering Rough Set

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.

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

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 710 ◽  
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Approximation Space ◽  
Matrix Representations ◽  
Neutrosophic Sets ◽  
Approximation Spaces ◽  
The Matrix ◽  
Novel Method ◽  
Covering Rough Set

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.

scholarly journals Characterizations of an MW-topological rough set structure

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2357-2366
Author(s):  
Sang-Eon Han
Keyword(s):  
Euclidean Space ◽  
Compact Subset ◽  
Rough Set ◽  
Dimensional Euclidean Space ◽  
Finite Covering ◽  
Locally Finite ◽  
Target Set ◽  
The Universe

Regarding the study of digital topological rough set structures, the present paper explores some mathematical and systemical structures of the Marcus-Wyse (MW-, for brevity) topological rough set structures induced by the locally finite covering approximation (LFC-, for brevity) space (R2,C) (see Proposition 3.4 in this paper), where R2 is the 2-dimensional Euclidean space. More precisely, given the LFC-space (R2,C), based on the set of adhesions of points in R2 inducing certain LFC-rough concept approximations, we systematically investigate various properties of the MW-topological rough concept approximations (D -M, D+M) derived from this LFC-space (R2,C). These approaches can facilitate the study of an estimation of roughness in terms of an MW-topological rough set. In the present paper each of a universe U and a target set X(? U) need not be finite and further, a covering C is locally finite. In addition, when regarding both an M-rough set and an MW-topological rough set in Sections 3, 4, and 5, the universe U(? R2) is assumed to be the set R2 or a compact subset of R2 or a certain set containing the union of all adhesions of x ? X (see Remark 3.6).

scholarly journals Intuitionistic L-fuzzy β-covering Rough Set

2021 ◽  
pp. 1-19
Author(s):  
Peng Yu ◽  
Xiao-gang An ◽  
Xiao-hong Zhang
Keyword(s):  
Rough Set ◽  
Covering Rough Set

Attribute reduction in fuzzy multi-covering decision systems via observational- consistency and fuzzy discernibility

2021 ◽  
pp. 1-15
Author(s):  
Rongde Lin ◽  
Jinjin Li ◽  
Dongxiao Chen ◽  
Jianxin Huang ◽  
Yingsheng Chen
Keyword(s):  
Rough Set ◽  
Attribute Reduction ◽  
Recursive Method ◽  
Redundant Information ◽  
Reduction Algorithm ◽  
Discernibility Matrix ◽  
Decision Systems ◽  
Theoretical Tool ◽  
Lower Ratio ◽  
Covering Rough Set

Fuzzy covering rough set model is a popular and important theoretical tool for computation of uncertainty, and provides an effective approach for attribute reduction. However, attribute reductions derived directly from fuzzy lower or upper approximations actually still occupy large of redundant information, which leads to a lower ratio of attribute-reduced. This paper introduces a kind of parametric observation sets on the approximations, and further proposes so called parametric observational-consistency, which is applied to attribute reduction in fuzzy multi-covering decision systems. Then the related discernibility matrix is developed to provide a way of attribute reduction. In addition, for multiple observational parameters, this article also introduces a recursive method to gradually construct the multiple discernibility matrix by composing the refined discernibility matrix and incremental discernibility matrix based on previous ones. In such case, an attribute reduction algorithm is proposed. Finally, experiments are used to demonstrate the feasibility and effectiveness of our proposed method.

Measures of uncertainty for a fuzzy probabilistic approximation space

2021 ◽  
pp. 1-24
Author(s):  
Lijun Chen ◽  
Damei Luo ◽  
Pei Wang ◽  
Zhaowen Li ◽  
Ningxin Xie
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Relation ◽  
Point Of View ◽  
Approximation Space ◽  
Fuzzy Approximation ◽  
Entropy Measurement ◽  
Fuzzy Relation Matrix ◽  
Relation Matrix

 An approximation space (A-space) is the base of rough set theory and a fuzzy approximation space (FA-space) can be seen as an A-space under the fuzzy environment. A fuzzy probability approximation space (FPA-space) is obtained by putting probability distribution into an FA-space. In this way, it combines three types of uncertainty (i.e., fuzziness, probability and roughness). This article is devoted to measuring the uncertainty for an FPA-space. A fuzzy relation matrix is first proposed by introducing the probability into a given fuzzy relation matrix, and on this basis, it is expanded to an FA-space. Then, granularity measurement for an FPA-space is investigated. Next, information entropy measurement and rough entropy measurement for an FPA-space are proposed. Moreover, information amount in an FPA-space is considered. Finally, a numerical example is given to verify the feasibility of the proposed measures, and the effectiveness analysis is carried out from the point of view of statistics. Since three types of important theories (i.e., fuzzy set theory, probability theory and rough set theory) are clustered in an FPA-space, the obtained results may be useful for dealing with practice problems with a sort of uncertainty.

scholarly journals Attribute Reduction Based on Consistent Covering Rough Set and Its Application

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianchuan Bai ◽  
Kewen Xia ◽  
Yongliang Lin ◽  
Panpan Wu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Relevance Vector Machine ◽  
Support Vector ◽  
Processing Step ◽  
Important Processing ◽  
Continuous Attribute ◽  
Covering Rough Set

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.

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