Approximation Operator Based on Neighborhood Systems

Wang, Pei; Wu, Qingjun; He, Jiali; Shang, Xiao

doi:10.3390/sym10110539

Cited by 4 publications

(1 citation statement)

References 37 publications

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“…For example, Zhang Y.L., et al studied the invariance of covering rough sets using compatible mappings [14], and Li J.J. studied covering generalized approximation spaces using topological methods [15,16]. Wang P., et al studied the necessary and sufficient conditions for the covering upper approximation operator to become a topological closure operator and investigated its membership functions [17,18]. Zhang W.X., et al studied the rough set of general relations, and so on [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations

Shang,

Wang,

et al. 2023

Symmetry

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In rough set theory, there are many covering approximation spaces, so how to classify covering approximation spaces has become a hot issue. In this paper, we propose the concepts of a covering approximation T1-space, F-symmetry, covering rough continuous mapping, and covering rough homeomorphism mapping, and we obtain some interesting results. We have used the above definitions and results to classify covering approximation spaces. Finally, we find a new method for constructing topologies, obtain some properties, and provide an example to illustrate our method’s similarities and differences with other construction methods.

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Section: Introductionmentioning

confidence: 99%

Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations

Shang,

Wang,

et al. 2023

Symmetry

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An incremental approach to feature selection using the weighted dominance-based neighborhood rough sets

Pan

Ran

2022

Int. J. Mach. Learn. & Cyber.

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Continuous Mapping of Covering Approximate Space and Topology Induced by Arbitrary Covering Relation

Shang¹,

Wang²,

Wu³

et al. 2023

Preprint

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In the study of rough sets, there are many covering approximation spaces, how to classify covering approximation spaces has become a hot issue. In this paper, we propose concepts covering approximation $T_{1}$-space, $F-$symmtry, covering rough continuous mapping, covering rough homeomorphism mapping to solve this question. We also propose a new method for constructing topology in Theorem 5.1, and get the following properties: (1) For each $x\in U$, $\{X_{i}:i\in I\}\subseteq \mathcal{P}(U)$ is all the subsets of $U$ which contains $x$ and $*$ is a reflexive relation on $U$. If $V\in \tau$ is a subset of $U$ and $x\in V$, then $\underline{*}(\bigcap \limits_{i\in I}X_{i})$ is the smallest subset of $U$ and $x \in \underline{*}(\bigcap \limits_{i\in I}X_{i})\subseteq V$. Denoted by $C(x)=\bigcap \{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$. (2)If $V\in \tau$ is a subset of $U$, then $V =$ $\bigcup \limits_{x\in V} C(x)$. (3) Let $\{\underline{*}(X_{i}):x\notin \underline{*}(X_{i}), i\in I\}$, then $\overline{\{x\}}$ $=$ $U \setminus \bigcup \limits_{x\notin \underline{*}(X_{i}), i\in I}\underline{*}(X_{i})$; (4) Let $*$ be a reflexive relation on $U$. For every $X\subseteq U$, we have $int(\underline{*}(X))=\underline{*}(X)$. Where $int(\underline{*}(X))$ represents the interior of $\underline{*}(X)$. (5) Let $\{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$ be a family subsets of $U$, then $\{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$ is a base for $(U,\tau)$ at the point $x$. \\

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Approximation Operator Based on Neighborhood Systems

Cited by 4 publications

References 37 publications

Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations

Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations

An incremental approach to feature selection using the weighted dominance-based neighborhood rough sets

Continuous Mapping of Covering Approximate Space and Topology Induced by Arbitrary Covering Relation

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