Uncertainty Measurement for a Set-Valued Information System: Gaussian Kernel Method

He, Jiali; Wang, Pei; Li, Zhaowen

doi:10.3390/sym11020199

Cited by 4 publications

(3 citation statements)

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“…(⇐) We can use a similar method to prove the converse; therefore, we omit it here. The topological operator plays an important role in general topology and rough sets and provides a method for exchanging information systems [22]. We discuss the necessary and sufficient conditions for D to be a topological closure operator.…”

Section: Separation Properties Of Covering Approximation Spacesmentioning

confidence: 99%

“…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]. There are many ways to generate approximation operators from the above.…”

Section: Introductionmentioning

confidence: 99%

“…A topological structure is one of the most crucial structures in mathematics, offering mathematical tools to deal with information systems and rough sets [22]. Using the topological method to study covering approximation spaces is a highly effective approach.…”

Section: Introductionmentioning

confidence: 99%

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

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et al. 2023

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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: Separation Properties Of Covering Approximation Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Shang,

Wang,

et al. 2023

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Multi-source information fusion based on rough set theory: A review

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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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Uncertainty Measurement for a Set-Valued Information System: Gaussian Kernel Method

Cited by 4 publications

References 58 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

Multi-source information fusion based on rough set theory: A review

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

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