三类覆盖逼近的拓扑刻画 运算符

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摘要翻译：
基于覆盖的粗糙集理论是处理信息系统中不精确、不确定或模糊知识的有效工具。拓扑学是数学中最重要的学科之一，为研究信息系统和粗糙集提供了数学工具和有趣的话题。本文给出了三类覆盖逼近算子的拓扑刻画。首先，我们研究了第六类覆盖下近似算子所诱导的拓扑性质。其次，给出了复盖下逼近算子是内部算子的拓扑刻画。我们发现由该算子和由第六类覆盖下近似算子导出的拓扑是相同的。第三，我们研究了第一类覆盖上逼近算子是闭包算子的条件，发现该算子所诱导的拓扑与第五类覆盖上逼近算子所诱导的拓扑相同。第四，给出了第二类覆盖上逼近算子是闭包算子的条件以及由闭包算子导出的拓扑性质。最后，对这三种拓扑空间进行了比较。总之，拓扑学为研究基于覆盖的粗糙集提供了一种有用的方法。
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英文标题：
《Topological characterizations to three types of covering approximation
  operators》
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作者：
Aiping Huang, William Zhu
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最新提交年份：
2012
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in studying information systems and rough sets. In this paper, we present the topological characterizations to three types of covering approximation operators. First, we study the properties of topology induced by the sixth type of covering lower approximation operator. Second, some topological characterizations to the covering lower approximation operator to be an interior operator are established. We find that the topologies induced by this operator and by the sixth type of covering lower approximation operator are the same. Third, we study the conditions which make the first type of covering upper approximation operator be a closure operator, and find that the topology induced by the operator is the same as the topology induced by the fifth type of covering upper approximation operator. Forth, the conditions of the second type of covering upper approximation operator to be a closure operator and the properties of topology induced by it are established. Finally, these three topologies space are compared. In a word, topology provides a useful method to study the covering-based rough sets.
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PDF链接：
https://arxiv.org/pdf/1210.0074

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关键词：运算符 Presentation Intelligence Mathematical Topological 拓扑 算子 type study 刻画