基于邻域的覆盖粗糙集方法 街区

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摘要翻译：
粗糙集理论是一种处理信息系统中不精确或不确定知识的数学工具，最初是通过等价关系来描述元素的不可区分性。覆盖粗糙集是经典粗糙集的自然推广，它将等价关系中的划分放宽到覆盖上。近年来，邻域等拓扑概念被应用于覆盖粗糙集。本文通过近似运算进一步研究了基于邻域的覆盖粗糙集。我们证明了基于邻域的上近似可以等价定义而不使用邻域。为了分析覆盖本身，我们引入了覆盖上的一元运算和复合运算。给出了一个同态概念，用来联系两个覆盖逼近空间。我们还分别考察了由运算和同态保持的逼近的性质。
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英文标题：
《Covering rough sets based on neighborhoods: An approach without using
  neighborhoods》
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作者：
Ping Zhu
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最新提交年份：
2010
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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：
  Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.
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PDF链接：
https://arxiv.org/pdf/0911.5394

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关键词：粗糙集 neighborhood Intelligence Presentation Mathematical 同态 Covering 工具 等价关系 approximation