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。几何格在各个领域有着广泛的应用，尤其是搜索算法的设计，在覆盖约简中起着重要的作用。本文通过拟阵构造了四种基于覆盖的粗糙集的几何格结构，并比较了它们之间的关系。首先，通过覆盖诱导的横向拟阵建立了基于覆盖的粗糙集的几何格结构，并研究了它的原子、模元和模对等特征。我们还在基于覆盖的粗糙集的背景下构造了这类几何格与横向拟阵之间的一一对应关系。其次，给出了三类覆盖上逼近算子是拟阵闭包算子的充要条件。通过闭包公理展示了三种类型的拟阵，进而得到了基于覆盖的粗糙集的三种几何格结构。第三，对这四种几何点阵结构进行了比较。利用几何格研究了基于覆盖的粗糙集的可约元等核心概念。总之，本工作为研究基于覆盖的粗糙集指出了一个有趣的视角，即几何格。
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英文标题：
《Geometric lattice structure of covering-based rough sets through
  matroids》
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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. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role in covering reductions. In this paper, we construct four geometric lattice structures of covering-based rough sets through matroids, and compare their relationships. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by the covering, and its characteristics including atoms, modular elements and modular pairs are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, sufficient and necessary conditions for three types of covering upper approximation operators to be closure operators of matroids are presented. We exhibit three types of matroids through closure axioms, and then obtain three geometric lattice structures of covering-based rough sets. Third, these four geometric lattice structures are compared. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely geometric lattice, to study covering-based rough sets.
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PDF链接：
https://arxiv.org/pdf/1210.0075