摘要翻译：
粗糙集主要研究对象通过等价关系在论域上的逼近。拟阵是向量空间中线性独立性的组合推广。本文定义了一个以论域的任意子集为参数的参数集族，用来连接粗糙集和拟阵。一方面，对于一个论域及其上的等价关系，通过下近似算子定义了一个参数集族。证明了这个参数集族满足拟阵的独立集公理，从而可以生成一个拟阵，称为粗糙集的参数拟阵。得到了参数集族的三种等价表示。此外，还证明了粗糙集的参数拟阵是一个分块回路拟阵与一个自由拟阵的直和。另一方面，由于划分电路拟阵通过下近似数得到了很好的研究，我们用它来研究粗糙集的参数拟阵。粗糙集参数拟阵的几个特征，如独立集、基、回路、秩函数和闭包算子，用下近似数表示。
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英文标题：
《Parametric matroid of rough set》
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作者：
Yanfang Liu and 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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一级分类：Computer Science        计算机科学
二级分类：Discrete Mathematics        离散数学
分类描述：Covers combinatorics, graph theory, applications of probability. Roughly includes material in ACM Subject Classes G.2 and G.3.
涵盖组合学，图论，概率论的应用。大致包括ACM学科课程G.2和G.3中的材料。
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英文摘要：
  Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.
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PDF链接：
https://arxiv.org/pdf/1209.4975