摘要翻译：
粗糙集理论是处理信息系统中不确定、粒度和不完全知识的有用工具。它是基于等价关系或划分的。拟阵理论是向量空间中推广线性无关性的一种结构，在许多领域有着广泛的应用。本文提出了一种新的矩阵，即由分块导出的分块电路矩阵。一个分块首先满足拟阵理论中的电路公理，然后它可以导出一个拟阵，称为分块-电路拟阵。在同一论域上，划分与等价关系是一一对应的，然后利用粗糙集理论研究了划分电路矩阵的一些特征。其次，类似于Wang和Zhu提出的上近似数，我们定义了下近似数。通过下逼近数和上逼近数，研究了分块电路矩阵及其对偶矩阵的一些性质。
---
英文标题：
《Characteristic of partition-circuit matroid through approximation number》
---
作者：
Yanfang Liu and William Zhu
---
最新提交年份：
2012
---
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。
--

---
英文摘要：
  Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence in vector spaces, and has a variety of applications in many fields. In this paper, we propose a new type of matroids, namely, partition-circuit matroids, which are induced by partitions. Firstly, a partition satisfies circuit axioms in matroid theory, then it can induce a matroid which is called a partition-circuit matroid. A partition and an equivalence relation on the same universe are one-to-one corresponding, then some characteristics of partition-circuit matroids are studied through rough sets. Secondly, similar to the upper approximation number which is proposed by Wang and Zhu, we define the lower approximation number. Some characteristics of partition-circuit matroids and the dual matroids of them are investigated through the lower approximation number and the upper approximation number.
---
PDF链接：
https://arxiv.org/pdf/1210.6209