摘要翻译：
在Pawlak的粗糙集理论中，集合由一对上下近似来近似。为了从数值上度量近似的粗糙度，Pawlak通过使用上下近似的基数之比引入了粗糙度的定量度量。尽管粗糙度度量是有效的，但它的缺点是对于分区上的标准排序不是严格单调的。最近通过考虑分区的粒度进行了一些改进。本文用公理化的方法对粗糙度测度进行了探讨。在公理化地定义了粗糙测度和划分测度的基础上，给出了粗糙测度的一个统一构造，称为强Pawlak粗糙测度，并探讨了该测度的性质。我们证明了文献中改进的粗糙度测度是我们的强Pawlak粗糙度测度的特例，并介绍了另外三种强Pawlak粗糙度测度。我们公理方法的优点是，粗糙度测度一旦满足相关的公理定义，它的一些性质就会立即得到。
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英文标题：
《An axiomatic approach to the roughness measure of rough sets》
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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：
  In Pawlak's rough set theory, a set is approximated by a pair of lower and upper approximations. To measure numerically the roughness of an approximation, Pawlak introduced a quantitative measure of roughness by using the ratio of the cardinalities of the lower and upper approximations. Although the roughness measure is effective, it has the drawback of not being strictly monotonic with respect to the standard ordering on partitions. Recently, some improvements have been made by taking into account the granularity of partitions. In this paper, we approach the roughness measure in an axiomatic way. After axiomatically defining roughness measure and partition measure, we provide a unified construction of roughness measure, called strong Pawlak roughness measure, and then explore the properties of this measure. We show that the improved roughness measures in the literature are special instances of our strong Pawlak roughness measure and introduce three more strong Pawlak roughness measures as well. The advantage of our axiomatic approach is that some properties of a roughness measure follow immediately as soon as the measure satisfies the relevant axiomatic definition.
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PDF链接：
https://arxiv.org/pdf/0911.5395