扩张原理的粗集表示

The Rough Set Representation for Fuzzy Extension Principle

粗集、模糊集均是处理不确定信息的数据分析工具,是数据挖掘的重要方法。由Zadeh首先提出的模糊扩张原理是模糊集理论的最基本的原理之一,粗集是通过上、下近似算子来发挥作用的。本文讨论扩张原理与粗集上近似之间的关系,证明了扩张原理可以表示成粗集上近似的形式,因此,扩张原理成了粗集与模糊集之间的桥梁。此外,借助粗集上、下近似算子的公理系统解决了扩张原理的反问题。

Rough set theory is an important tool for data-mining. Extension principle is one of the most important principles in fuzzy set theory. This paper studies the relationship between the rough upper approximations and extension principle in both crisp and fuzzy environment. We explain the extension principle as a result of the upper approximation operators. By using extension principle,the connection between rough sets and fuzzy sets is established. We also consider the inverse problem of the extension principle from the viewpoint of the rough set axiomatic approach.