关于粗糙集和灰色系统之间某些关系的探讨

首先介绍粗糙集与灰色系统两种理论,并对二者进行比较。接着介绍普通粗糙集、P-粗糙集以及灰色集的定义,并就灰色集、模糊集和经典集合三者进行对比分析。我们提出了点灰度和集灰度两种灰度概念用于描述灰色系统的信息不确定性。通过P粗糙集导出相应的灰色集,并研究相关的灰度、粗糙度与边界域的性质和关系。分析表明使用导出的灰色集对系统的信息不确定性的估计与相应的粗糙集是一致的,因此两种理论在描述和处理不确定性信息系统方面的一定的相关性,将两种理论相结合来处理某些不确定性信息系统可能更为有效。

Some Relationships of Rough Sets and Grey Systems

This paper first introduces the rough set theory and the grey system theory and gives a comparison of them. The definitions of ordinary rough sets and P-rough sets are presented. And the definition of grey sets is introduced; meanwhile, the comparisons among grey sets, fuzzy sets and classical sets are given. We propose the concepts of grey degrees describing uncertain information, including the point grey degree and the set grey degree. Then we induce the grey sets by P-rough sets and study the properties and the relations of the relevant point grey degrees, set grey degrees, rough degrees and boundary regions. The results show that the evaluations of uncertain information using the induced grey sets accord with those by the corresponding rough sets. We conclude that the two theories have some correlations in processing uncertain information, and combining them to handle uncertain problems may be more effective.