粗糙模糊集的近似表示

The Approximate Representation of Rough-fuzzy Sets

粗糙模糊集是利用粗糙集的Pawlak知识空间来近似刻画一个模糊集(不确定概念)的理论模型.粗糙模糊集用上、下近似模糊集作为目标概念的边界模糊集,它没有给出在当前知识基下如何得到目标模糊概念的近似模糊集或近似精确集的方法.文中首先给出模糊集的相似度(近似度)的概念,定义了Pawlak知识空间U/R下的阶梯模糊集、均值模糊集、0.5-精确集等概念;然后分析得出U/R知识空间下的均值模糊集是所有阶梯模糊集中与目标模糊集最接近的模糊集,U/R知识空间下0.5-精确集是目标模糊集最接近的近似精确集;分析了均值模糊集、0.5-精确集分别与目标模糊集之间的相似度随知识粒度变化的变化规律.从新的视角提出了不确定性目标概念的近似表示和处理的方法,促进了不确定人工智能的发展.

Rough-fuzzy set describes a fuzzy set（or an uncertain concept）by Pawlak＇s knowledge space in the classical rough set model.In rough-fuzzy sets model,upper-approximation fuzzy set and lower-approximation fuzzy set are considered as two boundary fuzzy sets of the target concept,and there are few methods for constructing a fuzzy approximation set or a crisp approximation set of a target fuzzy concept in current knowledge base.In this paper,the concept of similarity is presented first and then the definitions of step-fuzzy set,average-fuzzy set and 0.5-crisp set of a fuzzy set are proposed in the knowledge space U/R.The conclusions that the averagefuzzy set is the best fuzzy approximation set of the target fuzzy set in all step-fuzzy sets and the0.5-crisp set also is the best crisp approximation set of the target fuzzy set in all crisp sets in Pawlak＇s knowledge space are presented and proved.Moreover,the similarity degree between the average-fuzzy set and the target fuzzy,and the similarity degree between the 0.5-crisp set and the target fuzzy set are discussed respectively and the change rules of these similarity degrees with the changing knowledge granularity are analyzed in detail.This paper proposed a method in a new perspective to represent and process the uncertain target concept,and these results will promote the development of uncertain artificial intelligence.