摘要
本文首先将相似度理论进一步推广,给出了模糊相似度的公理化定义;然后给出了基于模糊相似度的推理算法,证明了该算法是规则再现的;进一步地,对基于模糊相似度推理算法构造的模糊系统的逼近性能进行了理论分析,给出了该系统具有插值性的充要条件,并给出了满足该条件的两个模糊相似度。最后,证明了当满足一定条件时,该系统具有二阶逼近精度。
Firstly, a kind of definition of fuzzy similarity degree is introduced, it is a generalization of the similarity measure. Secondly, a novel fuzzy reasoning, called fuzzy similarity-based reasoning method, is proposed. It is proved that this method possesses rule reappearance. Furthermore, the approximation abilities of fuzzy systems which are constructed by fuzzy similarity-based reasoning method are analyzed. The sufficient and necessary condition for the fuzzy systems possessing interpo- lation properties is obtained, and two fuzzy similarity measures which satisfy that condition are given. At last, it is proved that the corresponding fuzzy systems have second order accuracy approximation ability under some conditions.
出处
《工程数学学报》
CSCD
北大核心
2009年第3期423-430,共8页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(60774049)
国家863高技术计划课题(2006AA04Z163)
关键词
模糊推理
模糊控制
规则再现
模糊相似度
插值机理
fuzzy reasoning
fuzzy control
rule reappearance
fuzzy similarity degree
interpolation mechanism
