摘要
给出由关于规则后件单增的模糊蕴涵算子构造的乘积推理机、"单点"模糊化方法和中心平均解模糊化方法设计的模糊系统,并分析了它对紧集上连续可微函数的逼近特性。结果表明:当模糊蕴涵算子θ满足θ(a,1)=1时,模糊系统不具有逼近能力;当θ(a,1)=p(a)(当0<a<1时,0<p(a)<1)时,模糊系统是一阶精度逼近器。特别地,当θ(a,1)=a并且隶属函数取特殊的三角形隶属函数时,模糊系统是二阶精度逼近器。
The fuzzy systems constructed by some fuzzy implication operators are introduced and their approximation property to continuously differentiable functions on compact sets is discussed. These implication operators are monotonically increasing functions with respect to rule consequents. The results are shown that, if a implication operator θ satisfies θ（a, 1） = 1, this fuzzy system has no approximability, and if θ satisfies θ（a, 1） = p （a）（0 〈 p （a） 〈 1 if 0 〈 a 〈 1）, the fuzzy system is 1-order accuracy approximator. Particularly, if θ（a, 1） = a and the membership functions are special triangular, then the fuzzy system is 2-order accuracy approximator.
出处
《模糊系统与数学》
CSCD
北大核心
2008年第6期124-129,共6页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(60474023)
教育部博士点基金资助项目(20020027013)
教育部科学技术重点项目(03184)
973国家重大基础研究计划基金资助项目(2002CB312200)
关键词
模糊系统
模糊蕴涵算子
逼近性
Fuzzy Systems
Fuzzy Implication Operators
Approximability
