摘要
利用积分模(度量)研究模糊系统对可积函数类的逼近性是人们普遍关注的方法,而基于K-拟算术运算诱导的Kp-积分模不仅是一维积分模的推广,而且是刻画p-次可积函数类的重要工具.本文通过引入拟减运算重新定义Kp-积分模,且在Kp-积分模意义下讨论分片线性函数对一类μp-可积函数的逼近性,进而构造性地证明广义Mamdani模糊系统对μp-可积函数类仍有逼近性.最后通过实例分析说明广义Mamdani模糊系统的逼近效果.结果表明广义Mamdani模糊系统可以按任意精度逼近一类μp-可积函数.
Researching on the approximation of fuzzy system to integrable function class by means of the integral norm（ a metric） is one method of common concern to the people. The Kp-integral norm induced by the K-quasi-arithmetic operations is not only a generalization for a one dimensional integral norm,but also an important tool to describe the p-integrable function classes. In this paper,the Kp-integral norm is redefined by introducing the quasi-subtraction operator. In the sense of the Kp-integral norm,the approximation of the piecewise linear functions to a kind of μp-integrable functions is discussed. Then,we prove constructively that the generalized Mamdani fuzzy system has the approximation to a class of μp-integrable functions. Finally,by a practical example the approximation effect of the generalized Mamdani fuzzy systems is illustrated. The results showthat the generalized Mamdani fuzzy system can approximate a kind of μp-integrable functions to arbitrary accuracy.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2015年第11期2284-2291,共8页
Acta Electronica Sinica
基金
国家自然科学基金(No.61374009)
