一类模糊系统的逼近问题

APPROXIMATION PROBLEM OF A CLASS OF FUZZY SYSTEMS

讨论了一般模糊系统对任意连续函数的逼近问题 .找到了一类更一般的模糊系统 ,在这一类模糊系统中 ,对于任意给定的连续函数 ,总可以构造出一模糊系统 ,它可以按任意精度逼近该连续函数 ;得到了模糊划分与逼近精度之间的关系 ;此外还将主要定理推广到了Lp(1≤p <∞ )

Whether a general fuzzy system could approximate any continuous function on a compact domain is discussed. Firstly, a class of more general fuzzy systems is obtained. For any real continuous function on a compact domain, there exists a fuzzy system in this class which can uniformly approximate the continuous function to any degree of accuracy. Secondly, the relationship between the fuzzy partition and the accuracy of approximation has been found. Finally, the main theorem is generalized to L p (1≤p<∞) space.\;