一类Vague系统的万能逼近性

The Universal Approximation of A Class of Vague Systems

基于规则的模糊系统在表示信息方面受到模糊集隶属度不能区分正面证据和反面证据的限制.对此,该文提出了基于Vague规则的一类Vague系统,它包括SISO和MISOVague系统;证明了:对于定义在紧集上的连续函数f,存在一类Vague系统,其Vague关系ε逼近f;Vague关系被去Vague化后,得到的系统输出万能逼近f.一类Vague系统增强了不确定信息的表示能力,扩大了万能逼近的适用范围并提供了更优良的实际的万能逼近器.

In representing information, rule-based fuzzy systems were restricted by fuzzy sets which could not distinguish the positive and negative evidence for membership of an object in the sets. To solve the problem, this paper puts forward a class of Vague systems which consist of SISO and MISO Vague systems, proves that for any continuous function f on a compact set there exists a class of Vague systems whose Vague relation ε-approximates f, and proves that the output derived from devaguefication of Vague relations for a given input universally approximates the function. A class of Vague systems enhances the ability to represent uncertain information, expand the scope of application of universal approximation, and provides better and practical universal approximators.