模糊系统中方形分片线性函数依K-积分模的泛逼近性

Universal approximation of square pricewise linear functions in K-integral norms in fuzzy system

首先引入方形分片线性函数和K-拟可加积分的概念,应用诱导算子及积分转换定理证明了方形分片线性函数在K-积分模意义下对一类可积函数的泛逼近性.该结果表明:模糊系统中方形分片线性函数对连续函数的逼近能力可以推广为对一般可积系统的逼近能力.

The concepts of square pricewise linear function and K-quasi-additive integral are introduced. By using induced operator and theorem of integral transformation, it is proved that＇square pricewise linear functions possess universal approximation for a class of integrable functions in the sense of K-integral norm. The results show that the approximation capability of square pricewise linear functions for continuous functions can be extended to general integrable systems.