Zero-reconstructible Triangular Norms as Universal Approximators

Abstrakt

This paper is inspired by recent results which have shown that a multiplicative generator of a strict triangular norm can be reconstructed from the first partial derivatives of the triangular norm on the segment {0}x[0,1]. The strict triangular norms on which this method is applicable have been called zero-reconstructible triangular norms. This paper shows that every continuous triangular norm can be approximated (with an arbitrary precision) by a zero-reconstructible one and thus substantiates the significance of this subclass of strict triangular norms.