Zero-Reconstructible Triangular Norms As Universal Approximators

Summary

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This paper is inspired by recent results [15, 16] 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} × [0,1]. The strict triangular norms to 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.

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Zero-Reconstructible Triangular Norms As Universal Approximators

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1. Introduction

Although the notion of a triangular norm was originally introduced within the framework of probabilistic metric spaces [20] , it has found a successful application in the theory of fuzzy sets [21] and fuzzy logic [5, 7, 8]. In this section, we present some basic facts about triangular norms and, particularly, about strict triangular no...

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