Zero-reconstructible Triangular Norms as Universal Approximators

0329080 - ÚI 2011 RIV CZ eng J - Journal Article
Petrík, Milan - Sarkoci, P.
Zero-reconstructible Triangular Norms as Universal Approximators.
Neural Network World. Roč. 20, č. 1 (2010), s. 63-67. ISSN 1210-0552
R&D Projects: GA ČR GD401/09/H007
Institutional research plan: CEZ:AV0Z10300504
Keywords : zero-reconstructible strict triangular norm * approximation * multiplicative generator * reconstruction
Subject RIV: BA - General Mathematics
Impact factor: 0.511, year: 2010

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.
Permanent Link: http://hdl.handle.net/11104/0005437