Bounds of triangular subnorms and their algorithms

Abstract

This article deals with the upper and lower bounds of triangular subnorms generated by continuous, strictly decreasing additive generators. It first establishes necessary and sufficient conditions for the comparability of such triangular subnorms. It then explores the existence of strict (resp. nilpotent) bounds of a finite family of strict (resp. nilpotent) triangular subnorms generated by continuous, strictly decreasing additive generators. By duality, completely analogous results are derived for triangular superconorms generated by continuous, strictly increasing additive generators. In particular, it supplies the corresponding algorithms for computing those bounds, which are illustrated by several examples.