Continuous Archimedean t-norms and their bounds
Upper and lower bounds in the class of continuous Archimedean t-norms are studied. The existence of strict (nilpotent) bounds of finite families of strict (nilpotent) t-norms is shown in a constructive way, based on the additive generators of the corresponding t-norms. In general, a nilpotent lower bound and a strict upper bound of a finite system of any continuous Archimedean t-norms can be found. Some examples and some applications are given. By the duality, similar results for bounds of continuous Archimedean t-conorms can be derived. (C) 2001 Elsevier Science B.V. All rights reserved.
additive generator nilpotent t-norm strict t-norm subadditive function superadditive function