Semi-divisible triangular norms

Abstract

Semi-divisibility of left-continuous triangular norms is a weakening of the divisibility (i.e., continuity) axiom for t-norms. In this contribution we focus on the class of semi-divisible t-norms and show the following properties: Each semi-divisible t-norm with Ran(n T ) = [0, 1] is nilpotent. Semi-divisibility of an ordinal sum t-norm is determined by the corresponding property of its first component (which can be a proper t-subnorm, too). Finally, negations with finite range derived from semi-divisible t-norms are studied.