Semi-divisible t-norms on discrete scales

Semi-divisibility of left-continuous triangular norms is a weakened version of the divisibility axiom. The t-norms on L={0,1/n,2/n,…,1} which fulfil the semi-divisibility axiom are studied. The only semi-divisible t-norm with Ran(nT)=L is shown to correspond to the Łukasiewicz t-norm. Several examples of semi-divisible discrete t-norms are shown.