Smooth t-subnorms on finite scales

In this work smooth t-subnorms and boundary weak t-norms (bwt-norms) defined on a finite chain are studied. In the smooth case, it is proved that smooth bwt-norms reduces to smooth t-norms, whereas a classification of smooth t-subnorms as ordinal sums of a smooth t-norm and an Archimedean smooth t-subnorm is proved, in a similar way as in the case of [0,1]. With respect to Archimedean smooth t-subnorms, some cases depending on their zero-region are considered, classifying all of them in some cases and some specific families in others.