A characterization of ordinal sums being t-norms on bounded lattices by ordinal sums of drastic t-norms

In recent years, the use of t-norms is increasing on several areas of Soft Computing, as well as the ordinal sum of t-norms, which is used to construct other t-norms. In this paper, given a family of pairwise disjoint subintervals of a bounded lattice, we present a characterization of the ordinal sum on the lattice being always a t-norm, for any arbitrary family of t-norms on these subintervals. As a consequence, we provide a direct tool to verify if these ordinal sums are or are not t-norms. Moreover, we can easily construct t-norms from ordinal sums of t-norms and recognize the structure of the bounded lattices considered.