In this paper, we present several necessary and sufficient conditions to ensure an ordinal sum of t-norms is still a t-norm on bounded lattices. For a fixed or an arbitrary bounded sublattice of a bounded lattice, we provide a direct characterization theo-rem, respectively. Meanwhile, we extend these results to the ordinal sum for a family of pairwise disjoint bounded sublattices. Furthermore, we investigate ordinal sum of t-norms on product lattices and reveal that there exist ordinal sum t-norms on non-trivial bounded sublattices of product lattices, which is different from the previous results of ordinal sum of t-norms defined on subintervals.(c) 2022 Elsevier B.V. All rights reserved.
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