First, we present construction methods for interior operators on a meet semilattice. Second, under the assumption that the underlying meet semilattices constitute the range of an interior operator, we prove an ordinal sum theorem for countably many (finite or countably infinite) triangular norms on bounded meet semilattices, which unifies and generalizes two recent results: one by Dvořák and Holčapek and the other by some of the present authors. We also characterize triangular norms that are representable as the ordinal sum of countably many triangular norms on given bounded meet semilattices.

中文翻译：

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基于有界满足半格上的内部算子可表示为序数和的三角范数

首先，我们提出了满足半格上的内部算子的构造方法。其次，在底层满足半格构成内部算子范围的假设下，我们证明了有界满足半格上可数多（有限或可数无限）三角范数的序数和定理，它统一并推广了两个最近的结果：一个由Dvořák 和 Holčapek 以及其他一些现在的作者。我们还将三角范数刻画为可表示为给定有界交汇半格上可数许多三角范数的序数和。