This paper introduces two fundamental types of ordinal sum constructions for partially ordered monoids that are determined by two specific partial orderings on the disjoint union of the partially ordered monoids. Both ordinal sums of partially ordered monoids are generalized with the help of operators on posets, which combine, in some sense, the properties of interior and closure operators on posets. The proposed approach provides a unified view on several known constructions of ordinal sums of t-norms and t-conorms on posets (lattices) and introduces generalized ordinal sums of uninorms on posets (lattices).

中文翻译：

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关于部分有序幺半群的序数和：一种统一的方法来构造 t-范数、t-conorms 和 uninorms 的序数和

本文介绍了偏序幺半群的两种基本类型的序数和构造，它们由偏序幺半群的不相交并集上的两个特定偏序确定。偏序幺半群的两个序数和都在偏集上的算子的帮助下泛化，在某种意义上，它结合了偏集上的内部算子和闭包算子的性质。所提出的方法提供了关于 t-norms 和 t-conorms 的序数和的几种已知结构的统一观点，并引入了posets（格）上的 uninorms 的广义序数和。