发表机构
Sichuan Normal University（四川师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在有界伪序集上引入拟重叠与拟分组函数，研究其构造、不变性及相关性质，并提出两种基于边界忠实映射和伴随对的构造方法。
AI 中文摘要
本文首先在有界伪序集上分别引入拟重叠函数和拟分组函数，并给出它们各自的初步构造以及在商偏序集上诱导的拟重叠函数。随后，我们探讨了它们在加权和自同构下的不变性质。我们还引入了拟重叠函数的可迁移性、齐次性、幂等性、消去律、阿基米德性和极限性质，并讨论了它们之间的关系。最后，我们提出了两种构造拟重叠函数的方法，分别基于有界伪序集上的边界忠实映射和伴随对，以及有界格子的传递端点。相应的结论对拟分组函数同样成立。
英文摘要
In this article, we first introduce quasi-overlap and quasi-grouping functions on bounded pseudo-ordered sets, respectively, and give their respective preliminary constructions and the induced quasi-overlap functions on quotient posets.. We then explore the invariant properties under weighting and automorphisms. We also introduce the migrativity, the homogeneity, the idempotency, the cancellation law, the Archimedean and limiting properties of quasi-overlap functions and discuss their relations. We finally present two constructing methods of quasi-overlap functions, which are based on boundary-faithful mappings and adjunctions on bounded psosets and the transitive-endpoints of a bounded trellis, respectively. The corresponding statements are valid for quasi-grouping functions as well.
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