As one class of binary continuous aggregation functions which play an important role in practical applications, overlap functions defined on the unit closed interval have been developed rapidly in the past decade. At the same time, Paiva et al. recently extended the concept of overlap functions on unit closed interval to the lattice-valued status and called them quasi-overlap functions on bounded lattices. In this paper, we mainly study the extension methods of quasi-overlap functions and their three generalized forms on bounded partially ordered sets. More concretely, first, we show some new extension methods of quasi-overlap functions, $0_P$-quasi-overlap functions, $1_P$-quasi-overlap functions and $0_P,1_P$-quasi-overlap functions on any bounded partially ordered set P by the so-called ⋄-operators and 0,1-homomorphisms, 1-⋄-operators and 1-homomorphisms, 0-⋄-operators and 0-homomorphisms, and 0,1-⋄-operators and ord-homomorphisms, respectively, which are different from the extension methods obtained by Qiao lately. And then, as an application of the new extension methods, some concrete quasi-overlap functions, $0_P$-quasi-overlap functions, $1_P$-quasi-overlap functions and $0_P,1_P$-quasi-overlap functions on some certain bounded partially ordered set P are constructed. Finally, we prove that these extensions maintain idempotent and Archimedean property of the known quasi-overlap functions, $0_P$-quasi-overlap functions, $1_P$-quasi-overlap functions and $0_P,1_P$-quasi-overlap functions on any bounded partially ordered set P.

作为在实际应用中发挥重要作用的一类二元连续聚合函数，定义在单位闭区间上的重叠函数在过去十年中得到了迅速发展。同时，Paiva 等人。最近将单位闭区间上的重叠函数的概念扩展到格值状态，并将其称为有界格上的准重叠函数。本文主要研究拟重叠函数的扩展方法及其在有界偏序集上的三种广义形式。更具体地说，首先，我们展示了准重叠函数的一些新扩展方法，$0_{磷}$-准重叠函数，$1_{磷}$-准重叠函数和$0_{磷},1_{磷}$-由所谓的 ⋄-算子和 0,1-同态、1-⋄-算子和 1-同态、0-⋄-算子和 0-同态以及 0在任何有界偏序集P上的拟重叠函数，分别是1-⋄-算子和ord-同态，这与乔最近得到的扩展方法不同。然后，作为新扩展方法的应用，一些具体的准重叠函数，$0_{磷}$-准重叠函数，$1_{磷}$-准重叠函数和$0_{磷},1_{磷}$-在某些有界偏序集P上构建准重叠函数。最后，我们证明了这些扩展保持了已知准重叠函数的幂等性和阿基米德性质，$0_{磷}$-准重叠函数，$1_{磷}$-准重叠函数和$0_{磷},1_{磷}$- 任何有界偏序集P上的准重叠函数。