Recently, Qiao gave the concrete form of the continuity of overlap and grouping functions on complete lattices by using meet- and join-preserving properties. By eliminating the property join-preserving (resp. meet-preserving), one gets right (resp. left) continuous functions, namely, $C_R$- (resp. $C_L$-) overlap and grouping functions. In this paper, we extend the notion of ordinal sums of overlap functions from the unit interval to complete lattices directly and indicate it does not necessarily lead to an overlap function. We find that the ordinal sums of finitely many overlap functions can create an overlap function on a frame that can be partitioned into a chain of subintervals. We also investigate ordinal sums of $C_R$- and $C_L$-overlap functions on complete lattices, where the endpoints of summand carriers constitute a chain. Moreover, we have an analogous discussion on grouping functions on complete lattices.

最近，乔利用满足和保持连接的性质给出了完全格上重叠和分组函数的连续性的具体形式。通过消除属性连接保留（resp. meet-preserving），得到右（resp.left）连续函数，即，$C_R$- （分别。$C_{\mathrm{大号}}$-) 重叠和分组功能。在本文中，我们将重叠函数的序数和的概念从单位区间扩展到直接完成格，并表明它不一定会导致重叠函数。我们发现有限多个重叠函数的序数和可以在一个帧上创建一个重叠函数，该帧可以划分为一系列子区间。我们还研究了序数和$C_R$- 和$C_{\mathrm{大号}}$- 完全格上的重叠函数，其中被加数载波的端点构成一个链。此外，我们对完全格上的分组函数进行了类似的讨论。