Abstract In this paper, we present two methods for constructing new overlap functions on bounded lattices from given ones. At first, we introduce the notion of overlap functions on bounded lattices, which is a generalization of overlap functions on the real unit interval. Then we provide the ∧-extension of an overlap function on a subinterval and give the necessary and sufficient conditions for the ∧-extension to be an overlap function. Finally, we propose a definition of ordinal sum of finitely many overlap functions on subintervals of a bounded lattice, where the endpoints of the subintervals constitute a chain. Necessary and sufficient conditions for the ordinal sum yielding again an overlap function are provided.

中文翻译：

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有界格上重叠函数的构造

摘要 在本文中，我们提出了两种在给定格上构造新重叠函数的方法。首先，我们引入了有界格上重叠函数的概念，它是对真实单位区间上重叠函数的推广。然后我们提供了一个子区间上重叠函数的∧-扩展，并给出了∧-扩展是一个重叠函数的充要条件。最后，我们提出了在有界格子的子区间上有限多个重叠函数的序数和的定义，其中子区间的端点构成一个链。提供了再次产生重叠函数的序数和的充分必要条件。