As an important class of aggregation operators, the notion of overlap functions was first presented in 2009 in order to be considered for applications in image processing context. Later, many other researches arised bringing some variations of those functions for different purposes. Here, our main goal is defining overlap functions on lattices and discuss how a weakned version of it, named quasi-overlaps, works when continuity is eliminated from the definition. Some properties of quasi-overlaps on lattices, namely convex sum, migrativity, homogeneity, idempotency and cancellation law are investigated. Also, Finally, properties related to continuity as “Archimedean” and “limiting” are studied.

作为聚合运算符的重要一类，重叠函数的概念于2009年首次提出，以便考虑用于图像处理环境中。后来，出现了许多其他研究，为不同目的带来了这些功能的一些变化。在这里，我们的主要目标是在晶格上定义重叠函数，并讨论在定义中消除了连续性时，它的弱化版本（称为准重叠）如何工作。研究了格上拟重叠的一些性质，即凸和，迁移性，同质性，幂等性和抵消定律。另外，最后，研究了与连续性有关的属性，如“阿基米德”和“极限”。