In this paper, construction methods of overlap and grouping functions on complete lattices via complete homomorphisms and complete $0_L,1_L$-endomorphisms are investigated. At first, we propose the notion of O-generator triple of overlap functions. Then, properties such as $(\alpha ,B,C)$-migrativity, $(B,C)$-homogeneity, idempotency and cancellation law for the overlap functions obtained by such generator triples are discussed. Finally, we give an analogous discussion on grouping functions on complete lattices.

中文翻译：

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利用完全同态在完全格上构造重叠和分组函数

本文通过完全同态和完备格在完全格上构造重叠和分组函数的方法。 $0_{升},1_{升}$- 研究了内同态。首先，我们提出了重叠函数的O- generator三元组的概念。然后，属性如$(\alpha ,乙,C)$-迁移性， $(乙,C)$讨论了由这种生成器三元组获得的重叠函数的同质性、幂等性和抵消律。最后，我们对完全格上的分组函数进行了类似的讨论。