Abstract In this paper, we study uni-nullnorms with both neutral elements and zero elements on bounded lattices. In order to illustrate the existence of uni-nullnorms on bounded lattices, we present two construction methods for obtaining such a uni-nullnorm. Also, we show two additional methods for the construction of idempotent nullnorms on bounded lattices, which are generalizations of the one proposed by Cayli and Karacal. Furthermore, we discuss the presence of idempotent uni-nullnorms on bounded lattices, and propose two construction methods to obtain an idempotent uni-nullnorm on any bounded lattice.

中文翻译：

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有界格上的单零范数

摘要 在本文中，我们研究了有界格上具有中性元素和零元素的单零范数。为了说明有界格上单零范数的存在，我们提出了两种构造方法来获得这样的单零范数。此外，我们展示了在有界格上构造幂等零范数的两种额外方法，它们是 Cayli 和 Karacal 提出的方法的推广。此外，我们讨论了有界格上幂等单零范数的存在，并提出了两种构造方法来获得任何有界格上的幂等单零范数。