Nullnorms with a zero element being at any point of a bounded lattice are an important generalization of triangular norms and triangular conorms. This paper obtains an equivalent characterization for the existence of idempotent nullnorms with the zero element a on any bounded lattice containing only two distinct elements incomparable with a. Furthermore, some basic properties for the bounded lattice containing only two distinct elements incomparable with a are presented.

中文翻译：

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表征一类特殊的有界格上的幂等零范数

Nullnorms 在有界晶格的任何点处具有零元素是三角范数和三角共形的重要推广。本文获得了在任何仅包含两个与a不可比的不同元素的有界格上存在具有零元素a的幂等零范数的等效表征。此外，还介绍了仅包含两个与a不可比的不同元素的有界晶格的一些基本属性。