Recently, Zhang et al. studied the distributivity between uni-nullnorms and overlap (grouping) functions [68]. They obtained the sufficient and necessary conditions for the distributivity equations between them. However, the distributivity between null-uninorms and overlap (grouping) functions is missing. To fill this gap, in this paper, we explore some new results on the distributivity equations between overlap (grouping) functions and null-uninorms, which are the generalization of uninorms and nullnorms. Meanwhile, we give the full characterization of any idempotent null-uninorm.

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关于零一范数和重叠（分组）函数之间的分布方程

最近，张等人。研究了单零范数和重叠（分组）函数之间的分布[68]。他们得到了它们之间的分配方程的充分必要条件。然而，零一范数和重叠（分组）函数之间的分布缺失。为了填补这一空白，在本文中，我们探索了重叠（分组）函数和零不范数之间的分布方程的一些新结果，它们是不范数和零范数的推广。同时，我们给出了任何幂等零一范数的完整特征。