Abstract Nullnorms as a generalization of the concepts of t-norms and t-conorms admit a zero element to be any element in a bounded lattice. In this paper, we discuss the characterization of idempotent nullnorms on bounded lattices and investigate some of the main properties of them. We propose some new methods yielding nullnorms, in particular idempotent nullnorms, on bounded lattices with the fixed zero element under some additional constraints. Moreover, some illustrative examples are presented to demonstrate the feasibility of the proposed methods.

中文翻译：

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关于有界格上零范数的一些结果

摘要 Nullnorms 作为 t-norms 和 t-conorms 概念的概括，允许零元素是有界格中的任何元素。在本文中，我们讨论了有界格上幂等零范数的表征，并研究了它们的一些主要性质。我们提出了一些新方法，在一些附加约束下具有固定零元素的有界格上产生零范数，特别是幂等零范数。此外，还提供了一些说明性示例来证明所提出方法的可行性。