Construction methods for idempotent nullnorms on bounded lattices

摘要

In this paper, we discuss the presence of idempotent nullnorms on bounded lattices and investigate some properties of these operators. We introduce two new methods for constructing idempotent nullnorms on bounded lattices for a zero element under a constraint that all elements incomparable with the zero element are comparable with each other. In order to stress the role of this constraint satisfying that our constructions yield an idempotent nullnorm, some illustrative examples are added.