Uni-nullnorms and Null-uninorms on bounded trellises

Abstract

In 2024, L.Zedam et al. pointed out that the meet operation is not a t-norm on a proper bounded trellis. This finding highlights the differences between aggregation operators on bounded trellises and those on bounded lattices, thereby inspiring our research into aggregation functions on bounded trellises. In this paper, uni-nullnorms and null-uninorms of the bounded trellises are first defined. Then, uni-nullnorms and null-uninorms on bounded trellises are constructed by employing interior and closure operators, along with t-(sub)norms and t-(super)conorms. Especially, if [Formula: see text] (resp. [Formula: see text]), a new method of constructing uninorms (resp. nullnorms) on bounded trellises is obtained. Differences between our work and existing literature are also illustrated through comparative examples. Additionally, new methods for constructing nullnorms and uninorms on bounded lattices are naturally presented.