This paper introduces the concept of Galois adjunction on Psoset, studies its related properties, and further discusses the relationship between the internal operator, closure operator and Galois adjunction on Psoset.

The nullnorms as a class of hybrid aggregation operators, holds significant research value both in theory and practical applications, especially the nullnorms on ordered structures which has become a current research hotspot. Firstly, introduces the concept and basic properties of the nullnorms on a bounded Trellis. Secondly, it proposes a new construction method for the nullnorms on a bounded Trellis. Finally, it provides relevant examples of the nullnorms on a bounded Trellis.

As a class of mixed aggregation operators, uninorms hold significant research importance. In particular, uninorms on ordered structures are currently a research hotspot. This paper focuses on the construction of uninorms on bounded Trellis, proposing a new method for their construction. Additionally, it provides examples to illustrate the differences between this new method and existing approaches.