New constructions of t-norms and t-conorms on bounded lattices and trellises

In this paper, we propose a rather effective method to construct t-norms using weak interior operators on appropriate bounded lattices, which covers several construction methods in the literature. We also present a generic construction method for t-norms on bounded trellises with the help of quasi-interior operators. In particular, we give the necessary and sufficient condition for this kind of construction and discuss how to relax the condition. Finally, the dual results for construction of t-conorms via weak (quasi-)closure operators on bounded lattices (trellises) are presented.