The aim of the lecture is to present a new ordinal sum construction of t-norms and t-conorms on bounded lattices based on interior and closure operators and show its extension. The proposed construction method for ordinal sums of t-norms and t-conorms generalizes several recent constructions and provides a simple tool for introducing new classes of t-norms and t-conorms. Furthermore, a more general ordinal sum construction for partially ordered monoids will be presented, which unifies constructions of ordinal sums of t-norms and t-conorms on posets (lattices) and newly introduces generalized ordinal sums of uninorms on posets (lattices).