The structure of pseudo- n -uninorms with continuous underlying functions

The characterization of pseudo- n -uninorms with continuous underlying functions, i.e., the non-commutative version of n -uninorms, where all underlying (pseudo-)t-norms and (pseudo-)t-conorms are continuous, is discussed. The structure of an n -uninorm, which can be decomposed by the z -ordinal sum and the structure of a pseudo- n -uninorm, which cannot be decomposed by this approach, in general, are compared. It is shown that any pseudo- n -uninorm with continuous underlying functions can be decomposed via non-commutative ordinal sum into trivial and representable summands.