Structure of Uninorms

An exhaustive study of uninorm operators is established. These operators are generalizations of t-norms and t-conorms allowing the neutral element lying anywhere in the unit interval. It is shown that uninorms can be built up from t-norms and t-conorms by a construction similar to ordinal sums. De Morgan classes of uninorms are also described. Representability of uninorms is characterized and a general representation theorem is proved. Finally, pseudo-continuous uninorms are defined and completely classified.