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Structure of uninorms. (English) Zbl 1232.03015

Summary: 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.

MSC:

03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
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