Structure of uninorms. (English) Zbl 1232.03015

Fodor, János C.; Yager, Ronald R.; Rybalov, Alexander

Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5, No. 4, 411-427 (1997).

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.

Keywords:

triangular norms; triangular conorms; associative functions; neutral element; uninorms