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Discussion of the structure of uninorms. (English) Zbl 1249.03093
Summary: The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known that every uninorm is built up using some triangular norm and some triangular conorm. If we assume that uninorm fulfils additional assumptions, then this triangular norm and this triangular conorm have to be ordinal sums. The intervals in ordinal sums depend on the set of values of a decreasing function.

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