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Triangular norms – basic properties and representation theorems. (English) Zbl 1010.03046
Novák, Vilém (ed.) et al., Discovering the world with fuzzy logic. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 57, 63-81 (2000).
This is a review of the basic results on triangular norms (t-norms). The definition of a t-norm and its dual conorm is followed by examples of the most important t-norms and classes of t-norms (Frank, Yager). The mutual relations of continuous, strictly monotone, Archimedean and nilpotent norms are explained together with the respective proofs. The construction of new t-norms by ordinal sums is explained as well as their construction by additive and multiplicative generators. Basic statements on the connection between properties of generators and those of corresponding generated t-norms are proved.
For the entire collection see [Zbl 0979.00015].

MSC:
03E72 Theory of fuzzy sets, etc.
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