Triangular norms as ordinal sums of semigroups in the sense of A. H. Clifford. (English) Zbl 1007.20054

From the authors’ abstract: Ordinal sums of semigroups leading to triangular norms are studied, generalizing the ordinal sum of triangular norms. The summands of these general ordinal sums are fully characterized, and the ordinal irreducibility of triangular norms is investigated, inducing a natural partition of the class of all triangular norms.


20M05 Free semigroups, generators and relations, word problems
03E72 Theory of fuzzy sets, etc.
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