Triangular norms on product lattices
Fuzzy Sets and Systems - Special issue on triangular norms
On ordinal sums of triangular norms on bounded lattices
Fuzzy Sets and Systems
Triangular norms on partially ordered sets
Fuzzy Sets and Systems
OR/AND neurons for fuzzy set connectives using ordinal sums and genetic algorithms
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
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One of the most important operators in soft computing are the triangular norms (t-norms), as well as the combination among them. The ordinal sum of triangular norms on [0, 1] has been used to construct other triangular norms. However, on a bounded lattice, an ordinal sum of t-norms may not be a t-norm. Several necessary and sufficient conditions are presented in this paper for ensuring whether an ordinal sum on a bounded lattice of arbitrary t-norms is, in fact, a t-norm. Moreover, we show that a large set of ordinal sums verify these conditions. Hence, they are very interesting in order to verify whether an ordinal sum on a bounded lattice is a t-norm for a particular family of t-norms.