Semi-divisible t-norms on discrete scales

Authors:
A. Mesiarová-Zemánková
Affiliations:
Mathematical Institute of SAS, Štefánikova 49, 81473 Bratislava, Slovakia
Venue:
Fuzzy Sets and Systems
Year:
2007

Citing 2
Cited 1

Triangular norms on product lattices

Fuzzy Sets and Systems - Special issue on triangular norms
States on semi-divisible residuated lattices

Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue (pp 315-357) "Ordered structures in many-valued logic"

Some types of filters in MTL-algebras

Fuzzy Sets and Systems

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Abstract

Semi-divisibility of left-continuous triangular norms is a weakened version of the divisibility axiom. The t-norms on L={0,1/n,2/n,...,1} which fulfil the semi-divisibility axiom are studied. The only semi-divisible t-norm with Ran(n"T)=L is shown to correspond to the Lukasiewicz t-norm. Several examples of semi-divisible discrete t-norms are shown.