On Weakly Cancellative Fuzzy Logics
Journal of Logic and Computation
On the structure of left-continuous t-norms that have a continuous contour line
Fuzzy Sets and Systems
On the convex combination of TD and continuous triangular norms
Information Sciences: an International Journal
The triple rotation method for constructing t-norms
Fuzzy Sets and Systems
A note on the convex combinations of triangular norms
Fuzzy Sets and Systems
Rotation-invariant t-norms: The rotation invariance property revisited
Fuzzy Sets and Systems
Commutativity and self-duality: Two tales of one equation
International Journal of Approximate Reasoning
Rotation-invariant t-norms: Where triple rotation and rotation--annihilation meet
Fuzzy Sets and Systems
Convex combinations of strict t-norms
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special Issue on Fuzzy Set Theory and Applications; Guest Editors: Ferdinand Chovanec, Olga Nánásiová, Alexander Šostak
On the structure of special classes of uninorms
Fuzzy Sets and Systems
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Associativity of triangular norms is an algebraic property which, unlike for example their commutativity, is usually understood as hardly visually interpretable. This problem has been studied intensively in the last decade and, as a result, geometric symmetries of triangular norms with involutive level sets have been revealed. The presented paper intends to introduce a different approach which gives more general results. The inspiration is taken from web geometry, a branch of differential geometry, and its concept of Reidemeister closure condition which is known to provide a geometric characterization of associativity of loops. The paper shows that this concept can be adopted successfully for triangular norms so that it characterizes their associativity in a similar way. Moreover, the offered adaptation preserves the beneficial transparency and simplicity of the Reidemeister closure condition. This way, a visual characterization of the associativity, based on the geometry of the level sets, is provided for general, continuous, and continuous Archimedean triangular norms.