Talk:Construction of t-norms

Rotation t-norms and zero divisors

The introduction of t-norm rotations indicates "Let T be a left-continuous t-norm without zero divisors", and yet there is an example giving the rotation of the Lukasiewcz t-norm, which clearly does contain zero divisors, as it is a nilpotent Archimedean t-norm. The only thing I can come up with is that the translated Lukasiewicz t-norm, on the interval (.5,1], does not include the nilpotent elements (any element .5 or less). However, the original statement is misleading - it should indicate that the transformed Lukasiewicz t-norm contains no zero divisors, not the original t-norm itself.

Also, there exists an example giving the rotation of the drastic t-norm, which is not left-continuous, although it is right-continuous. I can't easily see how the translated drastic t-norm, on the interval (.5,1], becomes left-continuous by virtue of its translation. Which portion(s) of the rotation definitions is/are incorrect? Ajackson716 (talk) 00:15, 3 May 2023 (UTC)