nLab t-norm




A t-norm is a semicartesian commutative monoidal structure on the unit interval [0,1][0,1] as a poset.

That means it is a commutative monoid structure on the set [0,1][0,1] that is order-preserving in each argument and with 11 as the unit element.

T-norms are used in fuzzy logic.


  • T(x,y)=min(x,y)T(x,y) = \min(x,y). This is the cartesian monoidal structure, also known as the minimum t-norm or the Godel t-norm.
  • T(x,y)=xyT(x,y) = x y, the product t-norm.
  • T(x,y)=max(x+y1,0)T(x,y) = \max(x+y-1,0), the Lukasiewicz t-norm (see Lukasiewicz logic?). This monoidal structure is moreover star-autonomous with the obvious involution x *=1xx^\ast = 1-x.

Created on January 3, 2018 at 17:59:23. See the history of this page for a list of all contributions to it.