Rotation-invariant t-norms: The rotation invariance property revisited

Focusing on conjunctive, left-continuous, increasing [ 0 , 1 ] 2 → [ 0 , 1 ] functions T we redefine the rotation invariance property in terms of contour lines. Under the assumption of the existence of a neutral element e ∈ ] 0 , 1 ] , this rotation invariance property requires some partial commutativity and associativity. The functions that are rotation invariant w.r.t. all of their contour lines are characterized.