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

Abstract

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. © 2008 Elsevier B.V. All rights reserved.