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

  • Maes K
  • De Baets B
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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.

Author-supplied keywords

  • Contour line
  • Rotation invariance
  • T-norm
  • Uninorm

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