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

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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.

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Maes, K. C., & De Baets, B. (2009). Rotation-invariant t-norms: The rotation invariance property revisited. Fuzzy Sets and Systems, 160(1), 44–51. https://doi.org/10.1016/j.fss.2008.07.012

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