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

Authors:
Koen C. Maes;Bernard De Baets
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium
Venue:
Fuzzy Sets and Systems
Year:
2009

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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.