Rotation-invariant t-norms: Where triple rotation and rotation--annihilation meet

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

Generalizing the notion of a zoom of a t-norm not only allows to extend the triple rotation method and its corresponding decomposition, but also allows to describe the interface between the triple rotation method and the rotation(-annihilation) method. An alternative view on the partition behind the rotation(-annihilation) method is required to make both methods compatible. Besides zooms we also use contour lines and the companion of a t-norm to concisely formulate the results.