Abstract
T-norm properties for left-continuous, increasing [0,1]2→[0,1] functions can be fully described in terms of contour lines. For a left-continuous t-norm T, the rotation-invariance property comes down to the continuity of its contour line C 0. However, contour lines are inadequate to investigate the geometrical structure of these rotation-invariant t-norms. Enforced with the companion and zooms it is possible to totally reconstruct T by means of its contour line C 0 and its β-zoom, with β the unique fixpoint of C 0.
Keywords
- Rotation-invariant t-norm
- contour line
- companion
- zoom
- associativity
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Maes, K.C., De Baets, B. (2007). Advances in the Geometrical Study of Rotation-Invariant T-Norms. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_54
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DOI: https://doi.org/10.1007/978-3-540-72950-1_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
Online ISBN: 978-3-540-72950-1
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