Geodesic
A contour view on uninorm properties
Kybernetika, Tome 42 (2006) no. 3, pp. 303-318 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Any given increasing $[0,1]^2\rightarrow [0,1]$ function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.
Any given increasing $[0,1]^2\rightarrow [0,1]$ function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.
Classification : 03B52, 03E72, 06F05, 26B40
Keywords: uninorm; Contour line; Orthosymmetry; Portation law; Exchange principle; Contrapositive symmetry; Rotation invariance; Self quasi-inverse property 
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Maes, Koen C.; De Baets, Bernard. A contour view on uninorm properties. Kybernetika, Tome 42 (2006) no. 3, pp. 303-318. http://geodesic.mathdoc.fr/item/KYB_2006_42_3_a4/

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