Geodesic
A contour view on uninorm properties
Kybernetika, Tome 42 (2006) no. 3, pp. 303-318

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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.
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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     author = {Maes, Koen C. and De Baets, Bernard},
     title = {A contour view on uninorm properties},
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     zbl = {1249.26022},
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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/