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Kybernetika 42(3):303-318, 2006.

A Contour View on Uninorm Properties

Koen C. Maes and Bernard de Baets


Abstract:

Any given increasing $[0,1]^2\to[0,1]$ 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.


Keywords: uninorm; Contour line; Orthosymmetry; Portation law; Exchange principle; Contrapositive symmetry; Rotation invariance; Self quasi-inverse property;


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BIB TeX

@article{kyb:2006:3:303-318,

author = {M\aes, Koen C. and De Baets, Bernard},

title = {A Contour View on Uninorm Properties},

journal = {Kybernetika},

volume = {42},

year = {2006},

number = {3},

pages = {303-318}

publisher = {{\'U}TIA, AV {\v C}R, Prague },

}


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