A contour view on uninorm properties

Koen C. Maes; Bernard De Baets

Kybernetika (2006)

  • Volume: 42, Issue: 3, page 303-318
  • ISSN: 0023-5954

Abstract

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Any given increasing [ 0 , 1 ] 2 → [ 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.

How to cite

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Maes, Koen C., and De Baets, Bernard. "A contour view on uninorm properties." Kybernetika 42.3 (2006): 303-318. <http://eudml.org/doc/33807>.

@article{Maes2006,
abstract = {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.},
author = {Maes, Koen C., De Baets, Bernard},
journal = {Kybernetika},
keywords = {uninorm; Contour line; Orthosymmetry; Portation law; Exchange principle; Contrapositive symmetry; Rotation invariance; Self quasi-inverse property; uninorm; contour line; orthosymmetry; portation law; exchange principle; contrapositive symmetry; rotation invariance},
language = {eng},
number = {3},
pages = {303-318},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A contour view on uninorm properties},
url = {http://eudml.org/doc/33807},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Maes, Koen C.
AU - De Baets, Bernard
TI - A contour view on uninorm properties
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 3
SP - 303
EP - 318
AB - 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.
LA - eng
KW - uninorm; Contour line; Orthosymmetry; Portation law; Exchange principle; Contrapositive symmetry; Rotation invariance; Self quasi-inverse property; uninorm; contour line; orthosymmetry; portation law; exchange principle; contrapositive symmetry; rotation invariance
UR - http://eudml.org/doc/33807
ER -

References

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