[en] In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in this characterization, symmetry can be replaced with both bisymmetry and existence of a neutral element.
Disciplines :
Computer science Mathematics
Author, co-author :
Couceiro, Miguel; LORIA, CNRS - Inria Nancy Grand Est - Université de Lorraine
DEVILLET, Jimmy ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
MARICHAL, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
On idempotent discrete uninorms
Publication date :
June 2017
Event name :
Proc. 9th Int. Summer School on Aggregation Operators and their Applications (AGOP 2017)
Event organizer :
Vicenç Torra
Event place :
Skövde, Sweden
Event date :
from 19-06-2017 to 22-06-2017
Audience :
International
Main work title :
Aggregation Functions in Theory and in Practice
Author, co-author :
De Baets, Bernard
Editor :
Torra, Vicenç
Mesiar, Radko
Publisher :
Springer, Berlin, Germany
Edition :
2018
ISBN/EAN :
978-3-319-59306-7
Collection name :
Series: Advances in Intelligent Systems and Computing, Vol. 581
