[en] Due to their great importance in data fusion, aggregation functions have been extensively investigated for a few decades. Among these functions, fuzzy connectives (such as uninorms) play an important role in fuzzy logic.
We establish a remarkable connection between a family of associative aggregation functions, which includes the class of idempotent uninorms, and the concepts of single-peakedness and single-plateaudness, introduced in social choice theory by D. Black. Finally, we enumerate those orders when the underlying set is finite.
Disciplines :
Mathematics
Author, co-author :
Devillet, Jimmy ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Couceiro, Miguel; LORIA, CNRS - Inria Nancy Grand Est - Université de Lorraine
Marichal, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Single-peakedness in aggregation function theory
Publication date :
14 May 2019
Event name :
Séminaire de Mathématiques Discrètes, Optimisation et Décision (MDOD)
Event organizer :
Centre d'Economie de la Sorbonne Université Paris 1 - Panthéon Sorbonne
