Continuous generated associative aggregation operators

Authors:
T. Calvo;R. Mesiar
Affiliations:
Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa, km 7.5, Palma de Mallorca, Spain;Department of Mathematics, Slovak Technical University, Radlinského 11, Bratislava, Slovak Republic and Institute of Information Theory and Automation, Academy of Sciences of the Czech Republ ...
Venue:
Fuzzy Sets and Systems
Year:
2002

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Abstract

Continuous generated associative aggregation operators are discussed. The only asymmetric solutions are the trivial operators of the projection to the first or the last coordinate, respectively. The only nontrivial convenient aggregation operators are necessarily symmetric and they are either continuous Archimedean t-norms and t-conorms, or generated nullnorms. The latter may combine any nilpotent t-conorm and any t-norm with any prescribed annihilator k ∈ ]0, 1[.