Median preserving aggregation functions

Miguel Couceiro 1 Jean-Luc Marichal 2 Bruno Teheux 2
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : A median algebra is a ternary algebra that satisfies every equation satisfied by the median terms of distributive lattices. We present a characterization theorem for ag-gregation functions over conservative median algebras. In doing so, we give a characterization of conservative median algebras by means of forbidden substructures and by providing their representation as chains.
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Miguel Couceiro, Jean-Luc Marichal, Bruno Teheux. Median preserving aggregation functions. 8th International Summer School on Aggregation Operators and their Applications (AGOP 2015), Michał Baczyński, Bernard De Baets, Radko Mesiar, Jul 2015, Katowice, Poland. pp.85-89. ⟨hal-01184116⟩

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