k-maxitive Sugeno integrals as aggregation models for ordinal preferences

Quentin Brabant 1 Miguel Couceiro 1
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : We consider an order variant of k-additivity, so-called k-maxitivity, and present an axiomatization of the class of k-maxitive Sugeno integrals over distributive lattices. To this goal, we characterize the class of lattice polynomial functions with degree at most k and show that k-maxitive Sugeno integrals coincide exactly with idempotent lattice polynomial functions whose degree is at most k. We also discuss the use of this parametrized notion in preference aggregation and learning. In particular, we address the question of determining optimal values of k through a case study on empirical data.
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Quentin Brabant, Miguel Couceiro. k-maxitive Sugeno integrals as aggregation models for ordinal preferences. Fuzzy Sets and Systems, Elsevier, 2018, 343, pp.65-75. ⟨10.1016/j.fss.2017.06.005⟩. ⟨hal-01657107v2⟩

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