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Journal Articles Fuzzy Sets and Systems Year : 2018

k-maxitive Sugeno integrals as aggregation models for ordinal preferences

Quentin Brabant
Miguel Couceiro

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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Dates and versions

hal-01657107 , version 1 (12-01-2018)
hal-01657107 , version 2 (18-12-2018)

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Quentin Brabant, Miguel Couceiro. k-maxitive Sugeno integrals as aggregation models for ordinal preferences. Fuzzy Sets and Systems, 2018, 343, pp.65-75. ⟨10.1016/j.fss.2017.06.005⟩. ⟨hal-01657107v2⟩
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