Discrete integrals based on comonotonic modularity
Identifieur interne : 001342 ( Hal/Checkpoint ); précédent : 001341; suivant : 001343Discrete integrals based on comonotonic modularity
Auteurs : Miguel Couceiro [France] ; Jean-Luc Marichal [Luxembourg (pays)]Source :
Abstract
It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals as well as natural extensions of Sugeno integrals.
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DOI: 10.3390/axioms2030390
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<front><div type="abstract" xml:lang="en">It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals as well as natural extensions of Sugeno integrals.</div>
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