Bustince Sola, Humberto

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https://academica-e.unavarra.es/handle/2454/48764

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Bustince Sola

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Humberto

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Estadística, Informática y Matemáticas

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ISC. Institute of Smart Cities

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0000-0002-1279-6195

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88384

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278

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Author: Fernández Fernández, Francisco Javier × Subject: Mobius transform ×

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    PublicationOpen Access
    A generalization of the Choquet integral defined in terms of the Mobius transform
    (IEEE, 2020) Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Horanská, Lubomíra; Mesiar, Radko; Stupñanová, Andrea; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    In this article, we propose a generalization of the Choquet integral, starting fromits definition in terms of the Mobius transform. We modify the product on R considered in the Lovasz extension form of the Choquet integral into a function F, and we discuss the properties of this new functional. For a fixed n, a complete description of all F yielding an n-ary aggregation function with a fixed diagonal section, independent of the considered fuzzy measure, is given, and several particular examples are presented. Finally, all functions F yielding an aggregation function, independent of the number n of inputs and of the considered fuzzy measure, are characterized, and related aggregation functions are shown to be just the Choquet integrals over the distorted inputs.