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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2017 - 20202
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Author: Mesiar, Radko × Subject: Fuzzy measure ×

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Now showing 1 - 2 of 2
  • Thumbnail Image
    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.
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    PublicationOpen Access
    Construction of capacities from overlap indexes
    (Springer, 2017) Sanz Delgado, José Antonio; Galar Idoate, Mikel; Mesiar, Radko; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación
    In this chapter, we show how the concepts of overlap function and overlap index can be used to define fuzzy measures which depend on the specific data of each considered problem.