Paternain Dallo, Daniel
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Paternain Dallo
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Daniel
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Estadística, Informática y Matemáticas
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ISC. Institute of Smart Cities
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Publication Open Access The interval-valued Choquet integral based on admissible permutations(IEEE, 2018) Paternain Dallo, Daniel; Miguel Turullols, Laura de; Ochoa Lezaun, Gustavo; Lizasoain Iriso, María Inmaculada; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaAggregation or fusion of interval data is not a trivial task, since the necessity of arranging data arises in many aggregation functions, such as OWA operators or the Choquet integral. Some arranging procedures have been given to solve this problem, but they need certain parameters to be set. In order to solve this problem, in this work we propose the concept of an admissible permutation of intervals. Based on this concept, which avoids any parameter selection, we propose a new approach for the interval-valued Choquet integral that takes into account every possible permutation fitting to the considered ordinal structure of data. Finally, a consensus among all the permutations is constructed.Publication Open Access Dissimilarity based choquet integrals(Springer, 2020) Bustince Sola, Humberto; Mesiar, Radko; Fernández Fernández, Francisco Javier; Galar Idoate, Mikel; Paternain Dallo, Daniel; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaIn this paper, in order to generalize the Choquet integral, we replace the difference between inputs in its definition by a restricted dissimilarity function and refer to the obtained function as d-Choquet integral. For some particular restricted dissimilarity function the corresponding d-Choquet integral with respect to a fuzzy measure is just the ‘standard’ Choquet integral with respect to the same fuzzy measure. Hence, the class of all d-Choquet integrals encompasses the class of all 'standard' Choquet integrals. This approach allows us to construct a wide class of new functions, d-Choquet integrals, that are possibly, unlike the 'standard' Choquet integral, outside of the scope of aggregation functions since the monotonicity is, for some restricted dissimilarity function, violated and also the range of such functions can be wider than [0, 1], in particular it can be [0, n].Publication Open Access d-Choquet integrals: Choquet integrals based on dissimilarities(Elsevier, 2020) Bustince Sola, Humberto; Mesiar, Radko; Fernández Fernández, Francisco Javier; Galar Idoate, Mikel; Paternain Dallo, Daniel; Altalhi, A. H.; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Takáč, Zdenko; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These functions are a generalization of the 'standard' Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the class of all 'standard' Choquet integrals but the use of dissimilarities provides higher flexibility and generality. We show that some d-Choquet integrals are aggregation/pre-aggregation/averaging/functions and some of them are not. The conditions under which this happens are stated and other properties of the d-Choquet integrals are studied.