Paternain Dallo, Daniel

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https://academica-e.unavarra.es/handle/2454/49749

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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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0000-0002-5845-887X

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88758

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810056

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2012 - 20172
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End date: 2019 × Subject: Aggregation operators ×

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    PublicationOpen Access
    Pointwise aggregation of maps: its structural functional equation and some applications to social choice theory
    (Elsevier, 2017) Miguel Turullols, Laura de; Campión Arrastia, María Jesús; Candeal, Juan Carlos; Induráin Eraso, Esteban; Paternain Dallo, Daniel; Automática y Computación; Matemáticas; Automatika eta Konputazioa; Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    We study a structural functional equation that is directly related to the pointwise aggregation of a finite number of maps from a given nonempty set into another. First we establish links between pointwise aggregation and invariance properties. Then, paying attention to the particular case of aggregation operators of a finite number of real-valued functions, we characterize several special kinds of aggregation operators as strictly monotone modifications of projections. As a case study, we introduce a first approach of type-2fuzzy sets via fusion operators. We develop some applications and possible uses related to the analysis of properties of social evaluation functionals in social choice, showing that those functionals can actually be described by using methods that derive from this setting.
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    PublicationOpen Access
    Image reduction using means on discrete product lattices
    (IEEE, 2012) Beliakov, Gleb; Bustince Sola, Humberto; Paternain Dallo, Daniel; Automática y Computación; Automatika eta Konputazioa
    We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.