Artículos de revista DAC - AKS Aldizkari artikuluak

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Browsing Artículos de revista DAC - AKS Aldizkari artikuluak by Author "Baets, Bernard de"

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    PublicationOpen Access
    Convolution lattices
    (Elsevier, 2018) Miguel Turullols, Laura de; Bustince Sola, Humberto; Baets, Bernard de; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación
    We propose two convolution operations on the set of functions between two bounded lattices and investigate the algebraic structure they constitute, in particular the lattice laws they satisfy. Each of these laws requires the restriction to a specific subset of functions, such as normal, idempotent or convex functions. Combining all individual results, we identify the maximal subsets of functions resulting in a bounded lattice, and show this result to be equivalent to the distributivity of the lattice acting as domain of the functions. Furthermore, these lattices turn out to be distributive as well. Additionally, we show that for the larger subset of idempotent functions, although not satisfying the absorption laws, the convolution operations satisfy the Birkhoff equation.
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    PublicationOpen Access
    A historical account of types of fuzzy sets and their relationships
    (IEEE, 2016) Bustince Sola, Humberto; Barrenechea Tartas, Edurne; Pagola Barrio, Miguel; Fernández Fernández, Francisco Javier; Xu, Zeshui; Bedregal, Benjamin; Montero, Javier; Hagras, Hani; Herrera, Francisco; Baets, Bernard de; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación
    In this work we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.