Person:
Pereira Dimuro, Graçaliz

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Pereira Dimuro

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Graçaliz

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Automática y Computación

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0000-0001-6986-9888

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811336

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Now showing 1 - 3 of 3
  • PublicationOpen Access
    On fuzzy implications derived from general overlap functions and their relation to other classes
    (MDPI, 2023) Pinheiro, Jocivania; Santos, Helida; Pereira Dimuro, Graçaliz; Callejas Bedregal, Benjamin; Santiago, Regivan; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
    There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO, N)-implication functions. We also investigate their properties, the aggregation of (GO, N)-implication functions, their characterization and the intersections with other classes of fuzzy implication functions.
  • PublicationOpen Access
    General grouping functions
    (Springer, 2020) Santos, Helida; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Sanz Delgado, José Antonio; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
    Some aggregation functions that are not necessarily associative, namely overlap and grouping functions, have called the attention of many researchers in the recent past. This is probably due to the fact that they are a richer class of operators whenever one compares with other classes of aggregation functions, such as t-norms and t-conorms, respectively. In the present work we introduce a more general proposal for disjunctive n-ary aggregation functions entitled general grouping functions, in order to be used in problems that admit n dimensional inputs in a more flexible manner, allowing their application in different contexts. We present some new interesting results, like the characterization of that operator and also provide different construction methods.
  • PublicationOpen Access
    The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions
    (Elsevier, 2019) Pereira Dimuro, Graçaliz; Callejas Bedregal, Benjamin; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Pintor Borobia, Jesús María; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería
    Overlap and grouping functions are special kinds of non necessarily associative aggregation operators proposed for many applications, mainly when the associativity property is not strongly required. The classes of overlap and grouping functions are richer than the classes of t-norms and t-conorms, respectively, concerning some properties like idempotency, homogeneity, and, mainly, the self-closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap/grouping functions. In previous works, we introduced some classes of fuzzy implications derived by overlap and/or grouping functions, namely, the residual implications R-0-implications, the strong implications (G, N)-implications and the Quantum Logic implications QL-implications, for overlap functions O, grouping functions G and fuzzy negations N. Such implications do not necessarily satisfy certain properties, but only weaker versions of these properties, e.g., the exchange principle. However, in general, such properties are not demanded for many applications. In this paper, we analyze the so-called law of O-Conditionality, O(x, 1(x, y)) <= y, for any fuzzy implication I and overlap function O, and, in particular, for Ro-implications, (G, N)-implications, QL-implications and D-implications derived from tuples (O, G, N), the latter also introduced in this paper. We also study the conditional antecedent boundary condition for such fuzzy implications, since we prove that this property, associated to the left ordering property, is important for the analysis of the O-Conditionality. We show that the use of overlap functions to implement de generalized Modus Ponens, as the scheme enabled by the law of O-Conditionality, provides more generality than the laws of T-conditionality and U-conditionality, for t-norms T and uninorms U, respectively.