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Additive Generators of Overlap Functions

  • Conference paper
Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

Abstract

Overlap functions are a particular instance of aggregation functions, consisting by non-decreasing continuous commutative bivariate functions defined over the unit square, satisfying appropriate boundary conditions. Overlap functions play an important role in classification problems, image processing and in some problems of decision making based on fuzzy preference relations. The concepts of indifference and incomparability defined in terms of overlap functions may allow the application in several different contexts. The aim of this papers is to introduce the notion of additive generators of overlap functions, allowing the definition of overlap functions (as two-place functions) by means of one-place functions, which is important since it can reduce the computational complexity in applications. Also, some properties of an overlap function presenting a generator can be related to properties of its generator, pointing to a more systematic methodology for their selection for the various applications.

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Author information

Authors and Affiliations

  1. Programa de Pós-Graduação em Computação, Centro de Ciências Computacionais, Universidade Federal do Rio Grande, Av. Itália km 08, Campus Carreiros, 96201-900, Rio Grande, Brazil

    Graçaliz Pereira Dimuro

  2. Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Campus Universitário, 59072-970, Natal, Brazil

    Benjamín Bedregal

Authors
  1. Graçaliz Pereira Dimuro
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  2. Benjamín Bedregal
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Corresponding author

Correspondence to Graçaliz Pereira Dimuro .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

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Dimuro, G.P., Bedregal, B. (2013). Additive Generators of Overlap Functions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_19

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

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