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Penalty-Based Functions Defined by Pre-aggregation Functions

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Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 854))

Abstract

Pre-aggregation function (PAF) is an important concept that has emerged in the context of directional monotonicity functions. Such functions satisfy the same boundary conditions of an aggregation functions, but it is not required the monotone increasingness in all the domain, just in some fixed directions. On the other hand, penalty functions is another important concept for decision making applications, since they can provide a measure of deviation from the consensus value given by averaging aggregation functions, or a penalty for not having such consensus. This paper studies penalty-based functions defined by PAFs. We analyse some properties (e.g.: idempotency, averaging behavior and shift-invariance), providing a characterization of idempotent penalty-based PAFs and a weak characterization of averaging penalty-based PAFs. The use of penalty-based PAFs in spatial/tonal filters is outlined.

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Acknowledgments

Supported by Caixa and Fundación Caja Navarra of Spain, the Brazilian National Counsel of Technological and Scientific Development CNPq (Proc. 307781/2016-0, 33950/2014-1, 306970/2013-9), the Spanish Ministry of Science and Technology (TIN2016-77356-P) and by grant APVV-14-0013.

Author information

Authors and Affiliations

  1. Centro Ciências Computacionais, Universidade Federal do Rio Grande Campus Carreiros, Rio Grande, 96201-900, Brazil

    Graçaliz Pereira Dimuro

  2. Institute of Smart Cities, Universidad Publica de Navarra Campus Arrosadía, 31006, Pamploma, Spain

    Graçaliz Pereira Dimuro, Humberto Bustince & José Antonio Sanz

  3. Department of Mathematics, Slovak University of Technology, Radlinského 11, 81005, Bratislava, Slovakia

    Radko Mesiar

  4. Depto. of Automática y Computación, Universidad Publica de Navarra Campus Arrosadía, 31006, Pamplona, Spain

    Humberto Bustince, José Antonio Sanz & Giancarlo Lucca

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

    Benjamín Bedregal

Authors
  1. Graçaliz Pereira Dimuro
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  2. Radko Mesiar
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  3. Humberto Bustince
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  4. Benjamín Bedregal
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  5. José Antonio Sanz
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  6. Giancarlo Lucca
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Corresponding author

Correspondence to Graçaliz Pereira Dimuro .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Dimuro, G.P., Mesiar, R., Bustince, H., Bedregal, B., Sanz, J.A., Lucca, G. (2018). Penalty-Based Functions Defined by Pre-aggregation Functions. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_34

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  • DOI: https://doi.org/10.1007/978-3-319-91476-3_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91475-6

  • Online ISBN: 978-3-319-91476-3

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