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The Notions of Overlap and Grouping Functions

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 336))

Abstract

In this work, we make a review of the concepts of overlap and grouping functions, mainly from a theoretical point of view. In particular, we summarize some of the most relevant works that have been published in recent years about this topic.

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Notes

  1. 1.

    In this paper, an increasing (decreasing) function does not need to be strictly increasing (decreasing).

  2. 2.

    This kind of negation is called in the Literature strict.

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Acknowledgments

The authors have been supported by project TIN2013-40765-P.

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Authors and Affiliations

  1. Departamento of Automática y Computación and with the Institute of Smart Cities, Universidad Publica de Navarra, 31006, Navarra, Spain

    Humberto Bustince, Edurne Barrenechea, Miguel Pagola & Javier Fernandez

Authors
  1. Humberto Bustince
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  2. Edurne Barrenechea
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  3. Miguel Pagola
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  4. Javier Fernandez
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Corresponding author

Correspondence to Humberto Bustince .

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Editors and Affiliations

  1. Dept of Knowledge-Based Math. Systems, Johannes Kepler University Linz, Linz, Austria

    Susanne Saminger-Platz

  2. Dept. of Mathematics & Descriptive Geo., Slovak University of Technology, BRATISLAVA, Slovakia

    Radko Mesiar

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Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J. (2016). The Notions of Overlap and Grouping Functions. In: Saminger-Platz, S., Mesiar, R. (eds) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-319-28808-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-28808-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28807-9

  • Online ISBN: 978-3-319-28808-6

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