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A Review of the Relationships between Aggregation, Implication and Negation Functions

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Book cover Aggregation Functions in Theory and in Practise

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

Abstract

Aggregation functions, on one hand, and implication functions, on the other, play different although important roles in the field of fuzzy logic. Both have been intensively investigated in the last years, revealing the tide relationship that exists between them. The present work reviews the most relevant aspects of this relation, which most of the times also involves negation functions. In addition to the well-known use of aggregation and negation functions to build and to characterize implication functions, we analyze how new families of aggregation functions and negation functions can be obtained from implications, and we recall the main equations and inequations involving these three classes of functions.

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Author information

Authors and Affiliations

  1. Departamento de Ciencias de la Computación, Universidad Rey Juan Carlos, Madrid, Spain

    Ana Pradera

Authors
  1. Ana Pradera
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Corresponding author

Correspondence to Ana Pradera .

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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Pradera, A. (2013). A Review of the Relationships between Aggregation, Implication and Negation 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

  • eBook Packages: EngineeringEngineering (R0)

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