Generalized Pre-aggregations

  • Luis MagdalenaEmail author
  • Daniel Gómez
  • Javier Montero
  • Susana Cubillo
  • Carmen Torres
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)


In this paper we propose an extension of the concept of pre-aggregation at two diferent levels. On the one hand, we extend the definition of pre-aggregation to a more general framework where the space [0, 1] is replaced by a totally ordered set \(\mathcal {T}\) with maximum and minimum value. On the other hand, since \(\mathcal {T}\) could be even discrete, we generalize the concept of monotonicity for functions going from \(\mathcal {T}^n\) into \(\mathcal {T}\). In order to do so we introduce the concept of conditioned monotonicity based on the chains in \(\mathcal {T}^n\) and generalizing that of directional monotonicity.


Aggregation functions Pre-aggregation functions Directional monotonicity Conditioned monotonicity 



This research has been partially supported by the Government of Spain (grant TIN2015-66471-P), the Government of Madrid (grant S2013/ICCE-2845), Complutense University (UCM Research Group 910149 and grant PR26/16-21B-3) and Universidad Politécnica de Madrid.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.ETSI InformáticosUniversidad Politécnica de MadridMadridSpain
  2. 2.Faculty of StatisticsComplutense University of MadridMadridSpain
  3. 3.Faculty of MathematicsComplutense University of MadridMadridSpain

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