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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)

Abstract

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.

Keywords

Aggregation functions Pre-aggregation functions Directional monotonicity Conditioned monotonicity 

Notes

Acknowledgment

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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Copyright information

© 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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