A New Extension of Monotonicity: Ordered Directional Monotonicity

  • Humberto BustinceEmail author
  • Radko Mesiar
  • Anna Kolesárová
  • Mikel Sesma-Sara
  • Javier Fernandez
  • Mikel Galar
  • Mikel Elkano
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


In this work, we discuss a recent generalization of the classical notion of monotonicity, with a special focus on the idea of directional monotonicity. This idea leads to the concepts of pre-aggregation functions and of ordered directional monotonicity. For the former, the direction along which monotonicity is considered is the same for all the points of the domain and the same boundary conditions as for aggregation functions are imposed. For the latter, different directions of monotonicity may be considered at different points.


Aggregation function Pre-aggregation function Directional monotonicity Ordered-directional monotonicity 



The authors would like to thank research projects TIN2016-77356-P(AEI/FEDER, UE) and APVV-14-0013.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Humberto Bustince
    • 1
    • 2
    Email author
  • Radko Mesiar
    • 3
  • Anna Kolesárová
    • 4
  • Mikel Sesma-Sara
    • 1
    • 2
  • Javier Fernandez
    • 1
    • 2
  • Mikel Galar
    • 1
    • 2
  • Mikel Elkano
    • 1
    • 2
  1. 1.Department of Automation and ComputingPublic University of NavarraPamplonaSpain
  2. 2.Institute of Smart CitiesPublic University of NavarraPamplonaSpain
  3. 3.Slovak University of TechnologyBratislavaSlovakia
  4. 4.Institute of Information Engineering, Automation and MathematicsSlovak University of TechnologyBratislavaSlovakia

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