Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity

  • Mikel Sesma-SaraEmail author
  • Laura De Miguel
  • Radko Mesiar
  • Javier Fernandez
  • Humberto Bustince
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)


In this study we discuss some of the recent generalized forms of monotonicity, introduced in the attempt of relaxing the monotonicity condition of aggregation functions. Specifically, we deal with weak, directional, ordered directional and strengthened ordered directional monotonicity. We present some of the most relevant properties of the functions that satisfy each of these monotonicity conditions and, using the concept of pointwise directional monotonicity, we carry out a local study of the discussed relaxations of monotonicity. This local study enables to highlight the differences between each notion of monotonicity. We illustrate such differences with an example of a restricted equivalence function.



This work is supported by the project TIN2016-77356-P (AEI/FEDER, UE), by the Public University of Navarra under the project PJUPNA13 and by Slovak grant APVV-14-0013.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mikel Sesma-Sara
    • 1
    Email author
  • Laura De Miguel
    • 1
  • Radko Mesiar
    • 2
  • Javier Fernandez
    • 1
  • Humberto Bustince
    • 1
  1. 1.Public University of NavarraPamplonaSpain
  2. 2.Slovak University of TechnologyBratislavaSlovakia

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