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On Some Generalizations of the Choquet Integral

  • Humberto Bustince
  • Javier Fernandez
  • L’ubomíra HoranskáEmail author
  • Radko Mesiar
  • Andrea Stupňanová
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 981)

Abstract

In the present paper we survey several generalizations of the discrete Choquet integrals and we propose and study a new one. Our proposal is based on the Lovász extension formula, in which we replace the product operator by some binary function F obtaining a new n-ary function \(\mathfrak {I}^F_{m}\). We characterize all functions F yielding, for all capacities m, aggregation functions \(\mathfrak {I}^F_{m}\) with a priori given diagonal section.

Keywords

Aggregation function Choquet integral Capacity Möbius transform 

Notes

Acknowledgments

This work was supported by the Slovak Research and Development Agency under the contract no. APVV-17-0066, grant VEGA 1/0682/16, grant VEGA 1/0614/18 and TIN2016-77356-P(AEI/FEDER,UE).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Humberto Bustince
    • 1
  • Javier Fernandez
    • 1
  • L’ubomíra Horanská
    • 2
    Email author
  • Radko Mesiar
    • 3
  • Andrea Stupňanová
    • 3
  1. 1.Department of Statistics, Computer Science and Mathematics, Institute of Smart CitiesUniversidad Pública de NavarraPamplonaSpain
  2. 2.Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food TechnologySlovak University of Technology in BratislavaBratislavaSlovak Republic
  3. 3.Department of Mathematics and Descriptive Geometry, Faculty of Civil EngineeringSlovak University of Technology in BratislavaBratislava 1Slovak Republic

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