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Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes

Author

Listed:
  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Luc Marichal

    (Mathematics Research Unit - uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg)

  • Radko Mesiar

    (Department of Mathematics - Slovak Technical University)

  • Endre Pap

    (Department of Mathematics and Informatics - University of Novi Sad)

Abstract

In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions and on special classes of aggregation functions, covering the well-known con- junctive, disjunctive, and mixed aggregation functions. Some fields of applications are included.

Suggested Citation

  • Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Post-Print hal-00539032, HAL.
    • Handle: RePEc:hal:journl:hal-00539032
    DOI: 10.1016/j.ins.2010.08.040
    Note: View the original document on HAL open archive server: https://hal.science/hal-00539032v1
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    References listed on IDEAS

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    1. Alsina, Claudi & Nelsen, Roger B. & Schweizer, Berthold, 1993. "On the characterization of a class of binary operations on distribution functions," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 85-89, May.
    2. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: Means," Post-Print hal-00539028, HAL.
    3. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    4. Genest, C. & Quesada Molina, J. J. & Rodriguez Lallena, J. A. & Sempi, C., 1999. "A Characterization of Quasi-copulas," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 193-205, May.
    5. Dombi, J., 1982. "Basic concepts for a theory of evaluation: The aggregative operator," European Journal of Operational Research, Elsevier, vol. 10(3), pages 282-293, July.
    6. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
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    Cited by:

    1. Jaume Belles‐Sampera & Montserrat Guillén & Miguel Santolino, 2014. "Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 121-134, January.
    2. António Osório, 2017. "Judgement and ranking: living with hidden bias," Annals of Operations Research, Springer, vol. 253(1), pages 501-518, June.
    3. Osório, António (António Miguel), 2016. "Judgement and Ranking: Living with Hidden Bias," Working Papers 2072/267264, Universitat Rovira i Virgili, Department of Economics.
    4. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    5. Yuchu Qin & Xiaolan Cui & Meifa Huang & Yanru Zhong & Zhemin Tang & Peizhi Shi, 2019. "Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making," Complexity, Hindawi, vol. 2019, pages 1-33, December.
    6. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“Beyond Value-at-Risk: GlueVaR Distortion Risk Measures”," IREA Working Papers 201302, University of Barcelona, Research Institute of Applied Economics, revised Feb 2013.
    7. Roldán López de Hierro, Antonio Francisco & Martínez-Moreno, Juan & Aguilar Peña, Concepción & Roldán López de Hierro, Concepción, 2016. "A fuzzy regression approach using Bernstein polynomials for the spreads: Computational aspects and applications to economic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 13-25.
    8. Boonmee Prakassawat & Tasena Santi, 2020. "Quadratic transformation of multivariate aggregation functions," Dependence Modeling, De Gruyter, vol. 8(1), pages 254-261, January.
    9. de Hierro, A.F. Roldán López & Bustince, H. & Fernández, J. & Mesiar, R. & Roldán, C., 2018. "Two novel methodologies for considering aggregation functions by implicit equations and minimization problems," European Journal of Operational Research, Elsevier, vol. 270(2), pages 670-681.
    10. Boonmee Prakassawat & Tasena Santi, 2020. "Quadratic transformation of multivariate aggregation functions," Dependence Modeling, De Gruyter, vol. 8(1), pages 254-261, January.
    11. Erich Peter Klement & Radko Mesiar, 2018. "L -Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †," Mathematics, MDPI, vol. 6(9), pages 1-24, August.
    12. Gagolewski, Marek, 2015. "Spread measures and their relation to aggregation functions," European Journal of Operational Research, Elsevier, vol. 241(2), pages 469-477.

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