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Aggregation functions: Means

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

The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).

Suggested Citation

  • Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: Means," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00539028, HAL.
    • Handle: RePEc:hal:cesptp:hal-00539028
    DOI: 10.1016/j.ins.2010.08.043
    Note: View the original document on HAL open archive server: https://hal.science/hal-00539028v1
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    Cited by:

    1. Gholamreza Haseli & Reza Sheikh & Jianqiang Wang & Hana Tomaskova & Erfan Babaee Tirkolaee, 2021. "A Novel Approach for Group Decision Making Based on the Best–Worst Method (G-BWM): Application to Supply Chain Management," Mathematics, MDPI, vol. 9(16), pages 1-20, August.
    2. Ligang Zhou & Huayou Chen & Jinpei Liu, 2013. "Generalized Multiple Averaging Operators and their Applications to Group Decision Making," Group Decision and Negotiation, Springer, vol. 22(2), pages 331-358, March.
    3. 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.
    4. Merigó, José M. & Palacios-Marqués, Daniel & Ribeiro-Navarrete, Belén, 2015. "Aggregation systems for sales forecasting," Journal of Business Research, Elsevier, vol. 68(11), pages 2299-2304.
    5. 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.
    6. Veronica Cappelli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Stefania Minardi, 2021. "Sources of Uncertainty and Subjective Prices," Journal of the European Economic Association, European Economic Association, vol. 19(2), pages 872-912.
    7. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    8. Silvia Bortot & Ricardo Alberto Marques Pereira & Anastasia Stamatopoulou, 2020. "Shapley and superShapley aggregation emerging from consensus dynamics in the multicriteria Choquet framework," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 583-611, December.
    9. Mario Maggi & Maria-Laura Torrente & Pierpaolo Uberti, 2020. "Proper measures of connectedness," Annals of Finance, Springer, vol. 16(4), pages 547-571, December.
    10. Dombi, József & Jónás, Tamás, 2022. "Weighted aggregation systems and an expectation level-based weighting and scoring procedure," European Journal of Operational Research, Elsevier, vol. 299(2), pages 580-588.
    11. 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.
    12. Merigó, José M. & Palacios-Marqués, Daniel & del Mar Benavides-Espinosa, María, 2015. "Aggregation methods to calculate the average price," Journal of Business Research, Elsevier, vol. 68(7), pages 1574-1580.
    13. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00539032, HAL.
    14. Peláez, José Ignacio & Bernal, Rubén, 2016. "Selective majority additive ordered weighting averaging operatorAuthor-Name: Karanik, Marcelo," European Journal of Operational Research, Elsevier, vol. 250(3), pages 816-826.
    15. Pavel KOVÁŘ & Martin PELIKÁN & Darina HEŘMANOVSKÁ & Ivan VRANA, 2014. "How to reach a compromise solution on technical and non-structural flood control measures," Soil and Water Research, Czech Academy of Agricultural Sciences, vol. 9(4), pages 143-152.
    16. Brunelli, Matteo & Corrente, Salvatore, 2024. "Modeling criteria and project interactions in portfolio decision analysis with the Choquet integral," Omega, Elsevier, vol. 126(C).
    17. Merigó, José M. & Palacios-Marqués, Daniel & Zeng, Shouzhen, 2016. "Subjective and objective information in linguistic multi-criteria group decision making," European Journal of Operational Research, Elsevier, vol. 248(2), pages 522-531.
    18. Osório, António (António Miguel), 2016. "Judgement and Ranking: Living with Hidden Bias," Working Papers 2072/267264, Universitat Rovira i Virgili, Department of Economics.
    19. 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.
    20. Pérez-Fernández, Raúl, 2023. "On the use of robust estimators of multivariate location for heterogeneous data," Statistics & Probability Letters, Elsevier, vol. 203(C).
    21. 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.
    22. 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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