IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v270y2018i2p670-681.html
   My bibliography  Save this article

Two novel methodologies for considering aggregation functions by implicit equations and minimization problems

Author

Listed:
  • de Hierro, A.F. Roldán López
  • Bustince, H.
  • Fernández, J.
  • Mesiar, R.
  • Roldán, C.

Abstract

In this work, we consider the problem of defining aggregation functions by means of two distinct methodologies. In the first one, we obtain an aggregation function in an implicit way, from a function which fulfills appropriate conditions. The second methodology, related to the idea of penalty function, is based on the minimization of a distance or error and can be seen as a generalization of the idea of correlation in statistics. We analyze the aggregation functions obtained with both methodologies and we present an illustrative decision-making example to show their different behaviors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:670-681
    DOI: 10.1016/j.ejor.2018.04.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718303266
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.04.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bustince, H. & Jurio, A. & Pradera, A. & Mesiar, R. & Beliakov, G., 2013. "Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions," European Journal of Operational Research, Elsevier, vol. 225(3), pages 472-478.
    2. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: Means," Post-Print hal-00539028, HAL.
    3. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Post-Print hal-00539032, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Josef Jablonský & Michal Černý & Juraj Pekár, 2022. "The last dozen of years of OR research in Czechia and Slovakia," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 435-447, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Gagolewski, Marek, 2015. "Spread measures and their relation to aggregation functions," European Journal of Operational Research, Elsevier, vol. 241(2), pages 469-477.
    5. 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.
    6. Osório, António (António Miguel), 2016. "Judgement and Ranking: Living with Hidden Bias," Working Papers 2072/267264, Universitat Rovira i Virgili, Department of Economics.
    7. Mariani, Francesca & Ciommi, Mariateresa & Recchioni, Maria Cristina, 2024. "A new class of composite indicators: The penalized power mean," European Journal of Operational Research, Elsevier, vol. 317(3), pages 1015-1035.
    8. 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.
    9. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Post-Print hal-00539032, HAL.
    10. 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.
    11. 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.
    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. António Osório, 2017. "Judgement and ranking: living with hidden bias," Annals of Operations Research, Springer, vol. 253(1), pages 501-518, June.
    14. Brunelli, Matteo & Corrente, Salvatore, 2024. "Modeling criteria and project interactions in portfolio decision analysis with the Choquet integral," Omega, Elsevier, vol. 126(C).
    15. Kelin Luo & Yinfeng Xu & Bowen Zhang & Huili Zhang, 2018. "Creating an acceptable consensus ranking for group decision making," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 307-328, July.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Wang Feng, 2019. "Aggregation Similarity Measure Based on Hesitant Fuzzy Closeness Degree and Its Application to Clustering Analysis," Journal of Systems Science and Information, De Gruyter, vol. 7(1), pages 70-89, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:670-681. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.