IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v241y2015i2p469-477.html
   My bibliography  Save this article

Spread measures and their relation to aggregation functions

Author

Listed:
  • Gagolewski, Marek

Abstract

The theory of aggregation most often deals with measures of central tendency. However, sometimes a very different kind of a numeric vector’s synthesis into a single number is required. In this paper we introduce a class of mathematical functions which aim to measure spread or scatter of one-dimensional quantitative data. The proposed definition serves as a common, abstract framework for measures of absolute spread known from statistics, exploratory data analysis and data mining, e.g. the sample variance, standard deviation, range, interquartile range (IQR), median absolute deviation (MAD), etc. Additionally, we develop new measures of experts’ opinions diversity or consensus in group decision making problems. We investigate some properties of spread measures, show how are they related to aggregation functions, and indicate their new potentially fruitful application areas.

Suggested Citation

  • Gagolewski, Marek, 2015. "Spread measures and their relation to aggregation functions," European Journal of Operational Research, Elsevier, vol. 241(2), pages 469-477.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:2:p:469-477
    DOI: 10.1016/j.ejor.2014.08.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714007115
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.08.034?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. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: Means," Post-Print hal-00539028, HAL.
    2. Mesiar, R., 2007. "Fuzzy set approach to the utility, preference relations, and aggregation operators," European Journal of Operational Research, Elsevier, vol. 176(1), pages 414-422, January.
    3. Huang, Yeu-Shiang & Chang, Wei-Chen & Li, Wei-Hao & Lin, Zu-Liang, 2013. "Aggregation of utility-based individual preferences for group decision-making," European Journal of Operational Research, Elsevier, vol. 229(2), pages 462-469.
    4. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    5. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Post-Print hal-00539032, HAL.
    6. Bernasconi, Michele & Choirat, Christine & Seri, Raffaello, 2014. "Empirical properties of group preference aggregation methods employed in AHP: Theory and evidence," European Journal of Operational Research, Elsevier, vol. 232(3), pages 584-592.
    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. Kołacz, Adam & Grzegorzewski, Przemysław, 2016. "Measures of dispersion for multidimensional data," European Journal of Operational Research, Elsevier, vol. 251(3), pages 930-937.
    2. Bertoli-Barsotti, Lucio & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2024. "Gini-stable Lorenz curves and their relation to the generalised Pareto distribution," Journal of Informetrics, Elsevier, vol. 18(2).

    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. 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. 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.
    3. 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.
    4. 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.
    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. Osório, António (António Miguel), 2016. "Judgement and Ranking: Living with Hidden Bias," Working Papers 2072/267264, Universitat Rovira i Virgili, Department of Economics.
    7. Xia, Meimei & Chen, Jian, 2015. "Multi-criteria group decision making based on bilateral agreements," European Journal of Operational Research, Elsevier, vol. 240(3), pages 756-764.
    8. Elizabeth M. Caucutt & Lance Lochner & Youngmin Park, 2017. "Correlation, Consumption, Confusion, or Constraints: Why Do Poor Children Perform so Poorly?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(1), pages 102-147, January.
    9. Thomas Eichner & Andreas Wagener, 2002. "Increases in Risk and the Welfare State," CESifo Working Paper Series 685, CESifo.
    10. Kwame Addae‐Dapaah & Wilfred Tan Yong Hwee, 2009. "The unsung impact of currency risk on the performance of international real property investment," Review of Financial Economics, John Wiley & Sons, vol. 18(1), pages 56-65, January.
    11. Neus, Werner, 2014. "Eigenkapitalnormen, Boni und Risikoanreize in Banken," Die Unternehmung - Swiss Journal of Business Research and Practice, Nomos Verlagsgesellschaft mbH & Co. KG, vol. 68(2), pages 92-107.
    12. Jie Ning & Matthew J. Sobel, 2018. "Production and Capacity Management with Internal Financing," Manufacturing & Service Operations Management, INFORMS, vol. 20(1), pages 147-160, February.
    13. LaDue, Eddy L. & Allen, Sandra, 1993. "Regulatory, Efficiency, and Management Issues Affecting Rural Financial Markets," Staff Papers 121348, Cornell University, Department of Applied Economics and Management.
    14. Alessandro Spiganti, 2022. "Wealth Inequality and the Exploration of Novel Alternatives," Working Papers 2022:02, Department of Economics, University of Venice "Ca' Foscari".
    15. Durmaz, Tunç, 2016. "Precautionary Storage in Electricity Markets," Discussion Papers 2016/5, Norwegian School of Economics, Department of Business and Management Science.
    16. Freeman, Mark C. & Wagner, Gernot & Zeckhauser, Richard J., 2015. "Climate Sensitivity Uncertainty: When Is Good News Bad?," Working Paper Series rwp15-002, Harvard University, John F. Kennedy School of Government.
    17. Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2001. "Search under the Knightian Uncertainty," CIRJE F-Series CIRJE-F-112, CIRJE, Faculty of Economics, University of Tokyo.
    18. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    19. Baker, Erin, 2005. "Uncertainty and learning in a strategic environment: global climate change," Resource and Energy Economics, Elsevier, vol. 27(1), pages 19-40, January.
    20. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.

    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:241:y:2015:i:2:p:469-477. 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.