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Spread measures and their relation to aggregation functions

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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