Abstract
Since the Aumann-type expected value of a random interval is not robust, the aim of this paper is to propose a new central tendency measure for interval-valued data. The median of a random interval has already been defined as the interval minimizing the mean distance, in terms of an L 1 metric extending the Euclidean distance, to the values of the random interval. Inspired by the spatial median, we now follow a more common approach to define the median using an L 2 metric.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Math. Soft Comput. 2, 71–84 (1995)
Milasevic, P., Ducharme, G.R.: Uniqueness of the spatial median. Ann. Stat. 15, 1332–1333 (1987)
Gil, M.A., Lubiano, M.A., Montenegro, M., López-García, M.T.: Least squares fitting of an affine function and strength of association for interval data. Metrika 56, 97–111 (2002)
Gower, J.C.: Algorithm AS 78: The mediancentre. Appl. Stat. 23, 466–470 (1974)
Sinova, B., Casals, M.R., Colubi, A., Gil, M.Á.: The Median of a Random Interval. In: Borgelt, C., González-Rodríguez, G., Trutschnig, W., Lubiano, M.A., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds.) Combining Soft Computing and Statistical Methods in Data Analysis. AISC, vol. 77, pp. 575–583. Springer, Heidelberg (2010)
Sinova, B., Van Aelst, S.: Comparing the Medians of a Random Interval Defined by Means of Two Different \(\emph{L}^1\) Metrics. In: Borgelt, C., Gil, M.Á., Sousa, J.M.C., Verleysen, M. (eds.) Towards Advanced Data Analysis. STUDFUZZ, vol. 285, pp. 75–86. Springer, Heidelberg (2012)
Sinova, B., Gil, M.A., González-Rodríguez, G., Van Aelst, S.: An L2 median for random intervals (forthcoming)
Trutschnig, W., González-Rodríguez, G., Colubi, A., Gil, M.A.: A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread. Inf. Sci. 179, 3964–3972 (2009)
Vitale, R.A.: L p metrics for compact, convex sets. J. Approx. Theory 45, 280–287 (1985)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sinova, B., González-Rodríguez, G., Van Aelst, S. (2013). An Alternative Approach to the Median of a Random Interval Using an L 2 Metric. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-33042-1_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33041-4
Online ISBN: 978-3-642-33042-1
eBook Packages: EngineeringEngineering (R0)