A Function To Calculate the Median of a Sample of Fuzzy Numbers in R
Beatriz Sinova1, M. Asunciόn Lubiano1, Wolfgang Trutschnig2
1Universidad de Oviedo, Spain; 2European Centre for Soft Computing, Spain

The most usual central tendency measure for random fuzzy numbers, the Aumann-type expected value, is too much influenced either by the existence of great magnitude values among data or by data changes, like it happens in the real-valued case. With the aim of getting a more robust summary measure, an extension of the concept of median of the distribution of a random variable has been recently introduced. In accordance with this extension, the median of a random fuzzy number is defined as the fuzzy number which minimizes the distance (in terms of the so-called δ1 metric) to all the values the random fuzzy set can take on. In previous studies, several relevant properties of this median have been analyzed. Furthermore, a comparison with the Aumman-type expected value has been carried out not only by means of theoretical developments concerning the finite sample breakdown point, but also through empirical simulations. Knowing the numerous real life examples random fuzzy numbers can model, the need of an algorithm and program that calculates the estimate of the median arises. This will be made in the line of the algorithms already performed for other 'parameters' of the distribution of a random fuzzy number, by using the R package SAFD which contains functions for the basic operations and estimates on the class of fuzzy numbers.


Sinova, B., Gil, M.A., Colubi, A., Van Aelst, S., 2011. Median of a random fuzzy number. The 1-norm distance approach. Fuzzy Sets and Systems. (Submitted)

Trutschnig, W., Lubiano, M.A., 2010. SAFD: Statistical Analysis of Fuzzy Data (R package) (http://bellman.ciencias.uniovi.es/SMIRE/SAFDpackage.html).

Keywords: Median; R function; Random fuzzy numbers

Biography: Mrs. Beatriz Sinova is a Spanish young researcher. After her studies in the University of Oviedo (Spain), she graduated in Mathematics (Statistics Major) in 2009 and got the MSc degree in Mathematical Modelling, Statistics and Computation degree. She has participated in several international conferences on Statistics and submitted some papers for publication.