The median of a random fuzzy number. The 1-norm distance approach

Authors:
Beatriz Sinova;María Ángeles Gil;Ana Colubi;Stefan Van Aelst
Affiliations:
Departamento de Estadística, I.O. y D.M., Facultad de Ciencias, Universidad de Oviedo, E-33071 Oviedo, Spain;Departamento de Estadística, I.O. y D.M., Facultad de Ciencias, Universidad de Oviedo, E-33071 Oviedo, Spain;Departamento de Estadística, I.O. y D.M., Facultad de Ciencias, Universidad de Oviedo, E-33071 Oviedo, Spain;Department of Applied Mathematics and Computer Science, Faculty of Sciences, Universiteit Gent, B-9000 Gent, Belgium
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

In quantifying the central tendency of the distribution of a random fuzzy number (or fuzzy random variable in Puri and Ralescu's sense), the most usual measure is the Aumann-type mean, which extends the mean of a real-valued random variable and preserves its main properties and behavior. Although such a behavior has very valuable and convenient implications, 'extreme' values or changes of data entail too much influence on the Aumann-type mean of a random fuzzy number. This strong influence motivates the search for a more robust central tendency measure. In this respect, this paper aims to explore the extension of the median to random fuzzy numbers. This extension is based on the 1-norm distance and its adequacy will be shown by analyzing its properties and comparing its robustness with that of the mean both theoretically and empirically.