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The wabl/ldev/rdev median of a random fuzzy number and statistical properties. (English) Zbl 1337.62026

Grzegorzewski, Przemysław (ed.) et al., Strengthening links between data analysis and soft computing. Collected papers based on the presentations at the 7th international conference on soft methods in probability and statistics, SMPS 2014, Warsaw, Poland, September 22–24, 2014. Cham: Springer (ISBN 978-3-319-10764-6/pbk; 978-3-319-10765-3/ebook). Advances in Intelligent Systems and Computing 315, 143-150 (2015).
Summary: In this paper the population and sample medians of a real-valued random variable are generalized to deal with random fuzzy numbers. The extension is based on a representation of fuzzy numbers for which necessary and sufficient conditions to characterize them have been previously established. Relevant statistical properties for these medians are studied.
For the entire collection see [Zbl 1312.68007].

MSC:

62D05 Sampling theory, sample surveys
03E72 Theory of fuzzy sets, etc.
Full Text: DOI

References:

[1] Puri, M. L.; Ralescu, D. A., Fuzzy random variables, J. Math. Anal. Appl., 114, 409-422 (1986) · Zbl 0592.60004 · doi:10.1016/0022-247X(86)90093-4
[2] Sinova, B.; Casals, M. R.; Colubi, A.; Gil, M.Á.; Borgelt, C.; González-Rodríguez, G.; Trutschnig, W.; Lubiano, M. A.; Gil, M.Á.; Grzegorzewski, P.; Hryniewicz, O., The median of a random interval, Combining Soft Computing and Statistical Methods in Data Analysis, 575-583 (2010), Heidelberg: Springer, Heidelberg · doi:10.1007/978-3-642-14746-3_71
[3] Sinova, B.; De la Rosa de Sáa, S.; Gil, M. A., A generalized L^1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data, Inform. Sci., 242, 22-34 (2013) · Zbl 1322.62186 · doi:10.1016/j.ins.2013.03.063
[4] Sinova, B.; Gil, M. A.; Colubi, A.; Van Aelst, S., The median of a random fuzzy number, The 1-norm distance approach. Fuzzy Sets Syst., 200, 99-115 (2012) · Zbl 1260.60011 · doi:10.1016/j.fss.2011.11.004
[5] Sinova, B.; Gil, M. A.; López, M. T.; Van Aelst, S., A parameterized L^2 metric between fuzzy numbers and its parameter interpretation, Fuzzy Sets Syst., 245, 101-115 (2014) · Zbl 1315.62005 · doi:10.1016/j.fss.2014.01.006
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