Random fuzzy sets: a mathematical tool to develop statistical fuzzy data analysis. (English) Zbl 1331.62055

Blanco-Fernández, A.; Casals, M. R.; Colubi, A.; Corral, N.; García-Bárzana, M.; Gil, M. A.; González-Rodríguez, G.; López, M. T.; Montenegro, M.; Lubiano, M. A.; Ramos-Guajardo, A. B.; de la Rosa de Sáa, S.; Sinova, B.

Iran. J. Fuzzy Syst. 10, No. 2, 1-28 (2013).

Summary: Data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified. Often the underlying imprecision can be suitably described in terms of fuzzy numbers/values. For these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that of categorical data, and more accuracy and expressiveness than that of numerical/vectorial data. On the other hand, random fuzzy numbers/sets model the random mechanisms generating experimental fuzzy data, and they are soundly formalized within the probabilistic setting. This paper aims to review a significant part of the recent literature concerning the statistical data analysis with fuzzy data and being developed around the concept of random fuzzy numbers/sets.

MSC:

62A86	Fuzzy analysis in statistics
62-07	Data analysis (statistics) (MSC2010)
60A86	Fuzzy probability

Keywords:

distances between fuzzy numbers/values; fuzzy numbers/values; fuzzy arithmetic; random fuzzy numbers/sets; statistical methodology