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

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
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