## Reversing the order of integration in iterated expectations of fuzzy random variables, and statistical applications.(English)Zbl 0962.62005

Summary: Conditions are given to compute iterated expectations of fuzzy random variables irrespectively of the order of integration. To this purpose, some studies about the measurability and the integrable boundedness of the fuzzy expected value of a fuzzy random variable with respect to a regular conditional probability are first developed. The conclusions obtained are applied later to statistical problems involving fuzzy random variables, like those concerning some hierarchical models and mixture distributions (more precisely, some techniques to obtain fuzzy unbiased estimators and the Bayesian analysis of statistical problems).

### MSC:

 62A01 Foundations and philosophical topics in statistics 62C10 Bayesian problems; characterization of Bayes procedures 62C99 Statistical decision theory 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections 62H12 Estimation in multivariate analysis 62H15 Hypothesis testing in multivariate analysis 62H99 Multivariate analysis 03E72 Theory of fuzzy sets, etc.
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