Bayes statistical decisions with random fuzzy data—an application in reliability

Bayesian methods are widely accepted as the methodology for the analysis of reliability data. In practical applications such data are often expressed in an imprecise way. In such a case fuzzy sets are frequently used for modeling imprecision. In the paper we present some recent results on the application of the fuzzy Bayes methodology for the analysis of imprecise reliability data. We also present some useful approximations obtained using the concept of shadowed sets.