Uncertain input parameters may result from “fuzziness”, “randomness” or “fuzzy randomness”. With the use of fuzzy set theory, uncertain input parameters may be described mathematically as fuzzy variables or fuzzy random variables and may be integrated into safety assessment analysis. With the aid of α-discretization involving the multiple solution of special optimization problems, fuzzy input parameters are mapped onto the uncertain result set. If the deterministic input data are characterized by “fuzziness”, the fuzzy results are uncertain outcomes of the structural analysis; safety assessment may then be carried out using possibility theory. If the input parameters exist in the form of fuzzy random variables, the computed fuzzy failure probabilities may be used for safety assessment. A fuzzy 1st-order reliability method (FFORM) is proposed, which is capable of handling fuzzy as well as fuzzy random variables.