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Fuzzy probabilistic method for the safety assessment

The safety of structures may only be realistically assessed provided all input data are appropriately described and a realistic computational model is implemented. Input and model parameters are often only available in the form of uncertain parameters. Statistical methods are only suitable for describing uncertainty to a limited extent, however; the prognoses given by stochastic safety models are thus open to criticism. In this paper a new method of modeling uncertainty is presented, based on the theory of fuzzy random variables. Uncertain parameters, which partly exhibit random properties, but may not be modeled as random variables without an element of doubt, are described using fuzzy probability distributions. These enter the developed fuzzy probabilistic safety assessment as fuzzy probabilistic basic variables (data uncertainty). In contrast to probabilistic concepts, this new safety concept treats uncertain input and model parameters as fuzzy random variables, random variables and fuzzy variables. Random variables are additionally modeled as probabilistic basic variables (data uncertainty); fuzzy variables (model uncertainty) define the fuzzy limit state surface. Using the special extension of the First Order Reliability Method (FORM), namely the Fuzzy First Order Reliability Method (FFORM), the fuzzy reliability index is computed by -level optimization. This is compared with required values. Expert estimates are taken into consideration for assessing the fuzzy safety level. The fuzzy probabilistic safety assessment is demonstrated by way of an example.