An engineering analysis requires a realistic quantification of all input information. The amount and quality of the available information dictates the uncertainty model and its associated quantification concept. For inconsistent information, a distinction between probabilistic and non-probabilistic characteristics is beneficial. In this distinction, uncertainty refers to probabilistic characteristics and non-probabilistic characteristics are summarized as imprecision. When uncertainty and imprecision occur simultaneously, the uncertainty model fuzzy randomness appears useful. In a Bayesian approach the fuzzy probabilistic model provides the opportunity to take account of imprecision in data and in prior expert knowledge. The Bayesian approach ex-tended to inconsistent information is demonstrated by means of an example.