Engineering quantification of inconsistent information

In this paper, the specification of fuzzy random quantities is considered for selected cases of problematic information as it appears frequently in engineering practice. The problem of inconsistency regarding uncertainty and imprecision is addressed. Quantification strategies are proposed for the following cases: (i) samples of small size (ii) samples with imprecise elements and (iii) samples obtained under inconsistent environmental conditions. Typical expert knowledge is included in the considerations. For solution, traditional statistical methods are combined with non-stochastic models for dealing with imprecision. Statistical uncertainty and imprecision are reflected separately in the quantification results. The entire range of possible stochastic models is covered and can be forwarded to a structural analysis and reliability assessment. This provides valuable information for subsequent decision-making. The risk of deriving wrong decisions due to biased or narrowed uncertainty quantification can be reduced significantly. The proposed quantification strategies are demonstrated by way of numerical examples.