Uncertainty and imprecision: Modelling and analysis

Any statistical analysis or decision analysis contains numerical inputs of which analysts are unsure. Some uncertainty arises from physical randomness which can be modelled in various ways, ideally through probability. Some uncertainty relates to judgemental estimates of quantities about which analysts may be unsure in many different respects. There are other uncertainties involved, however: some relate to ambiguity and imprecision of meaning; some relate to lack of clarity in the objectives which the analysis seeks to meet; some relate to the numerical accuracy of calculations. How should the uncertainty arising from ambiguity be modelled? Other uncertainties can also impact on an analysis. Why is the analysis being conducted? Are the objectives clear?