We emphasize the distinction between two forms of uncertainty that arise in risk and reliability analyses: (1) that due to the randomness inherent in the system under investigation and (2) that due to the vagueness inherent in the assessor's perception and judgement of that system. It is proposed that whereas the probabilistic approach to the former variety of uncertainty is an appropriate one, the same may not be true of the latter. Through seeking to quantify the imprecision that characterizes our linguistic description of perception and comprehension, fuzzy set theory provides a formal framework for the representation of vagueness. In connection with the second form of uncertainty, fuzzy sets and the associated theory of “possibility” are considered as a basis upon which to model the imprecision and vagueness attached to the expert judgement of event likelihood (e.g. component failure). It is noted that from the perspective of the technical complexity of propagation, the possibilistic treatment of uncertainty compares favorably with the more familiar Bayesian approach.