Propagation of uncertainty in systems with both probabilistic and possibilistic inputs

This paper presents a method for generating a global quantification and characterization of the uncertainty in the output of a system with both probabilistic and possibilistic inputs. When we have evidence-based probability distributions of some of the inputs to the system but only possibilistic information about the uncertainties of others, neither standard statistics nor purely possibilistic analysis is entirely satisfactory. Suppose a system has a transfer function that has both probabilistic and interval-valued inputs. The upper probability density of any point in its input space is the joint probability density of the values of the probabilistic elements of the vector specifying the point. This forms the foundation for constructing the fuzzy membership function of the set of plausible outputs of the system. This fuzzy set of plausible outcomes can be used to model forward propagation of uncertainty to determine measures of generalized central tendency and generalized uncertainty, as well as the plausibility of failure. Another application of these concepts is backward propagation of uncertainty. For example, nondestructive testing measurements vary as a result of random variations in the materials and the measurement process, and also nonrandom defects in the objects under test. The total uncertainty in the measurement must be propagated backwards to determine the plausibility that the part is defective or not.