A measurement application of conditional possibility distributions

Conditional probability distributions and Bayes' theorem are an important and powerful tool in measurement, whenever a priori information about the measurand is available. It is well-known that the measurement result and associated uncertainty (a posteriori information) can be used to revise the a priori information and, hopefully, decrease its uncertainty. This tool can be used only if both a priori and a posteriori information can be expressed in terms of a probability distribution. A recent approach to uncertainty evaluation expresses measurement results in terms of Random Fuzzy Variables (RFVs), that is in terms of possibility distributions, instead of probability distributions. This paper proposes an extension of the concept of conditional distributions and Bayes theorem to the possibility distributions, and considers a simple measurement example to prove its validity.