Conditional Random-Fuzzy Variables Representing Measurement Results

Conditional probability distributions and Bayes´ theorem are important and powerful tools in measurement, whenever an a priori knowledge about the measurand is available. It is well known that, thanks to Bayes´ theorem, a new information about the measurand coming from a measurement result can be used to revise the a priori knowledge refining its uncertainty. Of course, this tool can be used only if both the a priori knowledge and the new information are expressed in terms of probability distributions. However, according to a recent approach to uncertainty evaluation, measurement results can be also expressed using random-fuzzy variables (RFVs), that is, using possibility distributions, instead of probability distributions. This paper proposes an extension of Bayes´ theorem to the possibility domain, thus leading to the definition of conditional RFVs. A simple experimental example is also considered to prove the effectiveness of the proposed extension.