The Goodman-Nguyen relation in uncertainty measurement

Abstract

The Goodman-Nguyen relation generalises the implication (inclusion) relation to conditional events. As such, it induces inequality constraints relevant in extension problems with precise probabilities. We extend this framework to imprecise probability judgements, highlighting the role of this relation in determining the natural extension of lower/upper probabilities defined on certain sets of conditional events. Further, a generalisation of the Goodman-Nguyen relation to conditional random numbers is proposed. © 2013 Springer-Verlag.