A unified framework for order-of-magnitude confidence relations
Résumé
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crossroads between possibility and probability theories. Such confidence relations between events are commonly found in nonmonotonic reasoning, inconsistency managment, or qualitative decision theory. They start either from probability theory, making it more qualitative, or from possibility theory, making it more expressive. We show these two trends converge to a class of genuine probability relations, numerically representable, that cumulate features of probability and possibility theories. We provide characterization results for these useful tools that preserve the qualitative nature of possibifity rankings, while enjoying the power of expressivity of additive representations.