We propose a general concept of conditional decomposable measures, deducing the axioms by introducing a pair of operations in a set of conditional events. So the starting point is a definition of conditional event E vertical bar H given in [6], which differs from many seemingly "similar" ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same "third" value a ("undetermined") to all conditional events, but make it depend on E vertical bar H, it turns out that this function t(E vertical bar H) can be taken as a general conditional uncertainty measure, whose properties depend on the choice of operations. We discuss also particular choices for which we can obtain well known conditional uncertainty measures
From conditional events to decomposable conditional measures
COLETTI, Giulianella
2005
Abstract
We propose a general concept of conditional decomposable measures, deducing the axioms by introducing a pair of operations in a set of conditional events. So the starting point is a definition of conditional event E vertical bar H given in [6], which differs from many seemingly "similar" ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same "third" value a ("undetermined") to all conditional events, but make it depend on E vertical bar H, it turns out that this function t(E vertical bar H) can be taken as a general conditional uncertainty measure, whose properties depend on the choice of operations. We discuss also particular choices for which we can obtain well known conditional uncertainty measuresI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
