We consider a class of general decomposable measures of uncertainty, which encompasses (as its most specific elements, with respect to the properties of the rules of composition) probabilities, and (as its most general elements) belief functions. The aim, using this general context, is to introduce (in a direct way) the concept of conditional belief function as a conditional generalized decomposable measure phi(.vertical bar.), defined on a set of conditional events. Our main tool will be the following result, that we prove in the first part of the article and which is a sort of converse of a well-known result (i.e., a belief function is a lower probability): a coherent conditional lower probability (P) under bar(.vertical bar K) extending a coherent probability P(H-i)-where the events H(i)s are a partition of the certain event Omega and K is the union of some (possibly all) of them-is a belief function.
Toward a general theory of conditional beliefs
COLETTI, Giulianella;
2006
Abstract
We consider a class of general decomposable measures of uncertainty, which encompasses (as its most specific elements, with respect to the properties of the rules of composition) probabilities, and (as its most general elements) belief functions. The aim, using this general context, is to introduce (in a direct way) the concept of conditional belief function as a conditional generalized decomposable measure phi(.vertical bar.), defined on a set of conditional events. Our main tool will be the following result, that we prove in the first part of the article and which is a sort of converse of a well-known result (i.e., a belief function is a lower probability): a coherent conditional lower probability (P) under bar(.vertical bar K) extending a coherent probability P(H-i)-where the events H(i)s are a partition of the certain event Omega and K is the union of some (possibly all) of them-is a belief function.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
