In this paper we deal with the problem of representing qualitative information focusing on the axiomatic aspect of the ordinal relations. We give an overview of different known axioms characterizing some classes of relations land their duals) and we make a deeper analysis of the comparative probabilities by proving that they are induced also by lambda -measures and c lambda -measures. We give a complete outline of the relationships among the different classes and we also characterize the "self-dual" relations (i.e. that ones representable, for example, simultaneously by a lower probability and by an upper probability). These results emphasize the difference between the qualitative and quantitative approach.
Relationships Among Ordinal Relations on a Finite Set of Events
CAPOTORTI, Andrea;
2000
Abstract
In this paper we deal with the problem of representing qualitative information focusing on the axiomatic aspect of the ordinal relations. We give an overview of different known axioms characterizing some classes of relations land their duals) and we make a deeper analysis of the comparative probabilities by proving that they are induced also by lambda -measures and c lambda -measures. We give a complete outline of the relationships among the different classes and we also characterize the "self-dual" relations (i.e. that ones representable, for example, simultaneously by a lower probability and by an upper probability). These results emphasize the difference between the qualitative and quantitative approach.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
