In this paper we focus on the theoretical properties of non-numerical representation of the uncertainty. As usual, this representation is realized by an ``ordinal relation'' (or, equivalently, by a ``comparative scale'') among the ``entities'' (events, alternatives or acts) of a specific problem. After giving an overview of di erent known axioms characterizing some classes of ordinal relations (and their duals), we introduce some axioms to enclose the necessary and su cient conditions for the representability of ordinal relations (defined on arbitrary finite sets of events) by the most-known uncertainty measures.
Axiomatic characterization of partial ordinal relations / Andrea, Capotorti; Vantaggi, Barbara. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - STAMPA. - 24:2-3(2000), pp. 207-219. (Intervento presentato al convegno 1st International Symposium on Impreeise Probabilities (ISIPTA) tenutosi a GHENT, BELGIUM nel JUN, 1999) [10.1016/s0888-613x(00)00035-9].
Axiomatic characterization of partial ordinal relations
VANTAGGI, Barbara
2000
Abstract
In this paper we focus on the theoretical properties of non-numerical representation of the uncertainty. As usual, this representation is realized by an ``ordinal relation'' (or, equivalently, by a ``comparative scale'') among the ``entities'' (events, alternatives or acts) of a specific problem. After giving an overview of di erent known axioms characterizing some classes of ordinal relations (and their duals), we introduce some axioms to enclose the necessary and su cient conditions for the representability of ordinal relations (defined on arbitrary finite sets of events) by the most-known uncertainty measures.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
