FIRST INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

Ghent, Belgium
30 June - 2 July 1999

ELECTRONIC PROCEEDINGS

Andrea Capotorti and Barbara Vantaggi

Axiomatic Characterization of Partial Ordinal Relations

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 different known axioms characterizing some classes of ordinal relations (and their duals), we introduce some axioms capable to enclose the necessary and sufficient conditions for the representability of ordinal relations defined on arbitrary finite sets of events by the best-known uncertainty measures.

Keywords. qualitative representation of uncertainty, axiomatic

The paper is available in the following formats and sites:

Authors addresses:

Andrea Capotorti

Dip. di Matematica e Informatica
Universita' di Perugia
via Vanvitelli 1
06123 Perugia - Italy

Barbara Vantaggi

Dip. di Statistica
Universit\'a di Perugia
via Pascoli
06123 Perugia - Italy

E-mail addresses:

Andrea Capotorti capot@dipmat.unipg.it
Barbara Vantaggi vant@stat.unipg.it


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