Axiomatic Characterization of Partial Ordinal Relations

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 to enclose the necessary and sufficient conditions for the representability of ordinal relations (defined on arbitrary finite sets of events) by the most-known uncertainty measures.