Partial representations of orderings
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS(2024)
摘要
In the present paper a new concept of representability is introduced, which
can be applied to not total and also to intransitive relations (semiorders in
particular). This idea tries to represent the orderings in the simplest manner,
avoiding any unnecessary information. For this purpose, the new concept of
representability is developed by means of partial functions, so that other
common definitions of representability (i.e. (Richter-Peleg) multi-utility,
Scott-Suppes representability,...) are now particular cases in which the
partial functions are actually functions. The paper also presents a collection
of examples and propositions showing the advantages of this kind of
representations, particularly in the case of partial orders and semiorders, as
well as some results showing the connections between distinct kinds of
representations.
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关键词
Partial representability, multi-utility, preorders, semiorders, intransitivity
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