Suchergebnisse

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. ; Asier Estevan acknowledges financial support from the Ministry of Economy and Competitiveness of Spain under grants MTM2012-37894-C02-02, MTM2015-63608-P and ECO2015-65031 as well as from the Basque Government under grant IT974-16. Gianni Bosi and Magali E. Zuanon acknowledge financial support from the Istituto Nazionale di Alta Matematica 'F. Severi' (Italy).