Munich Personal RePEc Archive

Representations of preorders by strong multi-objective functions

Alcantud, José Carlos R. and Bosi, Gianni and Zuanon, Magalì (2013): Representations of preorders by strong multi-objective functions.

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Abstract

We introduce a new kind of representation of a not necessarily total preorder, called strong multi-utility representation, according to which not only the preorder itself but also its strict part is fully represented by a family of multi-objective functions. The representability by means of semicontinuous or continuous multi-objective functions is discussed, as well as the relation between the existence of a strong multi-utility representation and the existence of a Richter-Peleg utility function. We further present conditions for the existence of a semicontinuous or continuous countable strong multi-utility representation.

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