Set-valued utilities for strict partial orders

So far, only weak utility functions have been used to represent strict part ial orders, but such a representation is not completely satisfactory, since we can not reconstruct the preference relation by simply knowing the weak utility function. The purpose of this paper is to present a type of numeric al representation for strict partial orders, in such a way that recovering the preference relation is possible. Taking into account that (2(R), supers et of) is a strict partial order, we consider set-valued utilities, namely, set-valued mappings, such that they admit a selection which is a weak util ity function. (C) 1999 Academic Press.