Necessary and sufficient conditions are presented for the existence of a pair < u; v > of positively homogeneous of degree one real functions representing an interval order < on a real cone K in a topological vector space E (in the sense that, for every x,y in K, x < y if and only if v(x) < u(y), with u lower semicontinuous, v upper semicontinuous, and u and v utilityfunctions for two complete preorders intimately connected with <. We conclude presenting a new approach to get such kind of representations, based on the concept of a biorder.

Existence of homogeneous representations of interval orders on a cone in a topological vector space

BOSI, GIANNI;
2005-01-01

Abstract

Necessary and sufficient conditions are presented for the existence of a pair < u; v > of positively homogeneous of degree one real functions representing an interval order < on a real cone K in a topological vector space E (in the sense that, for every x,y in K, x < y if and only if v(x) < u(y), with u lower semicontinuous, v upper semicontinuous, and u and v utilityfunctions for two complete preorders intimately connected with <. We conclude presenting a new approach to get such kind of representations, based on the concept of a biorder.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/1690967
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