Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals
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It is well known that interval orders are particularly interesting in decision theory, since they are reflexive, complete and nontransitive binary relations which may be fully represented by means of two real-valued functions. In this paper, we discuss the existence of a pair of nonnegative, positively homogeneous and semicontinuous real-valued functionals representing an interval order on a real cone in a topological vector space. We recover as a particular case a result concerning the existence of a nonnegative, positively homogeneous and continuous utility functional for a complete preorder on a real cone in a topological vector space.
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