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Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Matematica Applicata `Bruno de Finetti', Università di Trieste, Piazzale Europa 1, 34127, Trieste, Italy

    Gianni Bosi

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  1. Gianni Bosi
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Bosi, G. Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals. Theory and Decision 52, 303–312 (2002). https://doi.org/10.1023/A:1020298220758

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  • DOI: https://doi.org/10.1023/A:1020298220758

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