Extending Utility Representations of Partial Orders
<|reference_start|>Extending Utility Representations of Partial Orders: The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em separably increasing}. Explicit formulas are given for a class of extensions which involves an arbitrary bounded increasing function. Similar results are obtained for monotone functions that represent strict partial orders on arbitrary abstract sets X. The special case where P is a Pareto subset is considered.<|reference_end|>
@article{chebotarev2005extending,
    title={Extending Utility Representations of Partial Orders},
    author={Pavel Chebotarev},
    journal={In: Constructing and Applying Objective Functions. Lecture Notes
  in Economics and Math. Systems, Vol.510, Springer, 2002, P. 63-74},
    year={2005},
    doi={10.1007/978-3-642-56038-5_4},
    archivePrefix={arXiv},
    eprint={math/0508199},
    primaryClass={math.OC cs.DS math.FA}
}