Abstract
The paper deals with definition of supremal sets in a rather general framework where deterministic and random preference relations (preorders) and partial orders are defined by continuous multi-utility representations. It gives a short survey of the approach developed in (J. Math. Econ. 14(4–5):554–563, 2011 [4]), (J. Math. Econ. 49(6):478–487, 2013 [5]) with some new results on maximal sets.
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Notes
- 1.
Recall that \((x_{\alpha })_{\alpha \in I}\) designates a net, i.e. a sequence of elements in X indexed by an upward directed set I, such that for all open set \(\mathcal {O}\) containing x, \((x_{\alpha })_{\alpha \in I}\) eventually belongs to \(\mathcal {O}\).
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The research is funded by the grant 14. 12.31.0007.
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Kabanov, Y., Lepinette, E. (2015). On Supremal and Maximal Sets with Respect to Random Partial Orders. In: Hamel, A., Heyde, F., Löhne, A., Rudloff, B., Schrage, C. (eds) Set Optimization and Applications - The State of the Art. Springer Proceedings in Mathematics & Statistics, vol 151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48670-2_9
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