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Continuous multi-utility representations of preorders

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  • Bosi, Gianni
  • Herden, Gerhard

Abstract

Let (X,t) be a topological space. Then a preorder ≾ on (X,t) has a continuous multi-utility representation if there exists a family F of continuous and isotonic real-valued functions f on (X,≾,t) such that for all x∈X and all y∈X the inequalities x≾y mean that for all f∈F the inequalities f(x)≤f(y) hold. We discuss the existence of a continuous multi-utility representation by using suitable concepts of continuity of a preorder. In addition, we clarify in detail the relation between the concept of a continuous multi-utility representation and Nachbin’s concept of a normally preordered space.

Suggested Citation

  • Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:212-218
    DOI: 10.1016/j.jmateco.2012.05.001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Bosi, Gianni & Herden, Gerhard, 2016. "On continuous multi-utility representations of semi-closed and closed preorders," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 20-29.
    2. José Carlos R. Alcantud & Gianni Bosi & Magalì Zuanon, 2016. "Richter–Peleg multi-utility representations of preorders," Theory and Decision, Springer, vol. 80(3), pages 443-450, March.
    3. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0195-7 is not listed on IDEAS
    4. Shaofang Qi, 2016. "A characterization of the n-agent Pareto dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 695-706, March.
    5. Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2013. "Representations of preorders by strong multi-objective functions," MPRA Paper 52329, University Library of Munich, Germany.
    6. Bosi, Gianni & Herden, Gerhard, 2014. "Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation," MPRA Paper 53404, University Library of Munich, Germany.
    7. Nishimura, Hiroki & Ok, Efe A., 2016. "Utility representation of an incomplete and nontransitive preference relation," Journal of Economic Theory, Elsevier, vol. 166(C), pages 164-185.

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