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Continuous Utility Functions for Nontotal Preorders: A Review of Recent Results

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Preferences and Decisions

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 257))

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Summary

We present some recent and significant results concerning the existence of a continuous utility function for a not necessarily total preorder on a topological space.We first recall an appropriate continuity concept (namely, weak continuity) relative to a preorder on a topological space. Then a general characterization of the existence of a continuous utility function for a not necessarily total preorder on a topological space is presented and some consequences of this basic result are produced.

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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 & Romano Isler

Authors
  1. Gianni Bosi
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  2. Romano Isler
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Editor information

Editors and Affiliations

  1. Department of Economics and Quantitative Methods, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

  2. Department of Computer and Management Sciences, University of Trento, Via Inama 5, 38122, Trento, Italy

    Ricardo Alberto Marques Pereira

  3. Department of Economical and Social Sciences, University of Sannio at Benevento, Via delle Puglie, 82100, Benevento, Italy

    Massimo Squillante

  4. Machine Intelligence Institute, Iona College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

  5. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk

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Bosi, G., Isler, R. (2010). Continuous Utility Functions for Nontotal Preorders: A Review of Recent Results. In: Greco, S., Marques Pereira, R.A., Squillante, M., Yager, R.R., Kacprzyk, J. (eds) Preferences and Decisions. Studies in Fuzziness and Soft Computing, vol 257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15976-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-15976-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15975-6

  • Online ISBN: 978-3-642-15976-3

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