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A Compact Representation of Preferences in Multiple Criteria Optimization Problems

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  • Francisco Salas-Molina

    (Department of Management ”Juan José Renau Piqueras”, Faculty of Economics, Universitat de València, Av. Tarongers s/n, 46022 Valencia, Spain)

  • David Pla-Santamaria

    (Department of Economics and Social Sciences, Higher Polytechnic School of Alcoi, Universitat Politècnica de València, Ferrándiz y Carbonell, 03801 Alcoi, Spain)

  • Ana Garcia-Bernabeu

    (Department of Economics and Social Sciences, Higher Polytechnic School of Alcoi, Universitat Politècnica de València, Ferrándiz y Carbonell, 03801 Alcoi, Spain)

  • Javier Reig-Mullor

    (Department of Economics and Financial Studies, Faculty of Social Sciences and Law, Universitas Miguel Hernández, 03202 Elche, Spain)

Abstract

A critical step in multiple criteria optimization is setting the preferences for all the criteria under consideration. Several methodologies have been proposed to compute the relative priority of criteria when preference relations can be expressed either by ordinal or by cardinal information. The analytic hierarchy process introduces relative priority levels and cardinal preferences. Lexicographical orders combine both ordinal and cardinal preferences and present the additional difficulty of establishing strict priority levels. To enhance the process of setting preferences, we propose a compact representation that subsumes the most common preference schemes in a single algebraic object. We use this representation to discuss the main properties of preferences within the context of multiple criteria optimization.

Suggested Citation

  • Francisco Salas-Molina & David Pla-Santamaria & Ana Garcia-Bernabeu & Javier Reig-Mullor, 2019. "A Compact Representation of Preferences in Multiple Criteria Optimization Problems," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1092-:d:285793
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    References listed on IDEAS

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    Cited by:

    1. Francisco Salas-Molina & David Pla-Santamaria & Fernando Mayor-Vitoria & Maria Luisa Vercher-Ferrandiz, 2021. "A Multicriteria Extension of the Efficient Market Hypothesis," Mathematics, MDPI, vol. 9(6), pages 1-16, March.

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