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Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization

Author

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  • Giovanni Paolo Crespi

    (Department of Integrated Business Management, Università Cattaneo–LIUC, 21053 Castellanza, Italy)

  • Andreas H. Hamel

    (Faculty of Economics and Management, Free University of Bozen-Bolzano, I-39031 Bruneck-Brunico, Italy)

  • Matteo Rocca

    (Department of Economics, Università degli Studi dell'Insubria, 21100 Varese, Italy)

  • Carola Schrage

    (Faculty of Economics and Management, Free University of Bozen-Bolzano, I-39031 Bruneck-Brunico, Italy)

Abstract

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponding complete lattice of sets. Functions mapping into the preordered set are extended to complete lattice-valued ones, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared with existing ones in vector and set optimization. Its relevance is shown by means of many examples from multicriteria decision making, statistics, and mathematical economics and finance.

Suggested Citation

  • Giovanni Paolo Crespi & Andreas H. Hamel & Matteo Rocca & Carola Schrage, 2021. "Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 361-381, February.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:1:p:361-381
    DOI: 10.1287/moor.2020.1060
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    References listed on IDEAS

    as
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    Cited by:

    1. Andreas H. Hamel & Frank Heyde, 2021. "Set-Valued T -Translative Functions and Their Applications in Finance," Mathematics, MDPI, vol. 9(18), pages 1-33, September.

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