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

Giovanni Paolo Crespi (), Andreas H. Hamel (), Matteo Rocca () and Carola Schrage ()
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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

Mathematics of Operations Research, 2021, vol. 46, issue 1, 361-381

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.

Keywords: set relation; hull operator; complete lattice; set optimization; approximate solution; well-posedness (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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