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Russia Moscow; Orekhovo-Zuevo
Section Mathematics
Title A new approach to multicriteria problems under uncertainty
Author(-s) Vysokos M.I.a, Zhukovskii V.I.b, Kirichenko M.M.b, Samsonov S.P.b
Affiliations Moscow State Regional Institute of Humanitiesa, Lomonosov Moscow State Universityb
Abstract The applicability and novelty of this research lies in that the decision-maker in a multicriteria problem aims not only to maximize guaranteed values of each criterion, but also to minimize the guaranteed risks accompanying the said maximization. The topic of the research lies at the interface of the multicriteria problem theory and the Savage-Niehans minimax regret principle: the concept of a weakly effective estimate has been derived from the MP theory, while estimation of risks with values of the Savage-Niehans regret function has been derived from the minimax regret principle. The scope of this research is limited to interval uncertainties: the decision-maker only knows the limits of the interval, and probabilistic characteristics are missing. A new term is introduced, namely, “strongly guaranteed solution under outcomes and risks”; its existence for “regular”-confined-strategies for the mathematical programming is established. As an example of a practical application, the problem of diversification of a multi-currency deposit is suggested and solved.
Keywords multicriteria problems, strong guarantee, Slater and Pareto maximum, minimax regret, deposit diversification
UDC 519.858
MSC 90C29
DOI 10.20537/vm170101
Received 11 December 2016
Language Russian
Citation Vysokos M.I., Zhukovskii V.I., Kirichenko M.M., Samsonov S.P. A new approach to multicriteria problems under uncertainty, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 1, pp. 3-16.
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