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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 1, Pages 3–16 (Mi vuu564)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

A new approach to multicriteria problems under uncertainty

M. I. Vysokosa, V. I. Zhukovskiib, M. M. Kirichenkob, S. P. Samsonovb

a Moscow State Regional Institute of Humanities, ul. Zelenaya, 22, Orekhovo-Zuevo, 142611, Russia
b Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russia

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-90408_Укр_а
National Academy of Sciences of Ukraine 03-01-14


DOI: https://doi.org/10.20537/vm170101

Full text: PDF file (344 kB)
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Bibliographic databases:

UDC: 519.858
MSC: 90C29
Received: 11.12.2016

Citation: M. I. Vysokos, V. I. Zhukovskii, M. M. Kirichenko, S. P. Samsonov, “A new approach to multicriteria problems under uncertainty”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017), 3–16

Citation in format AMSBIB
\Bibitem{VysZhuKir17}
\by M.~I.~Vysokos, V.~I.~Zhukovskii, M.~M.~Kirichenko, S.~P.~Samsonov
\paper A new approach to multicriteria problems under uncertainty
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 1
\pages 3--16
\mathnet{http://mi.mathnet.ru/vuu564}
\crossref{https://doi.org/10.20537/vm170101}
\elib{http://elibrary.ru/item.asp?id=28808551}


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    This publication is cited in the following articles:
    1. N. N. Petrov, N. V. Petrova, “K zadache o diversifikatsii rublya”, Izv. IMI UdGU, 51 (2018), 123–135  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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