Geodesic
A new approach to multicriteria problems under uncertainty
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 1, pp. 3-16

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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
Mots-clés : deposit diversification. 
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     title = {A new approach to multicriteria problems under uncertainty},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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M. I. Vysokos; V. I. Zhukovskii; M. M. Kirichenko; S. P. Samsonov. A new approach to multicriteria problems under uncertainty. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/VUU_2017_27_1_a0/