Minimaximax approach for finding optimal decisions’ subset regarding changes of the loss function

  • Vadym Vasyliovyc Romanuke
Keywords: decision, minimax, metastate, loss function, minimaximax

Abstract

A generalization of the decision (loss or utility) function is suggested. An ordinary decision function is defined on a Cartesian product of a decisions’ set and a set of states, but the generalized decision function has the third variable called a metastate. Metastates are generated due to uncertain evaluation of ordinary situations, or influence of the time course. For minimizing losses under poor or unreliable statistics, the rule of minimaximax is fully described. For correctly transferring from minimaximax to Bayesian criterions, the rules of minimizing expected losses for the generalized loss function are formalized. All the suggested criterions are re-formalized for the case of the utility function.

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References

Трухаев Р. И. Модели принятия решений в условиях неопределённости / Трухаев Р. И. — М. : Наука, 1981. — 258 с.

Lark R. M. The implicit loss function for errors in soil information / R. M. Lark, K. V. Knights // Geoderma. — 2015. — Vol. 251 — 252. — P. 24 — 32.

Biederman D. K. A strictly-concave, non-spliced, Giffen-compatible utility function / D. K. Biederman // Economics Letters. — 2015. — Vol. 131. —
P. 24 — 28.

Li Y. P. A robust interval-based minimax-regret analysis approach for the identification of optimal water-resources-allocation strategies under uncertainty / Y. P. Li, G. H. Huang, S. L. Nie // Resources, Conservation and Recycling. — 2009. — Vol. 54, Iss. 2. — P. 86 — 96.

Dong C. An interval-parameter minimax regret programming approach for power management systems planning under uncertainty / C. Dong, G. H. Huang, Y. P. Cai, Y. Xu // Applied Energy. — 2011. — Vol. 88, Iss. 8. — P. 2835 — 2845.

Information, Inference and Decision / Ed. by G. Menges. — Dordrecht : D. Reidel Publishing Company, 1974. — 201 p.

Moon J. Minimax estimation with intermittent observations / J. Moon, T. Başar // Automatica. — 2015. — Vol. 62. — P. 122 — 133.

Romanuke V. V. Meta-minimax approach for optimal alternatives subset regarding the change of the risk matrix in ensuring industrial and manufacturing labor safety / V. V. Romanuke // Herald of Khmelnytskyi national university. Technical sciences. — 2015. — № 6. — P. 97 — 99.

Romanuke V. V. Multiple state problem reduction and decision making criteria hybridization / V. V. Romanuke // Research Bulletin of NTUU “Kyiv Polytechnic Institute”. — 2016. — № 2. — С. 51 — 59.
Published
2017-05-29
How to Cite
Romanuke, V. V. (2017). Minimaximax approach for finding optimal decisions’ subset regarding changes of the loss function. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 33, 81-89. Retrieved from https://periodicals.karazin.ua/mia/article/view/9190
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Статті