Abstract
The article is devoted to the study of an abstract function of choice and classes of such functions. We use the language of upper cuts for a formal description of binary relations. This approach makes is possible to consider different models of choice from unified theoretical positions.
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Belokurov, S.V. and Sysoev, V.V., Classification of Situations of Choice and Analysis of Technques for Formalization of Numerical Vector Schemes, in Komp’yuternye tekhnologii avtomatizirovannogo proektirovaniya sistem mashinostroeniya i aerokosmicheskoi tekhniki (Computer Technologies for Automated Design of Machine-building System and Aerospace Technics), Voronezh: Voronezh. Gos. Tekhn. Univ., 2002, pp. 88–106.
Belokurov, S.V., Velichko, S.V., and Solovey, D.E., Sintez funktsii vybora na iteratsiyakh poiska v chislennykh modelyakh mnogokriterial’noi optimizatsii (Synthesis of Functions of Choice on Iterations of Search in Numerical Models of Multicriterion Optimization), Voronezh: Voronezh. Gos. Univ., 2004.
Belokurov, S.V., Serbulov, Yu.S., Bugaev, Yu.V., and Chikunov, S.V., Modeli vybora nedominiruemykh variantov v chislennykh skhemakh mnogokriterial’noi optimizatsii (Models of Choice of Nondominated Variants in Numerical Schemes of Multicriterion Optimization), Voronesh: Nauchnaya Kniga, 2005.
Belokurov, S.V., Sumin, V.I., Pitolin, M.V., and Kashutin, S.V., A Problem of Choice of Optimal Variants Based on the Probabilistic Approach, Vest. VGTU, Ser. Radioelektron. Sist. Svyazi, 2006, no. 7, pp. 59–62.
Aizerman, M.A. and Aleskerov, F.T., Vybor variantov: osnovy teorii (Choice of Variants: Principles of the Theory), Moscow: Nauka, 1990.
Berezovskii, V.A., Kempner, L.M., and Borzenko, V.I., Binarnye otnosheniya v mnogokriterial’noi optimizatsii (Binary Relations in Multicriterion Optimization), Moscow: Nauka, 1981.
Borzenko, V.I. and Polishchuk, M.V., Geometriya invariantnykh funktsii vybora i binarnykh otnoshenii (Geometry of Invariant Functions of Choice and Binary Relations), Moscow: Inst. Probl. Upravlen., 1987.
Barndorff-Nielsen, O.E. and Sobel, M., On the Distribution of the Number of Admissible Points in a Vector Random Sample, Theor. Veroyat. Primen., 1966, vol. 11, no. 2, pp. 249–269.
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Original Russian Text © S.V. Belokurov, 2008, published in Sistemy Upravleniya i Informatsionnye Tekhnologii, 2008, No. 1, pp. 25–29.
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Belokurov, S.V. Construction of invariant functions of choice and study of probabilistic characteristics for binary relations on the Pareto set. Autom Remote Control 72, 2395–2401 (2011). https://doi.org/10.1134/S0005117911110130
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DOI: https://doi.org/10.1134/S0005117911110130