Maximum likelihood solutions for multicriterial choice problems

Podinovski V.V.

doi:10.1016/j.ejor.2020.03.028

Publications

Article

Maximum likelihood solutions for multicriterial choice problems

European Journal of Operational Research. 2020. Vol. 286. P. 299-308.

Podinovski V.V.

We introduce the notion of a maximum likelihood optimal decision alternative for the choice problem with a finite set of decision alternatives, assuming a general parametric preference model of the decision maker. We also develop an optimization-based method for the identification of such alternatives for the cases in which the parametric preference model is based on uncertain intervals for criterion trade-offs. The suggested approach can be seen as generalising stochastic multicriteria acceptability analysis (SMAA) to a wider modelling setting. It also provides a maximum likelihood interpretation of the SMAA acceptability index.

Research target: Mathematics

Priority areas: IT and mathematics

Language: English

Full text (PDF, 684 Kb)

DOI

Keywords: multicriteria decision analysis choice problem surrogate solutions stochastic multicriteria acceptability analysis (SMAA)

Publication based on the results of: Decision making and data analysis in socio-economic and political systems(2020)

Согласительные решения для задач выбора при неполной информации о предпочтениях

Подиновский В. В. В кн.: VIII Московская международная конференция по исследованию операций (ORM2016): Москва, 17-22 октября 2016 г.: Труды. Т. II. М.: ФИЦ ИУ РАН, 2016. С. 77-78.

Added: Oct 28, 2016

Model for organizing cargo transportation with an initial station of departure and a final station of cargo distribution

Khachatryan N., Akopov A. S. Business Informatics. 2017. No. 1(39). P. 25-35.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Added: Apr 18, 2017

Nullstellensatz over quasi-fields

Trushin D. Russian Mathematical Surveys. 2010. Vol. 65. No. 1. P. 186-187.

Added: Feb 20, 2018

Математическая статистика

Энатская Н. Ю., Хакимуллин Е. Р. М.: МИЭМ, 2011.

Added: Apr 26, 2012

Деловой климат в оптовой торговле во II квартале 2014 года и ожидания на III квартал

Лола И. С., Остапкович Г. В. Современная торговля. 2014. № 10.

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Деловой климат в оптовой торговле в I квартале 2012 года

Лола И. С., Лукашина Ж. Е., Пахомова О. П. М.: НИУ ВШЭ, 2012.

Added: May 21, 2012

Laminations from the Main Cubioid

Timorin V., Blokh A., Oversteegen L. et al. arxiv.org. math. Cornell University, 2013. No. 1305.5788.

According to a recent paper \cite{bopt13}, polynomials from the closure $\ol{\phd}_3$ of the {\em Principal Hyperbolic Domain} ${\rm PHD}_3$ of the cubic connectedness locus have a few specific properties. The family $\cu$ of all polynomials with these properties is called the \emph{Main Cubioid}. In this paper we describe the set $\cu^c$ of laminations which can be associated to polynomials from $\cu$.

Added: Oct 6, 2013

Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles

Bufetov A. I., Mkrtchyan S., Scherbina M. et al. arxiv.org. math. Cornell University, 2013. No. 1301.0342.

Added: Feb 21, 2013

Введение в математическую статистику

Ивченко Г. И., Медведев Ю. И. М.: ЛКИ, 2010.

Added: Apr 12, 2012

Bounded limit cycles of polynomial foliations of ℂP²

Goncharuk N. B., Kudryashov Y. arxiv.org. math. Cornell University, 2015. No. 1504.03313.

In this article we prove in a new way that a generic polynomial vector field in ℂ² possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain.

Added: Apr 15, 2015

Разложения решений пятого уравнения Пенлеве вблизи его неособой точки

Брюно А. Д., Парусникова А. В. Институт прикладной математики им. М.В. Келдыша Российской академии наук, 2011. № 18.

Added: Apr 18, 2012

Многовариантный анализ процессов прокатки на базе компьютерного моделирования

Аксенов С. А., Чумаченко Е. Н., Сырчина О. О. Вестник Воронежского государственного технического университета. 2011. Т. 7. № 11.2. С. 62-64.

Added: Apr 12, 2012

Автоматическая обработка текстов на естественном языке и компьютерная лингвистика

Большакова Е. И., Клышинский Э. С., Ландэ Д. В. и др. М.: Московский государственный институт электроники и математики, 2011.

Added: Apr 12, 2012

Асимптотические разложения решений пятого уравнения Пенлеве

Парусникова А. В., Брюно А. Д. Институт прикладной математики им. М.В. Келдыша Российской академии наук, 2010. № 39.

Added: Apr 18, 2012

Локальные разложения решений пятого уравнения Пенлеве

Брюно А. Д., Парусникова А. В. Институт прикладной математики им. М.В. Келдыша Российской академии наук, 2010. № 72.

Added: Apr 18, 2012

Труды ХХ Международного совещания «Радиационная физика твердого тела» (Севастополь, 5 июля - 10 июля 2010 г.)

Edited by: Г. Г. Бондаренко Т. 1-2. М.: ФГБНУ "НИИ ПМТ", 2010.

Added: Apr 12, 2012

Труды ХХI Международного совещания «Радиационная физика твердого тела» (Севастополь, 22-27 августа 2011 г.)

Бондаренко Г. Г. Т. 1-2. М.: ФГБНУ "НИИ ПМТ", 2011.

Added: Apr 12, 2012

Применение информационных и космических технологий в задачах о движении небесных объектов

Чумаченко Е. Н., Кулагин В. П., Назиров Р. Р. и др. Информатизация образования и науки. 2011. № 3 (11). С. 178-187.

One of directions of activity of the scientifically-educational centre "SPACE" created by the Moscow state institute of electronics and mathematics (technical university) and Space research institute of the Russian Academy of Sciences is discussed. The general statements of problems connected with working out of models of movement of asteroids and comets taking into account not gravitational indignations and construction of models for measurement of trajectories are considered. On a space vehicle orbit in a vicinity of libration’s points the traffic control model is discussed with application of a solar sail with operated reflective characteristics.

Added: Apr 12, 2012

Анализ методов компьютерного моделирования механических испытаний

Чумаченко Е. Н., Аксенов С. А., Борхсениус С. С. Вестник Воронежского государственного технического университета. 2011. Т. 7. № 11.2. С. 9-11.

Added: Apr 12, 2012