Committees of systems of linear inequalities / Mazurov V.D., Khachai M.Yu. // Automation and Remote Control. - 2004. - V. 65, l. 2. - P. 193-203.

ISSN:

00051179

Type:

Conference Paper

Abstract:

The conceptual issues of the theory of committee decision rules were considered, and its close relationship with the theory of substantiation of collective decision making and teaching neural networks was demonstrated. The problem of the minimum committee of an incompatible system of constraints, which arises at the stage of constructing the committee decision rule with a small number of elements, was discussed by itself. The problem of the minimum committee is known to be NP-hard. Results concerning estimation of the computational complexity of allied problems were obtained. To solve the problem of minimum committee of an incompatible system of linear inequalities, an effective approximate algorithm was suggested, its correctness was proved and computational complexity and guaranteed precision were estimated.

Author keywords:

Index keywords:

Affine inequalities; Decision rules; Linear inequalities; Problem solutions; Algorithms; Approximation theory; Computational complexity; Decision making; Neural networks; Problem solving; Teaching; Li

DOI:

10.1023/B:AURC.0000014716.7751

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84904239990&doi=10.1023%2fB%3aAURC.0000014716.77510.61&partnerID=40&md5=cdb0454e91920e555ddcd5d10b5d1745

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Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84904239990&doi=10.1023%2fB%3aAURC.0000014716.77510.61&partnerID=40&md5=cdb0454e91920e555ddcd5d10b5d1745
Affiliations	Inst. of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation
References	Mazurov, V.D., (1990) Metod Komitetov v Zadachakh Optimizatsii i Klassifikatsii (Method of Committees in Optimization and Classification), , Moscow: Nauka; Mazurov, V.D., Khachai, M.Y., Committee constructions (1999) Izv. Ural. Univ. Math. Mech., 2 (14), pp. 77-109; Mazurov, V.D., Khachai, M.Yu., Rybin, A.I., Committee constructions (2002) Proc. Steklov Inst. Math., pp. 67-101; Khachai, M.Yu., Rybin, A.I., A new estimate of the number of members in a minimum committee of a system of linear inequalities (1998) Pat. Recog. Image Anal., 8 (4), pp. 491-496; Eremin, I.I., Mazurov, V.D., (1979) Nestatsionarnye Protsessy Matematicheskogo Programmirovaniya (Non-stationary Processes of Mathematical Programming), , Moscow: Nauka; Mazurov, V.D., Pattern recognition and neural networks in modeling of technical and economic systems (2000) Novye Informatsionnye Tekhnologii v Issledovanii Diskretnykh Struktur (New Information Technologies in Studying Discrete Structures), , Tomsk: Tomsk. Gos. Univ; (2001) Neironnye Seti: Istoriya Razvitiya Teorii (Neural Networks: History of Theory Development), , Moscow: Radiotekhnika; Mazurov, V.D., Decision making on the basis of precedence-classification principle (2002) Strategiya Razvitiya RF v Period Rynochnykh Reform (Russian Development Strategy at the Time of Market Reforms), , Ekaterinburg: Ural. Gos. Univ; Mazurov, V.D., Contradictory choice, relation of tolerance and classification (2002) Logika Tolerantnosti (Logic of Tolerance), , Ekaterinburg: Ural. Gos. Univ; Khachai, M.Yu., On a game with nature relating to majority decision making (2002) Zh. Vychisl. Mat. Mat. Fiz., 42 (10), pp. 1609-1616; Mazurov, V.D., On constructing a committee system of convex inequalities (1967) Kibernetika, (2), pp. 56-59; Williamson, D.P., The primal-dual method for approximation algorithms (2002) Math. Program., 91 (3), pp. 447-478; Gale, D., Neighboring vertices on a convex polyhedron (1956) Linear Inequalities and Related Systems, pp. 255-263. , Kuhn, H.W. and Tucker, A.W., Eds., Princeton: Princeton Univ. Press
Correspondence Address	Mazurov, V.D.; Inst. of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation
Language of Original Document	English
Abbreviated Source Title	Autom. Remote Control
Source	Scopus