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Committees: History and Applications in Machine Learning

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

The article outlines a brief history and applications of the committee theory. The use of committees in the problems of recognition and optimization is discussed. The application of the committee structures, ambiguous interpretation of non-formalized and contradictory data are given. The ways of rational regard on environmental factors in the context of a lack of resources are considered. The question of the numerical finding of committee structures is discussed, and these results are directly related to the theory of voting. The class of non-classical logics also contains MK-logic (Mazurov, Khachay). This section of non-classical logic includes the works by N. A. Vasiliev, L. Wittgenstein, J. Lukashevich, and Latin American mathematicians having a wrong term in their titles parainconsistent logic. One of the important results achieved by M. Yu. Khachay: For arbitrary positive integers q and k,  \(k<q,\) the minimum estimate of the subsystem power is given that is resolvable by a committee of k-elements for the inconsistent system having a committee of q-elements. Further the history of this field will be mentioned.

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Notes

  1. 1.

    i.e. \(E\varGamma \ne \varnothing \).

  2. 2.

    For which the condition \(x_{i_1}=x_{i_2}\) implies \(y_{i_1}=y_{i_2}\).

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Author information

Authors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Vladimir D. Mazurov

  2. Ural Federal University, Ekaterinburg, Russia

    Vladimir D. Mazurov & Ekaterina Yu. Polyakova

Authors
  1. Vladimir D. Mazurov
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  2. Ekaterina Yu. Polyakova
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Corresponding author

Correspondence to Vladimir D. Mazurov .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Mazurov, V.D., Polyakova, E.Y. (2019). Committees: History and Applications in Machine Learning. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_1

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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