Mathematical Optimization Theory and Operations Research: 18th International Conference, MOTOR 2019, Ekaterinburg, Russia, July 8 - 12, 2019, Revised Selected Papers

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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