The object of the study is the sealing elements of the packer. The fundamental principle of the cluster model is the assumption that the sum of the relative volume fractions of two structural elements of a natural nanocomposite (loosely packed matrix and nanoclusters) is equal to one –  This approach is incorrect because it is violated when the nanoclusters are immersed in a loosely packed matrix. In this regard, a new relationship is proposed that relates the relative volume fractions of the loosely packed matrix and the part of nanoclusters immersed in it –  Calculation formulas are obtained for the relative fractions of the loosely packed matrix and the interphase region. The paper shows that such an assumption is unfounded due to the indispensable immersion of clusters in a loosely packed matrix, and in this regard, a new relationship is proposed linking the relative volume fractions of the loosely packed matrix and the part of nanoclusters immersed in it. For a composite with a matrix, a mixture of synthetic butadiene nitrile and hydrogenated butadiene nitrile rubber and the addition of a copper nanoparticle, it is shown that in a natural nanocomposite, which is the polymer under study in an amorphous state, the time dependences of the relative volume fractions of the regions of inter-component adhesion and the loosely packed matrix coincide quite well with each other. The application of the above relationship between the volume fractions of a loosely packed matrix and nanoclusters allows to reformulate the known equations of parallel and sequential micromechanical models, as well as the Kerner equation for a more complex micromechanical model used to describe the effect of strengthening the elastic modulus of nanocomposites

One of the main problems of decision-making tasks is the need to take into account subjective expert assessments, the complete consistency of which is rare, and the choice of the best alternative. The complexity of the connections between the many-sided aspects of the decision-making situation and the lack of an accurate forecast of the consequences leads to the fact that when assessing and choosing alternatives, it is possible, and often necessary, to use and process qualitatively fuzzy estimates. In decision-making situations, when at least one of the elements (outcomes, criteria, preferences, expert opinions, etc.) is described qualitatively, indistinctly, there are problems of multi-criteria decision-making with fuzzy initial information. Let’s consider the solution to the problem of multi-criteria choice based on the rules of fuzzy conditional inference, which have the form of fuzzy statements, the conditions and conclusions of which, along with expert assessments of the criteria, are presented in the form of interval fuzzy numbers of the second type (IT2FN). The convolution of private implications in each statement is made according to Lukasiewicz's rule. To reduce the type and defuzzify the resulting IT2FN, the Karrnik-Mendel algorithm was used to construct the minimum and maximum centroids of nested fuzzy sets of the first type, which give an estimate of the utility interval for each alternative. To refine the obtained utility estimates, under conditions of incomplete definiteness of statements, using the generalized Bayesian inference mechanism, adjusted estimates of the utility intervals of alternatives are constructed. By comparing these intervals, a larger interval is determined and the corresponding alternative is taken as a solution to the problem under consideration. The application of the proposed approach to solving the problem of multicriteria selection of the most corroded section of a gas pipeline with ambiguous expert opinions is shown. To date, specific practical and theoretical results have been obtained for decision-making problems with fuzzy initial information

Based on the general theory of semi-Markov recovery processes and their application to Markov recovery processes, the applicability of stationary reliability indicators to assessing the reliability of electric locomotives with an asynchronous motor, the functioning of which is considered as a superposition of independent alternating semi-Markov processes, is shown. By calculating the main indicators of system reliability in a steady state, a comparative analysis of the operational reliability of electric locomotives with an asynchronous DC and AC motors, used respectively on the Azerbaijan and Kazakhstan railways, was carried out.

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