Military training programs have been developed to enhance soldier resilience competencies, which are necessary for soldiers to perform their duties effectively under stress. The ongoing military conflict in Ukraine and the experience of previous military missions abroad emphasize the need for effective training that helps soldiers recover quickly and continue their missions. However, selecting the most suitable resilience training program is challenging and the selection criteria need to be optimized to ensure the most needed competencies are considered. This study aimed to utilize a fuzzy MCDM method to establish the priority weight of decision-making criteria, identifying the core competencies necessary for soldier resilience training, and utilizing the fuzzy TOPSIS method to rank and select the most appropriate training program. The evaluation results were calculated using the MATLAB (R2020b) mathematical package developed by MathWorks. The application of the hierarchical MCDA model based on fuzzy sets theory indicated that mental agility is the most important competence in high-stress environments. The study found that the Mindfulness-Based Mind Fitness Training (MMFT) program, which is intended to regulate soldiers’ emotions, had the highest rank among evaluated options according to the combined FAHP sub-factor fuzzy weights and alternatives evaluation conducted using FTOPSIS. The study provides valuable information on the selection of military resilience training programs.

The paper focuses on finding the guaranteed estimates for rectangular matrices that satisfy the linear operator equations with unknown right-hand sides. Under certain assumptions, it is shown that guaranteed estimates of matrices can be found as the solutions of systems of operator equations. In the case where observation data are given with deterministic errors, which belong to certain bounded sets, we obtain the expressions for upper and lower estimates of the solutions of such equations, as well as expressions for upper and lower errors of such estimates. The obtained results are illustrated by an example. Keywords: linear operator equation, operator core, conjugate operator, guaranteed a posteriori estimate of matrix, guaranteed a posteriori error of the estimate of matrix, minimum by norm solution of the equation.

In this paper, we investigate the predictive estimates of the model which at the initial time interval describes a slower population growth, and later turns into a model with a rapid growth of such a population. For considered problem, with unknown initial conditions and parameters of differential equations, however for a known number of persons in the population at certain moments of time, we obtain the predictive sets at a given time under certain conditions and substantiate the formulas for calculating the minimum and maximum number of persons in the population.

Based on observations of the implementation of a non-stationary random process on a finite interval and at individual points, the problem of estimating linear functionals from spectral functions of signals that are included in the average values of such processes was investigated. Under the conditions that the correlation function of the random process and the spectral function of the signal are unknown and belong to certain bounded sets, expressions for guaranteed mean-square linear estimates of a set of linear functionals from spectral functions were found. In a particular case, it is shown that such estimates are expressed in terms of solutions of certain linear integral and linear algebraic equations. The use of a guaranteed approach for finding linear mean-square estimates of the corresponding linear functionals is illustrated by test examples. Keywords: Implementation of a scalar random process, matrix function, signal spectrum, linear functional, linear vector estimate, guaranteed mean-square vector estimate, vector estimate error.

In this article, we investigate the problem of estimating the spectral characteristics of the intensity of moving objects under stochastic uncertainty based on the results of measuring the magnitudes of wave fields at separate points. We assume that the unknown spectral functions belong to known sets from the functional space, and certain restrictions are given for the unknown correlation matrices. For linear guaranteed estimates of the set of linear functionals from spectral functions, we prove that the guaranteed mean square estimates are expressed in terms of solutions of a certain system of linear algebraic equations.