The object of research is the process of selecting a synergistically determined pair for the elements of complex systems in the design, manufacture or repair. One of the most problematic places in the selection is the need to numerically evaluate the result of combining the elements, taking into account the explicit, additive properties of elements and hidden manifestations of the pair that are unusual for the elements alone (emergence). Lack of accounting for emergence can significantly distort the apparent picture of the processes taking place in systems, which makes many existing models of such processes inadequate. During the research, methods of extracting information from arrays known, hidden for direct observation were used. In particular, four-layer hidden Markov models with an additional hidden layer were used. The models were trained by the Baum-Welch method, adapted to work with an additional layer. As training samples used data obtained as a result of statistical processing of information available for object monitoring, expert assessments, as well as data obtained in the world's computer networks. The test of the method and model on real medical and technical objects confirms their clinical and technical effectiveness. In particular, thanks to this in the medical industry: in the medical industry, the incidence of thromboembolism of the branches of the pulmonary artery and deep veins of the thigh and lower leg are decreased by 65 %; frequency of postoperative bleeding is decreased by 43 %; by 36 % the total number of drug-related medicines aimed at correcting the blood coagulation system is decreased. In the technical field, the test results confirm the increase in the service life of rubber-metal shock absorbers by 14.5 %. This is due to the fact that the proposed method has a number of features, in particular, for the first time in its evaluation of emergence a four-layer hidden Markov model is used. The results obtained in the work make it possible to propose a general scheme of an intellectual decision support system in the selection of a synergistically determined pair of elements for complex systems of various purposes.