The paper deals with the problems associated with the development of modern computer technologies for decision-making in the digital economy, as well as methods, algorithms and software for solving management problems and decision-making in socio-economic production systems. We propose a promising approach with an interdisciplinary character, spanning such areas as hybrid intelligent systems, synergistic artificial intelligence, neuro and psychophysiology, philosophy, cybernetics, economic and mathematical modeling, etc. The paper discusses the basics of structural organization of functional hybrid intelligent decision-making systems designed to solve productional and economic problems that are hard to formalize, and proposes a new cognitive approach to integration and effective management of formalized and poorly formalized knowledge in decision-making systems. Theoretical and applied fundamentals of hybrid computational (simulation) modeling based on hybrid computational intelligence are presented as a promising interdisciplinary scientific direction which allows, based on flexible calculations, to integrate and manage accurate, inaccurate and uncertain knowledge in one system, providing a new level of simulation of complex processes and phenomena (including nonlinear) and synthesis of effective application tools. Concepts of an inhomogeneous task-system and an integrated method-system are introduced, serving as a basis for a fundamentally new approach in the field of modeling complex poorly formalized multicomponent economic systems that operate under conditions of uncertainty and the corresponding hard-to-formalize productional and economic problems. The proposed approach was used to formulate for the first time the methodological and technological foundations for creating applied, functional hybrid intelligent decision-making systems, which, as practice has shown, can successfully cope with the complexity of hard-to-formalize productional and economic problems and develop qualitatively new solutions in different subject areas. At present, the proposed methods, technologies and applied tools to create functional hybrid intelligent decision-making systems in solving a number of hard-to-formalize productional and economic problems are successfully applied in different subject areas, such as oil and gas, agro-industrial or industrial production, heavy engineering, etc. Active research in this area continues.