The article deals with the management of human-machine (ergatic) systems in the conditions of digital transformation in relation to their functioning in the presence of NON-factors, such as: uncertainty, complexity, instability, ambiguity. Modern conditions for the formation of the digital economy imply the search and use of a new methodology in the organization of management activities, including the regional level. This process is carried out through the widespread use of human-machine systems with a high level of intellectualization of the machine component, the use of hybrid intelligence and the formation of bionts. We show a variant of classification of ergatic systems, focused on socio-economic systems. We propose a method for choosing a rational alternative to support the management of human-machine systems in the conditions of vagueness and ambiguity of the initial data and approaches to the management quality criteria. A fuzzy approach to a multi-criteria problem is proposed. It leads to a certain combination of fuzzy selection criteria, and to the study of complex systems as a hierarchical structure, with the representation of system elements and its qualitative properties as fuzzy mathematical models, the combination of which will give a mathematical model of the systems.