The article develops the conceptual foundations of natural and artificial intellectualization of the enterprise, as well as the combination of artificial and natural intelligence in managing business processes in the context of modern challenges of the business environment. Based on the methods of structural design, a system model of the enterprise is developed as the basis for intelligent management. Quantitative and qualitative effects of human–cyber–physical systems, which are the result of management intellectualization, are highlighted. The possibilities of using deviation and perturbation management methods in managing the state of enterprise development with the support of decision-making and implementation of an intelligent information system are considered. The features of making managerial decisions during intelligent enterprise management are considered. The place of the human factor in such intellectual management is highlighted, in particular, in terms of improving the intelligence of employees and the natural intellectualization of the enterprise. The problem of assessing and forecasting the state of enterprise development in the context of intellectual management is highlighted. In this context, the expediency of using mathematical methods of Markov process theory, using systems of Kolmogorov differential equations and their solutions, using numerical methods and applied software products is justified. This made it possible to study the dynamics of probabilities of states and stability of development of enterprises and their employees; the dynamics of probabilities of states of innovative and technological processes; scientific and technological, environmental, social and economic efficiency of a business. To test the proposed mathematical models for assessing and predicting the state of development of enterprises and their employees, appropriate studies were conducted on the sanatorium–resort complex in Truskavets (Ukraine).

The peculiarities of construction of the International Carpathian Valeological Innovation System at different levels of its organization were investigated. The expediency of creating territorial production associations is substantiated. The essence of the category of valeological innovation system is covered as a set of interconnected organizations (enterprises) engaged in production and commercialization of valeological innovative products within the boundaries of recreational zones, which may cover the territories of several or one country. The infrastructural components of the valeological innovation system are distinguished, which include recreation parks, recropolises and resorts, recreational business incubators and valeological innovation centers, as well as legal, financial and social institutions providing and maintaining valeological innovation processes.The organizational model of the valeological innovation enterprise is developed. In order to increase the efficiency of the Valeological Innovation Enterprise, the systems of its management were analysed based on the use of systematic, synergistic, homeostatic and intellectual approaches.It has been found that the management object (valeological innovation process) and the management bodies that are part of the valeological innovation enterprise structure are characterized by unlimited development.The feasibility of modelling the International Carpathian Valeological Innovation System by network model is substantiated. This model was formed in the form of a cluster, territorial-hierarchical model as one of the varieties of network models, which can be components of the Carpathian valeological innovation systems of the Carpathian Euroregion countries.