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Topicality. The steady increase of tension in the world, defined by sociologists and politicians as a "global risk society", is one of the main features of the development of modern civilization.The problematization of modern society is moving in the direction of exacerbating the global problems of human life (demography, food, drinking water, ecology, climate change, pandemics, etc.); an increase in the potential for conflict and crisis (military-political, interethnic and religious conflicts, an increase in the gap between rich and poor, an increase in nationalism, radical fundamentalism, etc.). Aim and tasks. The aim of the work is to discuss: topical issues of modern transformations, which are acquiring a stable character of the systemic crisis of society, defined by politicians as a civilizational crisis; to consider the priority directions of the strategy for overcoming the crisis. The anti-crisis strategy is based on the ideologemes of development of a new international economic, ecological and social order, focused on the formation of a new civilization. Research results. The paper assesses the trends of modern negative transformations, which take the form of various challenges and provoke countless threats and dangers for human life and the sustainable development of the world community as a whole. Increasing the intensity of use of the natural habitat of humans and animals is considered one of the main threats to the environment. The paradigm of the development of the "new world", "new international order" (NIO) as an imperative strategy for overcoming the civilizational crisis is considered. Attention is drawn to the features of such basic components of the NIO as the "new international economic order", the new "environmental (economic-environmental) order", "the new social order". In the context of the NIO, issues of enhancing the role of the UN, other international organizations and the international community as a whole in solving the problems of survival and sustainable development are being discussed. Conclusion. The paper argues that the development of an integrated "new international order" will serve as the basis for the formation of a new civilization of the approaching era of artificial intelligence. The analytical generalizations of the problems of modern globalization and the aggravation of crisis phenomena carried out in this paper provide grounds for the assertion that effective solutions to the tasks of ensuring security and sustainable development of human survival are connected with the formation of international order (NIO) - economic, environmental and social. The implementation of the NIO on the principles of noospherization and artificial intelligence will be the basis for the formation of a new prosperous civilization.

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Topicality. In recent decades, the problem of methodological and ideological comprehension of the nonlinear ideologemes of cognition of complex developing processes formed in the physical, chemical and other natural sciences, in the context of their use in economic and environmental research in management practice, has been increasingly.The statement of this problem is conditioned by the established traditions of simplifications in the knowledge of real economic phenomena and processes. The consequence of the simplification in understanding the complexities of economic and other activities is the prevailing phenomenon of nonlinear thinking and linear perception of the surrounding world. Currently, the problem of nonlinear complexities of socio-economic and economic-ecological systems is extremely poorly developed. Aim and tasks. The aim of this work is to discuss topical issues of the implementation of modern ideologemes of nonlinearity in the study of economic and environmental phenomena and processes, as well as in the systems of substantiating management decisions in the development of programs (projects) for territorial, sectoral and other development. The goal-setting system discussed in the work focuses on the solution of applied problems of the implementation of the ideology of nonlinearity in practice. Research results. Implementation is considered as a category of the theory of nonlinear control, as a formal hypothetical-deductive system for organizing knowledge about the management of complex nonlinear economic and environmental processes in interrelation and interdependence. The principles of nonlinearity and nonlinear approach to the study and management of systems related to the greening of the economy have been formed. The research results presented in the work are based on a comprehensive analysis of the formation of a new post-nonclassical stage in the development of modern science. The tendencies of radical changes in the foundations of science and the nature of scientific activity are taken into account. Special attention is paid to the increasing actualization of the formation of nonlinear research methods and scientific directions (synergetics, nonlinear dynamics, catastrophe theory, etc.), focused on the knowledge of complex nonlinear processes and the solution of strategic problems of nonlinear control.In the context of nonlinear paradigms, the author considers the search for new imperatives of economic science aimed at forming the conceptual foundations of a new scientific paradigm in economics and a new intellectual economy. The work focuses on the need to develop the theory of nonlinear management of complex processes of social and economic development, including those related to the management of the greening of the economy. The applied problems of the implementation of nonlinear ideologemes in the economy and ecology are considered in the interests of the national security of Ukraine. Conclusion.The presented results of theoretical and methodological comprehension of the modern problem of nonlinear world outlook are a certain basis for a new nonlinear approach to the study of complex processes and its implementation in the management of economic and environmental processes.

Topicality. Modern challenges associated with both radical changes in the economic development of the technological order, and certain shifts in the foundations of science, predetermine the need for a new understanding of the methodology of cognition of the increasingly complex phenomena and processes of socio-economic, economic-ecological and other transformations. Aim and tasks. In this work, the goal is to give a critical assessment of the state of development of the methodology of cognition of development processes and to draw attention to the need for a new understanding of the methodology of science in general and specific scientific areas. The goal-setting of methodological problems is focused on solving the problems of developing new methods and theoretical means of cognition, problems of forecasting and constructing future social reality. Research results. The general and special issues of the development of the methodology of cognition of complex systems are considered. In the classical sense, methodology is interpreted in a widely known sense as the science of methods, as a set of methods used in any science. The work pays special attention to the three-dimensional functional model of the methodology that implements the functions of obtaining new knowledge, structuring it and organizing the use of new knowledge, clarifies the concept of "cognition" in three-dimensional dimensions. The work confirms the feasibility and details the methodological and methodological possibilities of using the general parametric system theory according to A.I. Uyemov. Using the example of the coastal zone, a methodological approach to the description and analysis of a complex developing system in the context of solving problems of substantiating management decisions is considered. Attention is also paid to the possibility of using other methodological approaches to understanding complex processes, in particular, the use of a hypothetical-deductive method. In this paper, the problems of methodology of cognition and management are considered taking into account the paradigm of nonlinearity of complex systems. Conclusions. The paper presents the results of the discussion of the problems of development of the methodology for the study of complex developing systems both in terms of their knowledge and in terms of substantiating management decisions. The problems of the methodology are considered in a multidimensional dimension, in particular, in the classical and post-non-classical interpretation. The research results are focused on solving modern socio-ecological and economic problems and future problems associated with the development and implementation of artificial intelligence technologies.