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In the article, based on an analysis of the use of national armed forces and other militarized formations during the elimination of the consequences of emergency situations of a natural, man-made and military emergencies, conceptual foundations were proposed that are based on the identified trends, established conformities, formulated principles and the developed concept of such an application. The basic idea of these conceptual foundations is minimizing the risk of personnel when it is used during emergency situations of a natural, man-made and military nature, including the elimination of their consequences in order to manage technological safety.The conceptual foundations for the use of troops (forces) of the Armed Forces of Ukraine and other militarized formations during the elimination of the consequences of emergency situations of a natural, man-made and military emergencies is the rationale for developing a set of methods, techniques, models and algorithms for such an application and assessing its effectiveness, which, in turn, will allow to develop recommendations and proposals on the use of troops (forces) of the Armed Forces of Ukraine and other militarized formations during emergency situations of a natural, man-made and military nature taking into account the risk of professional activity of the involved personnel. The results of the study can be used in organizing the elimination of the consequences of emergency situations of a natural, man-made and military nature and the implementation of technological safety management by minimizing the risk of the personnel involved.

The article discusses some of the problematic issues of ecological (technogenic) safety management, which are normative in nature, and, to a greater extent, related to the imperfection of Ukrainian legislation in the aspects of the formation and implementation of state environmental policy. At the same time, for the authors, it seems interesting to focus on adapting the policy to a paradigm of a risk-based approach, taking into account the problems of technological safety (the state of protection of the population, territory, objects from the negative consequences of technological emergencies) of Crimea, eastern Ukraine and troops (forces) that take participation in the operation of the Joint Forces. This is due to the fact that in the leading countries of the world funding for scientific research in the field of risk analysis and assessment is constantly increasing, scientific areas of risk research have been formed: in transport, industry, natural and man-made emergencies, special tasks, and professional safety activity, risk, in particular, during the performance of tasks in emergency situations of natural, man-made and military nature. The results of the study can be used in organizing the liquidation of the consequences of emergency situations of various nature and in managing technogenic safety by minimizing the risk of personnel during the use of defense forces in emergency situations, including in the operation of the Joint Forces.

In the work examined: possibility of the use of vectorial optimization at a management technogenic safety; some problem aspects of such use; general issue of vectorial optimization at a management technogenic safety and mathematical formalization of this problem comes true.The marked is caused: by complication and importance of practical problems at military to business, for the decision of that the vehicle of analysis of operations is attracted; by inaccuracy of traditional methods of scalar (onecriterion) optimization at the decision of similar problems; by possibilities of vectorial, multicriterion approach in relation to a search and optimization of administrative decisions at consideration of difficult processes and systems of any nature, including, management technogenic safety.It is set that basic difficulties of decision of vectorial tasks to optimization of decisions in relation to a management technogenic safety are related to the specification of the initial formalized model, with transformation of her to the kind, comfortable for a choice optimal decision. Thus there is a necessity for the decision of three fundamental problems on that the rightness of optimal choice depends in a great deal: choice of principle of optimality; choice of principle of normalization; choice of principle of taking into account of priority.Research results can be drawn on during organization of liquidation of consequences of emergencies of different character and realization of management technogenic safety in the aspect of search of optimal decision of such management, including, during the conduct of operation of Incorporated forces.