Decision-making in conditions of dilemma: risks and mixed information uncertainty

In modern conditions of crises and instability of the functioning and development of socio-economic systems, an important problem of providing management tools and making effective decisions is the development of models, methods and information technologies for optimization and decision-making in a situation of risk and in a mixed information environment. Moreover, the widespread introduction of optimization methods, decision making and optimal control was facilitated by the fact that applied optimization problems in most cases are reduced to standard problems solved, and the growth of the power of updated computer tools contributes to the expansion of the spheres of successful application of decision optimization methods in solving complex and diverse economic problems. The paper proposes models of risk functions related to the decision-making task for harmonizing and optimizing risks and security of a complex system in a mixed information environment, and also proposes a model of penalties for damage to ensure the safety of functioning of complex systems. The work is a continuation of some of the authors' research in the field of modeling, forecasting and managing complex socio-ecological and economic systems to ensure safe, sustainable, sustainable and harmonious development in the face of modern risks and crises.