The problem of the construction of a system for making the compromise solution for subjects with different goals is considered. The problem is solved within the framework of a systemic approach. Procedures of decomposition and composition of partial criteria in multicriteria decision-making problems are described. A compromise solution can be obtained by extremizing the scalar convolution of partial criteria reflecting the degree of attaining goals of subjects. The fundamental role of constraints in optimization problems is shown. We describe types of scalar convolutions used in multicriteria problems. The concept of a nonlinear compromise scheme, based on the principle "away from restrictions"is formulated. Extremization of the objective function leads to the general compromise solution, which moves away to the greatest extent partial criteria from its constraints. Both tasks significant for the general application and the tasks with the main semantic essence of satisfying the individual advantages of the decision making person (DMP) are solved using a common ideological basis. The apparatus of a nonlinear compromise scheme, designed as a formalized tool for studying the system of decision-making and control systems with conflicting criteria enables the solving of multicriteria problems of a wide class. Multicriteria is the implementation of the principle of complementarity in the methodology of the study of complex systems. In general, a simultaneous description of a phenomenon (object) from several sides always gives a qualitatively new, more perfect imagination about the described phenomenon (object) in comparison with any "unilateral"description. So, even two flat images forming a stereo pair form a volumetric image of an object, not to mention potentials of the holography. The multi-criteria approach, giving a "stereoscopic"look at the estimation of the system functioning opens new ways for the perfection of complex control systems and decision making. For the integral perception of a complex system under different conditions of its operation it is necessary to apply the multi-criteria approach. © 2020 by Begell House Inc.
