Decomposition in problems of design of systems with a block structure (Q1085783)

\textit{P. S. Krasnoshchekov, V. V. Morozov} and \textit{V. V. Fedorov} [Izv. Akad. Nauk SSSR, Tekh. Kibern. 1979, No.5, 5-12 (1979)] proposed an approach to analyzing the topic of design of complex technical systems, involving the setting up of a hierarchy of design problems based on descriptions of the system being designed of various degrees of detail. It was not taken into account that any complex technical system consists of interconnected subsystems, each of which can be designed with a considerable degree of independence from the others. This makes it possible to simplify the solution of design problems, since, first, each subsystem is a less complicated system than the initial one; and, second, it becomes possible to parallel the process of design of the entire system. In a paper of \textit{A. E. Dmitrovskij} and \textit{V. V. Fedorov} [Eng. Cybern. 19, No.3, 25-30 (1981; Zbl 0513.90048)] a hierarchy of design problems of this type was set up for a two-level system (subsystems do not break down into subsystems). It was assumed that the preference relations specified on the set of descriptions of the system are Pareto relations. Here we will construct a hierarchy of design problems for a multilevel system. The preference relations on the sets of descriptions of the system being designed have a common form. We will employ properties of binary relations.