Description of Complex Hierarchical Systems by Matrix-Predicate Method

摘要

Multi-unit, multi-link, and multi-channel complex systems which have a hierarchical structure and represent a multitude of interacting objects, subsystems, components, etc., are necessary for management solutions and decision-making. In this work the possibility of describing complex systems of a hierarchical structure using a matrix-predicate method is considered. This will facilitate the interaction of structure elements and help to avoid possible isomorphism when performing logical and theoretical operations on the units of complex systems. It is offered to present a technological process performing object as a finite number (r) of interacting components K. Components are easy to create in the matrix-predicate form as they are small, well-accessible and easily corrected with the use of matrices. The interaction of components is determined by r-relation which is assigned in the form of a compatibility table. In this work the possibility of describing complex hierarchical production system using a matrix which elements represent the true value of pentad predicate. The possibility of the description by square matrix in the matrix-predicate form will be provided by an example of a two-level hierarchical structure.