Developing Interconnection Matrices in Structural Modeling

TLDR

The study assumes the modeled contextual relation is transitive and notes that structural modeling largely relies on computers, leaving developers to provide substantive system knowledge. The paper proposes a procedure to develop an interconnection matrix that specifies a cascade connection of two known digraphs. The method derives a characteristic logic equation from partitioning a binary relation and uses it as the basis for constructing the interconnection matrix. The authors demonstrate that interconnection possibilities are fully prescribed by a characteristic logic equation and illustrate its application with an example.

Abstract

A procedure is described for developing an interconnection matrix that specifies a cascade connection of two known digraphs to form a digraph. The solution of this form of the interconnection problem can be applied to complete the process of description of a binary relation initiated by the process of partitioning on elements described in a companion paper [3]. It is assumed that the contextual relation being modeled is transitive. Based on this assumption, it is shown that the possibilities of interconnection can be completely prescribed in a characteristic logic equation. This equation can be used as the complete basis for development of an interconnection matrix. An example of its use is given. Much of the burden of structural modeling is assigned to the computer, leaving to the developer the tasks requiring substantive knowledge of the system being modeled.