On the Decomposition of General Systems: Simulation by Coupling Quotients

Abstract

In problem-solving (in the widest sense) using a (mathematical) model the following can be seen: (a) the problem-solver must concentrate his attention on certain “parts” of the model, (b) he is interested to get “parts” in the right “form” so that effective methods for problem solution are available, (c) since each “part” has to be seen in connection with the model as a whole, knowledge on how the parts are coupled is essential. Decomposition methods are one help in this direction. My paper discusses this topic and develops some ideas for decomposing I/O relations, parameterized I/O relations, fuzzyfied I/O relations and finally finite discrete dynamical systems. These ideas are seen from the viewpoints of mathematics, more or less well-known and not really exciting. But from the viewpoint of general systems theory they may deserve interest.