Normal sum decomposition of general systems

Abstract

This paper introduces normal systems and the normal sum of general systems. A system S=(M,R) is normal if and only if any two relations in R are not contained in the same Cartesian product Mⁿ for any ordinary number n. Normal sum is a new kind of decomposition (composition) of general systems. Given a normal system S=(M,R), and two subsets A₁⊆M and A₂⊆M. One of the main results is that the normal sum of the A₁‐related subsystem and the A₂‐related subsystem of S equals the (A₁∪A₂)‐related subsystem of S. This implies that every normal system is a normal sum of its subsystems which are non‐trivial and non‐discrete.

Citation

Liu, G. (2003), "Normal sum decomposition of general systems", Kybernetes, Vol. 32 No. 5/6, pp. 640-643. https://doi.org/10.1108/03684920210443725