Connectedness in systems theory

Finite state machines and directed graphs share certain fundamental properties. This can be seen from the natural way a directed graph can be associated with a finite state machine to describe the state transition of the finite state machine. Likewise, fuzzy finite state machines and fuzzy directed graphs share these fundamental properties. As a matter of fact, all four of these systems together with those of information retrieval systems and fuzzy systems share these properties, namely those of the notions of successor and source. This paper gives an axiomatic treatment of the notion of a type of connectedness defined in terms of successor and source. Structural results are obtained which can be applied to the above systems.