Abstract
A similarity between finite state machines and directed graphs 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, there is a similarity between fuzzy finite state machines and fuzzy directed graphs. As a matter of fact, all four of these concepts, together with that of information retrieval systems and fuzzy systems, share this similarity, namely that of the notion of successor. This paper gives an axiomatic treatment of the notion of successor in such a way that all of the above systems fall under this axiomatic approach.
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