Approximation and robustness of fuzzy finite automata ★

In previous work we have shown that nondeterministic fuzzy finite automata (or NFFAs, for short) under max-∗ compositional inference for some t-norm ∗ and deterministic fuzzy finite automata (or DFFAs, for short) are not necessarily equivalent. We continue to study the approximation and robustness of fuzzy finite automata in this paper. In particular, we show that we can approximate an NFFA by some DFFA with any given accuracy when the NFFA is not equivalent to any DFFA, and the related construction is also presented. Some characterizations of NFFA and DFFA are given. We study the robustness of fuzzy finite automata against imprecision of fuzzy transitions, and some interesting results are obtained.