Brzozowski type determinization for fuzzy automata

In this paper we adapt the well-known Brzozowski determinization method to fuzzy automata. This method gives better results than all previously known methods for determinization of fuzzy automata developed by Bělohlávek [4], Li and Pedrycz [20], Ignjatović et al. [15], and Jančić et al. [18]. Namely, as in the case of ordinary nondeterministic automata, Brzozowski type determinization of a fuzzy automaton results in a minimal crisp-deterministic fuzzy automaton equivalent to the starting fuzzy automaton, and we show that there are cases when all previous methods result in infinite automata, while Brzozowski type determinization results in a finite one. The paper deals with fuzzy automata over complete residuated lattices, but identical results can also be obtained in a more general context, for fuzzy automata over lattice-ordered monoids, and even for weighted automata over commutative semirings.