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Determinization of fuzzy finite automata is understood here as a procedure oftheir conversion into equivalent crisp-deterministic fuzzy automata, which canbe viewed as being deterministic with possibly infinitely many states, but withfuzzy sets of terminal states. Particularly significant determinization methodsare those that provide a minimal crisp-deterministic fuzzy automaton equivalentto the original fuzzy finite automaton, called canonization methods. Onecanonization method for fuzzy finite automata, the Brzozowski typedeterminization, has been developed recently by Jan\v{c}i\'{c} and\'{C}iri\'{c} in [10]. Here we provide another canonization method for a fuzzyfinite automaton $\cal A=(A,\sigma, \delta,\tau)$ over a complete residuatedlattice $\cal L$, based on the degrees of inclusion of the right fuzzylanguages associated with states of $\cal A$ into the left derivatives of thefuzzy language recognized by $\cal A$. The proposed procedure terminates in afinite number of steps whenever the membership values taken by $\delta $,$\sigma $ and $\tau $ generate a finite subsemiring of the semiring reduct of$\cal L$. This procedure is generally faster than the Brzozowski typedeterminization, and if the basic operations in the residuated lattice $\cal L$can be performed in constant time, it has the same computational time as allother determinization procedures provided in [8], [11], [12].

Determinization of fuzzy automata by means of the degrees of language inclusion