Determinization of fuzzy automata by factorizations of fuzzy states and right invariant fuzzy quasi-orders

In this paper we provide improvements of determinization methods, based on factorization of fuzzy states, for fuzzy finite automata that accept fuzzy languages of infinite range. The improvements are based on the usage of the fuzzy relational calculus, namely, on the usage of the right invariant fuzzy quasi-orders. Our algorithms perform better in the sense that they produce smaller automata, while require the same computation time. In addition, they can produce finite deterministic automata in cases when previous algorithms result in infinite deterministic automata. We show that the weak representable-cycles property is necessary and sufficient condition for determinization of a fuzzy automaton via a maximal factorization of fuzzy states. This condition is more general than the representable-cycles property previously determined as the necessary and sufficient condition for determinization of a fuzzy automaton via a maximal factorization of fuzzy states.