Fuzzy Finite Automata And Their Minimizations

In this paper, based on fuzzy finite automata, the algorithms ofminimal fuzzy automata are concerned.At first, the conceptions of fuzzy set, automata and fuzzy automata aregiven. Secondly, we define the concept of equivalence state in Mealy fuzzyfinite automaton. The equivalent has been expanded to the alphabetic stringself being dependent on the alphabetic string length but being not one kindweak equivalent, which has a more widespread application then before. Someproperties of Mealy fuzzy finite automaton are discussed. Further more, theexpression of minimization is determined. At last, minimization algorithm isshown. Once more, the concept of Mealy fuzzy finite automaton whose inputsare words is established. Namely we have made the corresponding expansionto the fuzzy states function and the fuzzy output function. Properties of Mealyfuzzy finite automaton are discussed. We describe its minimization algorithmon the basis of foregoing analysis being shown above. Finally, we introducea new Mizumoto finite automaton, which is di?erent from general formMasaharu Mizumoto defined. The important di?erence lies in final states withmembership degree. Further more, the equivalence of the type of Mizumotofinite automaton and canonical fuzzy finite automaton with single initial stateand deterministic transition function is established. Then we present a methodto minimize the states of automaton in canonical form.