Determinization of Fuzzy Automata by Means of the Degrees of Language Inclusion

PROJECT TITLE :

Determinization of Fuzzy Automata by Means of the Degrees of Language Inclusion

ABSTRACT:

Determinization of fuzzy finite automata is understood here as a procedure of their conversion into equivalent crisp-deterministic fuzzy automata, that will be viewed as being deterministic with doable infinitely many states, however with fuzzy sets of terminal states. Significantly, vital determinization ways are those that provide a minimal crisp-deterministic fuzzy automaton love the original fuzzy finite automaton called canonization ways. One canonization method for fuzzy finite automata, the Brzozowski sort determinization, has been developed recently by Jančić and Ćirić in [10]. Here we have a tendency to offer another canonization method for a fuzzy finite automaton $cal A=(A,sigma, delta, tau)$ over a whole residuated lattice $cal L$ , based mostly on the degrees of inclusion of the right fuzzy languages associated with states of $cal A$ into the left derivatives of the fuzzy language recognized by $cal A$. The proposed procedure terminates in an exceedingly finite range 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 usually faster than the Brzozowski sort determinization, and if the essential operations within the residuated lattice $cal L$ will be performed in constant time, it's the same computational time as all alternative determinization procedures provided in [8], - xref ref-sort="bibr" rid="ref11">[eleven], and [twelve].

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