MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA

In this note, by considering the notions of the intuitionistic general L-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{L}$, there exists a minimal intuitionistic general L-fuzzy automaton recognizing $mathcal{L}$.We prove that the minimal intuitionistic general L-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, beta)$-reduced max-min intuitionistic general L-fuzzy automaton.%Also, we prove that the minimal intuitionistic general L-fuzzy automaton is an $(alpha, beta)$-reduced.Also, we show that  for any strong deterministic max-min intuitionistic general L-fuzzy automaton there exists a statewise $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton.In particular, a connection between the minimal and statewise  $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton is presented.%We show if $tilde{F}^*$ is an $(alpha, beta)$-complete $(alpha, beta)$-accessible deterministic max-min intuitionistic general L-fuzzy automaton and it is recognizing $(alpha, beta)$-language $mathcal{L}$, then the minimal $tilde{F}^*_{mathcal{L}}$ is homomorphism with threshold $(alpha, beta)$ to statewise $(alpha, beta)$-minimal $tilde{F}_{m}^*$, where $tilde{F}_{m}^*$ is statewise $(alpha, beta)$-equivalent to $tilde{F}^*$.Also, for a given intuitionistic general L-fuzzy automaton, we present two algorithms, which determinesstates of the minimal intuitionistic general L-fuzzy automaton and the statewise $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton.Finally, by giving some examples, we comparison minimal intuitionistic general L-fuzzy automaton and statewise $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton.