minimal and statewise minimal intuitionistic general l-fuzzy automata
minimal and statewise minimal intuitionistic general l-fuzzy automata
Abstract
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.