γ-Generalized directable fuzzy automata

The purpose of this paper is to study the structural characterizations of $\gamma$-generalized directable fuzzy automata. We introduce $\gamma$-necks, $\gamma$-local necks, $\gamma$-directable, $\gamma$-trap-directable, $\gamma$-monogenically directable, $\gamma$-monogenically strongly directable, $\gamma$-monogenically trap directable, $\gamma$ - uniformly monogenically directable, $\gamma$-uniformly monogenically strongly directable, $\gamma$-uniformly monogenically trap-directable fuzzy automata. We prove $\gamma$-generalized directable fuzzy automaton is an extension of a $\gamma$-uniformly monogenically strongly directable fuzzy automaton by a $\gamma$-uniformly monogenically trap-directable fuzzy automaton. We obtain equivalent conditions of $\gamma$-generalized directable fuzzy automaton.