K. Abolpour - Department of Mathematics, Kazerun Branch, Islamic Azad University, Kazerun, Iran
M. M. Zahedi - Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran

The present paper has been an attempt to investigate the general fuzzy automata on the basis of complete residuated lattice-valued (L-GFAs). The study has been chiefly inspired from the work by Mockor \cite{۱۵, ۱۶, ۱۷}. Regarding this, the categorical issue of L-GFAs has been studied in more details. The main issues addressed in this research include: (۱) investigating the relationship between the category of L-GFAs and the category of non-deterministic automata (NDAs); as well as the relationship between the category of generalized L-GFAs and the category of NDAs; (۲) demonstrating the existence of isomorphism between the category of L-GFAs and the subcategory of generalized L-GFAs and between the category of L-GFAs and the category of sets of NDAs; (۳) and further scrutinizing some specific relationship between the output L-valued subsets of generalized L-GFAs and the output L-valued of NDAs.

General fuzzy automata, Active state set, Residuated-lattice, Isomorphism of category, functor