GENERAL FUZZY AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED

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.

Keywords:

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